CQ). Here, the origin of CQ, howit contributes to the total capacitance, the possible strategies toimprove it, and the state-of-art CQ ofelectrode materials, including carbon, two-dimensional materials,and their composites, are discussed. Although most of the studieson quantifying CQ are theoretical, somecase studies on experimental measurements using standard electrochemicaltechniques are summarized. With an overview and critical analysisof theoretical studies on quantum capacitance of electrode materials,this review critically examines the supercapacitor design strategies,including choosing the right materials and electrolytes. These insightsare also relevant to other types of clean energy storage technologies,including metal-ion capacitors and batteries.Electrochemical energy storage technology has emergedas one ofthe most viable solutions to tackle the challenge of fossil-fuel-basedtechnology and associated global pollution. Supercapacitors are widelyused for high-power applications, and there is tremendous ongoingeffort to make them useful for high-energy storage applications. Whileelectrode materials of supercapacitors play a central role in chargestorage performance, insights into the contribution from differentcharge storage mechanisms are crucial from both fundamental and appliedaspects. In this context, apart from the electric double layer andfast redox reaction at/near the surface, another pronounced contributionfrom the electrode is quantum capacitance ( Indeed, it can storea charge around 10–100 times higher than the conventional dielectriccapacitor and is well-known for its superiority in high-power applicationsover conventional batteries. battery 1.2 The rE) via the relation E = 1/2CV2, where C is the specific capacitance and V is the voltageof the device. There are two types of energy storage mechanisms inSCs: one is storing the charge via double-layer formation at the electrode/electrolyteinterface, and the other mechanism is based on the rapid redox reactionsat the surface or near-surface. The former mechanism is known as theelectric double-layer capacitance (EDLC), whereas the latter mechanismis called the pseudocapacitance. Among them, the pseudocapacitor canstore 10–100 times higher charge than the electric double-layer(EDL) capacitor, whereas the latter features excellent electrochemicalstability, rate performances, and better charge-transfer kinetics.Like other electrochemical energy storage devices,SCs mainly consistof electrode materials and electrolytes. Thus, one can easily identifythat the electrode materials are one of the keys to enhance the energydensity of the device (Cdl) is related to the surface area (A) of active materials as0 = 8.85 × 10–12 F/m, ε is the dielectric constant of the electrolyte, A is the surface area, and d is the radiusof the counterions. It can be seen from 7 Apartfrom the gravimetric capacitance, the high areal and volumetric capacitancesmake it highly desirable to use the SC for high-power applicationsover a small footprint area. Importantly, considering the surfacearea of 1500 m2/g, Cdl shouldbe 30–70 μF/cm2 depending upon the choiceof electrolyte. However, the areal capacitance obtained with porouscarbon was only 4–5 μF/cm2.7 Furthermore, graphene, with a theoretical surface areaof 2600 m2/g, showed the areal (gravimetric) capacitanceof 13.5 μF/cm2 (355 F/g),7 and activated microwave-expanded graphite oxide with a surface areaof 3100 m2/g exhibited the areal (gravimetric) capacitanceof 6 μF/cm2 (200 F/g) in an aqueous electrolyte.8 Although predicted, the gravimetric capacitanceof graphene of around 550 F/g has not been achieved thus far. Theseobservations certainly ensured that increasing the surface area isnot the only solution for enhancing the specific capacitance. Moreover,the higher surface area reduces the volumetric capacitance of thesupercapacitor electrodes.In the case of the EDLC mechanism, the specific  capacitance.12 In all cases, one can see that the major changesin the pristine structure are surface area modification and micro-,macro-, and mesopore optimization for the effective electrolyte ionicaccessibility to the entire surface of an electrode, improvement inelectrical conductivity and/or structure for better charge-transferkinetics, changes in wettability to improve the electrode/electrolyteinteraction, etc. To explore the phenomena at the surface in dynamicconditions (during charging/discharging), major attention is givento the in situ investigations by Raman spectroscopy,X-ray diffraction techniques, microscopic techniques, etc. These investigationsprovide a wealth of information to understand the charge storage mechanismsand help improve the electrode material structure, morphology, andproperty by means of standard synthesis and/or post-synthesis methods,to choose the appropriate electrolyte or the electrolyte modification,etc. Besides the changes in the structural, morphological, and otherintrinsic properties of pristine materials by the above-mentionedmethods, electronic DOS is also affected. While functional groupsor dopants and heterostructures mostly contribute via pseudocapacitance,the changes in the DOS of electrode material are responsible to contributeto quantum capacitance (CQ). While modifyingthe carbon structures with the above-mentioned methods, one can noticethat the modified structure can provide a higher surface charge densityand higher CQ in either positive or negativebias. This fact is quite important to decide whether the electrodecan be used for a symmetric supercapacitor or an asymmetric supercapacitor.The lower values of capacitance and energy densityof carbon-basedmaterials are due to the low packing density, chemical inertness,hydrophobicity in aqueous electrolyte, and low density of states (DOS).17 Hence, a proper combination of pristine electrode materials, heteroatoms,defects, and types of electrolyte ions is necessary to obtain thebest quantum capacitance value and, hence, the total capacitance,energy/power density, and other key parameters of SCs.Besides carbon-based materials, such as MXene, and transition metalchalcogenides also provide quantum capacitance that can be increasedfurther by modifying the structure. The physical properties of carbonand two-dimensional (2D) material electrode are summarized in 2CQ and how it can be tailored.Indeed, there are some experimental attempts to evaluate CQ using the standard electrochemical characterizationapproach. However, there is no exhaustive coverage on this specifictopic of quantum capacitance of supercapacitor electrodes, exceptthe partial discussion in ref –1.2 to (≥)1.2 V for ionic/organic electrolytes3. This fThere is plentyof theoretical research based on density functionaltheory (DFT), first-principles calculations, etc. to understand theimportance of n in ref . This ren in ref 2. To proCQ uponthe temperature and electrolyte used, respectively. While discussingthe quantum capacitance of the supercapacitor electrode materials,we also shed light on the experimental viewpoints or the experimentalfeasibility of the theoretically predicted strategies to enhance CQ. CQ of the electrode using standard electrochemicalcharacterization. Finally, the challenges and outlook are discussedin In the present review, 325 The difference in electrochemicalpotential (V) can be expressed as eV = eφ + μ, where φ is the potential drop between theelectrodes and μ is the chemical potential. Upon differentiationof the above equation with respect to the carrier concentrationCEE is thecapacitance as a result of the electrode/electrolyte interaction, n is the carrier concentration, and dn/dμis the thermodynamic DOS  and CQ are in a similar order.Because the electrochemical energy storage device is a combinationof electrodes and electrolytes  and normal metal electrodes separated by insulating materials,as shown in amic DOS 4B. The cCQ is an intrinsicproperty of thematerials, which arises from the kinetic, exchange–correlation,and electron–phonon interaction energies in the total energyfunctional.27 For the graphene–vacuum–graphenecapacitor, considering the kinetic term kBT ≪ eV, CQ can be expressed as24CQ can be expressed asCQ cannot be zero at room temperature and hasa minimum positive value at 0 V because there is always thermal broadeningof the electron energy distribution.28431 The reason behind this is, as the activated carbon stores the chargevia a EDLC  and, hence, better power density,cycle life, and chemical stability can be obtained, surface morphologyand porosity can be tailored. Carbon-based materials offer certainbenefits, such as having different dimensionality [from zero-dimensional(0D) to three-dimensional (3D)], and their optical, electrical, mechanical,biocompatible, and other properties can be effectively controlled.32 The main carbon nanostructures discussed in this section are graphene,carbon nanotubes (CNTs), graphyne, etc. Thanks to the unique propertiesand structure of graphene that are quantified by numerical modelingand simulations, graphene engineering becomes possible. Thus, grapheneis adapted as a model structure. Moreover, by rolling, folding, cutting,etc., one can transform graphene into carbon nanotubes, fullerene,and graphene nanoribbons. If CNTs are taken as an example, strain,curvature, and chirality  should be considered.Importantly, reduced graphene oxide (RGO) or graphene nanoplatelets(GNPs) cannot be defined as graphene; they are the members of thewider graphene family. Unfortunately, RGO or GNPs are termed as graphenein many works, while we are strict on the definition of graphene,where sp2-bonded carbon is arranged in a single-layer hexagonalhoneycomb lattice and without attached functional groups. Becausethe CQ value of pristine graphene is limited,it is possible to increase it by adjusting the number of graphenelayers,7 doping or functionalizing,33 surface rippling, and causing tensile strain,24 as discussed below.Among the SCelectrode materials, the mostly studied and even commerciallyused materials  are carbon-based materials.4.1CQ can be enhanced by increasing the number of layers, and onecan reach the saturation value (mostly after four layers), beyondwhich the enhancement in CQ is quite negligible.On the basis of the theoretical results, the effect of the graphenelayer on CQ can be realized . This result reflectsthat dopants or foreign atoms have a significant effect on the enhancementof CQ. More details are given in CQ compared to co-doped single-layer graphene (163.19 μF/cm2 at positive bias), which is attributed to the interactionof dopants located in the adjacent layers.35 This observation suggests that merely increasing the number of graphenelayers of the doped graphene-based structures may not be the mosteffective way to boost DOS or CQ.Dependent upon the number of layers, one cancategorize them into graphene (one layer only), bilayer graphene,trilayer graphene, few-layer graphene, or multi-layered graphene (numberof layers being ≥4). It is well-known that the intrinsic propertiesof graphene strongly depend upon the number of layers. It is quiteinteresting, as seen from realized 5B, and og effect 5C. As a 4.2CQ may not be significant, as seen from panels A and B of CQ for pristine grapheneand graphene with a single vacancy (SV), double vacancy (DV), triplevacancy (TV), and quadruple vacancy (QV) was estimated, using DFTcalculations, to be 10.72 μF/cm2 at 0.6 V, 107.61μF/cm2 at −0.04 V, 39.16 μF/cm2 at 0.6 V, 160.29 μF/cm2 at 0.02 V, and 119.6 μF/cm2 at −0.06 V, respectively.37 This result reflects that a triple vacancy in graphene leads tothe highest CQ. The defect concentrationsfor graphene with SV, DV, TV, and QV were 3.12, 6.25, 9.37, and 12.5%,respectively. Eventually, the vacancy defect was found to be moreinfluential (120.72 μF/cm2) compared to the othertypes of defects, like the Stone–Wales defect (44.38 μF/cm2), where theoretically estimated CQ of pristine graphene was 21.37 μF/cm2.38 It is important to note that modified graphenedoes not lose its conductivity even after introducing vacancy andStone–Wales defects.38 The vacancydefect induces p-type behavior as a result of the electron deficiencyand, hence, shifts the Fermi level into the valence band. However,there is a trade-off between CQ and thermodynamicstability of defected graphene,37 whichhas been tackled by introducing nitrogen in the graphene matrix. Thehighest integrated CQ (260.68 μF/cm2 at 0.04 V) with the least formation energy (0.25 eV/Å)was found from simulation results for single-vacancy trimerized nitrogen37 to lower the formation energy feasible to synthesizethe material experimentally. It can be enhanced further by increasingthe defect concentration up to a certain limit  and local curvature was also found to be influentialin enhancing the quantum capacitance . Indeed, the theoretical study reveals that the presenceof edges on the graphene surface is also beneficial to improve theDOS.4.341 The highest CQ values obtained for the graphene functionalizedwith the acetone radical and phenol radical are 235 and 237 μF/cm2, respectively.41 The substitutedgroup is categorized into groups I, II, and III, which is shown in 42 On the basis of the result obtained from this study,42 group I functionalized material can be usedas both positive and negative electrodes, whereas group II and IIIfunctionalization is recommended as a negative electrode. Whateverthe case, a recent study42 reveals that−NH2-functionalized graphene showed the highesttheoretical integrated CQ .45 According to the DFT calculations, the electrochemically oxidizedCNT yarn resulted in 0.016 electron transfer (0.001 for pristine CNTyarn) during the interaction with a single water molecule.46 On the other hand, graphene oxide (GO), whichcan be treated as highly oxidized graphene, has received significantattention as a result of its mass production, easy synthesis, lowcost, and unavoidably relatively higher amounts of oxygen functionalgroups.48 The oxygen functional groups that are attachedon the edge plane of GO in large quantities are epoxy and hydroxyl,whereas small amounts of carboxyl (−COOH) and carbonyl (C=O)are attached on the basal plane. Among them, the higher hydroxyl group(−C–OH) in the carbon matrix leads to a higher CQ, as obtained from the simulation result, whichis attributed to the enhanced electronic states near the Fermi level, it has been seen from the experimentalinvestigation that RGO has poor cyclability (70%) and higher equivalentseries resistance after several charge–discharge cycles.47 To obtain an overall idea of the differencesin properties and performance between GO and RGO, see The carbon surface, including most of the nanocarbons,is basicallyfunctionalized with physisorbed oxygen-related functional groups.This can be easily identified from the typical X-ray photoelectronspectra.mi level7A.49 Mor4.49 Because onecan tailor the doping concentrations, the number of dopants (co-doping),and the defect level associated with doping, there are multiple optionsto enhance the quantum capacitance of the electrode in the structures,53 which is discussed in the following sections.For oxygen, two configurationscan be considered: oxygen functionalization  comparable size and ability to form strong valencebonds with carbon atoms, (ii) N doping being quite simple to manipulatethe local electronic structures, and (iii) N–C bond distancebeing similar to the C–C bond length and, hence, the graphenesymmetry being preserved even after N doping.54 Eventually, on the basis of the binding energy calculations, N-dopedgraphene is more stable than defected graphene.55 However, although the charge transfer/atom to N from thegraphene sheet is 0.5e compared to that of P (0.3e),54 DFT calculations showed that P-doped graphene deliveredhigher CQ (143.42 μF/cm2 at 0.57 V) than S-doped graphene (95.78 μF/cm2 at0.54 V) and N-doped graphene (135.50 μF/cm2 at 0.23V).35 Moreover, P-doped graphene has newstates around the Fermi level without any shift56 and showed the capability to store the charge at an extendedpotential window in an aqueous electrolyte.57 On the basis of theoretical studies, Cl doping allows for the highest CQ values to be obtained in comparison to dopingwith other elements, as evidenced by the maximum charge redistributionon graphene, shown in CQ. Importantly, one must pay attention to the atomic radiusof the dopant. The dopant with a larger size than the carbon atomcan produce severe stress in the structure, and hence, there willbe failure of structural stability of the doped structure.Obviously, each dopanthas preferential adsorption sites on the graphene matrix 8A.13 One4.4.2CQ of the final structure. At higher doping concentrations, CQ is found theoretically to be higher for N-dopedgraphene  > graphitic (123.77μF/cm2 at −0.54 V) > Stone–Wales(110.85 μF/cm2 at −0.41 V) > pyridinic(91.39 μF/cm2 at 0.6 V) > pristine graphene (22.17μF/cm2 at−0.6 V).60 Surprisingly, the maximum CQ is found to be increased theoretically to215.55 μF/cm2 at −0.07 V when combined withStone–Wales defects and 486.32 μF/cm2 at 0.2V at 6.38% concentration of pyrrolic N.60 When the stability of the structure is considered, the graphiticstructure stands out as a better candidate compared to the pyridinicand pyrrolic structures being the least stable structures.60 Thus, the discrepancy between the above reportson the role of pyrrolic N needs further clarification.Many configurationsexist for the dopants on the parent matrix. Considering nitrogen asa dopant for graphene, the possible configurations are pyridine (N-6),pyrrolic N/pyridone N (N-5), quaternary/graphitic nitrogen (N-Q),oxidized pyridine N (N-X), and nitrogen oxide (N-Ox). It has beenpredicted that CQ of doped graphene. Three different configurations for dopants taken into consideration are pyrrolic X, triangularpyridinic-like X doped (SVD-X), and pyridinic X -defected graphenecompared to doped graphene. Among the doping configurations, pyrrolicN and pyrrolic B exhibited the highest CQ, whereas the highest maximum CQ is obtainedfrom pyridinic F and SVD-S  doping], for all doping with model c [single-vacancy graphene withthe double N  doping], except P doping, which has nolocalized states near the Fermi level, and all doping for the tripleB, N, P, and S doping with model d , N–S–S is found theoretically tobe the most stable structure and provides the highest CQ, which ensures that the 1:2 ratio of N/S co-doping isthe most optimum ratio  doping] performed best ata positive potential and triple S doping with a single vacancy performedbest at a negative potential.58 One needsto note that the co-dopants occupying the sites near the vacancy arequite stable compared to the occupied sites away from the vacancy.58 It has also been theoretically reported in thepresence of pyrrolic N that the S dopant tends to dislocate from thegraphene plane by approximately 1.32 Å to form the sp3 hybridization, whereas S-embedded pyridinic N-doped graphene retainsthe sp2 hybridization and showed the highest quantum capacitanceeven at a low S concentration.55Co-doping is found tobe an appealing approach because it provides more stability over singledoping with vacancies model d 10A.58 AmCQ by choosing the structureto be defected. To be specific, the defected graphene–CNT hybridexhibited a peak CQ of 85.72 μF/cm2 at 0.4 V, whereas the pristine graphene-defective CNT hybridexhibited a peak CQ of 69.04 μF/cm2 at −0.4 V.63For the heterostructure of graphene/CNT, it hasbeen shown thatone can tune 4.564 For example, Zn-doped RGO is named in ref  substitutionin the graphene matrix (atomic radius of carbon is 70 pm), for example,may not be feasible experimentally. In the experimental point of view,most of the fabrication methods produce nanoparticle-decorated nanocarbon.d in ref , where o68 However, allthe structures are not stable .69 Moreover, the charge transferfor 3D GO/Co3O4 and 3D G*/Co3O4 is estimated to be 1.99e and 2.25e, respectively, which ishigher than the other possible composites .69 Consequently, the maximum CQ valuesobtained theoretically from 3D G*/Co3O4 and3D G/Co3O4 are 862.81 and 880.34 F/g, respectively.69 This result again supports the necessity ofa 3D film over the 2D film as an effective electrode material andsuggests that forming a heterostructure on graphene with in-plane oxygen could be the better possible strategy to obtain a high chargestorage property compared to the heterostructure on oxygen-functionalizedgraphene. However, we also emphasize that the structure, like Ni@Gand Co@G, could be impressive to deliver higher theoretical CQ. There are many misleading experimental reportson these materials, where one can clearly see a battery-like featureinstead of pseudocapacitance from them.70 Of course,one needs to choose a proper electrolyte and proper range of potential,where one can obtain pseudocapacitive behavior experimentally . It has been shown that notonly is the specific capacitance of graphyne higher than that of graphenebut also the quantum capacitance as well. The minimum CQ values of α- and β- graphynes estimatedusing the DFT calculation are 78.7 and 541.3 F/g at 0 V, which arehigher than that of graphene (42.6 F/g).19 The doping affects graphyne too, which depends upon the positionof the dopants  at the D1 position, 4120.7 F/g (0.27 V) atthe D1 position, and 1472.9 F/g (0.12 V) at the D2 position.19 It should be noted that thegraphene structures are distorted when B and N are doped.Besides graphene, there are emerging 2D carbon structures, such asgraphynes and graphdiynes, that are formed by sp- and sp dopants 12. AmongCQ was 1805 F/g at −0.6 V, which is muchhigherthan that of graphene (285 F/g). It has been simulated that differential CQ of B-doped graphdiyne increases with the dopingconcentration and depends upon the position of the dopant. The B-dopedgraphdyine doped at site III with a doping concentration of 5.56%delivered the maximum theoretical differential CQ of 4317 F/g.73 However, the moststable site of boron in the graphdiyne matrix is site I. Likewise,N-doped graphdiyne doped at site II with a concentration of 5.56%exhibited differential CQ of 6150 F/gat 0.6 V. The theoretical report also estimated integrated CQ, because total storage capacity depends uponit, with the B-doped graphdiyne as the anode and N-doped graphdyineas the cathode being 10 557 and 6938 F/g at the doping concentrationof 5.56%, respectively.73 For further enhancement,Cu adsorption on B/N-doped graphdyne presented a compelling advantageover the doping alone case.14 These high CQ values are appealing and, thus, need furtherinvestigations.In the case of graphdiyne, simulated differential 2-hybridized carbon atoms. It could be possible thatthe outstanding theoretical CQ of graphynemay be due to the presence of sp carbon. Moreover, the appealing propertiesof sp-hybridized carbons include a very high theoretical surface areafor H2 of 13 000 m2/g, Young’smodulus of 32 TPa, specific stiffness of 109 Nm/kg, thermal conductivityof 80 ± 26 kW m–1 K–1 atroom temperature, and tunable electronic properties depending uponthe bonding arrangement.77 Looking over it, the experimental investigation iscarried out with a carbyne structure, and the areal capacitance ofthe supercapacitor device is found to be superior to many carbon nanostructures.78 There are also reports on sp-carbon-rich orcarbyne-rich nanostructures as supercapacitor electrodes in three-electrodeconfigurations.80 The maximum gravimetric capacitance obtained is 106.12 F/g (53.06 mF/cm2) for carbyne-enriched carbon anchored on nickel foam at a5 mV/s scan rate in a 1 M Na2SO4 electrolyte,79 and the maximum areal capacitance is 0.32 mF/cm2 at 0.05 V/s for carbyne-rich nanostructured carbon in anionic electrolyte.80 It is important tonote that there is a major issue with the structural stability ofas-synthesized carbyne.As seen from 582 The general chemical formula of transition metal dichalcogenidesis MX2, where M is the transition metals  and X is chalcogens .Layered 2D transition metal dichalcogenides have received significantattention for energy storage applications as a result of their highsurface area, hydrophilic nature, variable oxidation states, highvolumetric capacitance, etc.2 isactively researched both theoretically and experimentally as a promisingSC electrode as a result of its high volumetric capacitance of 400–700F/cm3 for the metallic 1T phase compared to graphene (300F/cm3). Other phases that exist are the semiconducting2H phase, 3R phase, and distorted 1T′ phase. Among them, 1T-MoS2 is hydrophilic and much more electrically conducting . The hydrophilic surfacesare advantageous for a better electrode/electrolyte interaction, andgood electrical conductivity is needed for excellent electronic transportation.The 2H phase shows a bandgap of 1.65 eV with zero DOS at the Fermilevel, whereas both metallic 1T and 1T′ phases exhibit plentyof DOS around the Fermi level. Thus, CQ is found to be higher for MoS2 with the metallic 1T phase(321 μF/cm2 at −0.6 V) and 1T′ phase(395 μF/cm2 at 0.6 V) than 2H-MoS2  (18 Distorted 1T′-MoS2 can be achieved by introducing carbon nanostructures (CNT or graphene)underneath, which induces localized strain effects leading to thedistortion and phase transformation.18 Incomparison to 1T′-MoS2/graphene , 1T′-MoS2/CNTshowed the enhanced DOS and, hence, theoretical CQ of 500 μF/cm2.18 Moreover, heterostructures are not always profitable to have a higher CQ. For example, theoretical CQ of MoS2/graphene is 0.28 μF/cm2 at 0 V, which was even lower than that of graphene (2.55μF/cm2) and the MoS2 monolayer (65.22μF/cm2).83 Of course,one can tailor the vacancy in MoS2/graphene, such as Mo,S, and C vacancies. S-vacancy MoS2/graphene showed a highertheoretical CQ (273.98 μF/cm2) compared to its C vacancy (72.93 μF/cm2) and Mo vacancy (257.15 μF/cm2). The simulationresult also shows that the maximum CQ ofFe-doped Mo-vacancy defected MoS2/G was 346.99 μF/cm2 at a positive bias.83 On the contrary,it has also been reported that the Mo vacancy can change the electronicstructure drastically compared to the S vacancy, such that a largeamount of DOS was introduced, which, in turn, enhances CQ to 209.733 μF/cm2.84Among thetransition metal dichalcogenides, MoSi level) 13.18 DisCQ is obtained for the N-substituted MoS2 monolayer (203.047 μF/cm2). However, thereare no observable changes in the electronic states for the Se doping.For the group VII functionalization, CQ is 139 and 252 μF/cm2 for F and Cl. In the caseof Mo substitution, vanadium (V) could be the best choice becauseestimated CQ is 263.721 μF/cm2 among Co, Cu, and Ni.84 It hasbeen reported that substituting S by Al in single-vacancy MoS2 could be the choice for symmetric SC application and substitutingS by B in pristine MoS2 could be the choice for asymmetricSC application among the Ti-, Au-, Ag-, Cu-, Al-, B-, N-, and P-dopingpristine and single-vacancy MoS2 monolayer.87 Further enhancement of maximum CQ and surface charge density can be achieved by increasingthe doping concentration. It could be interesting to investigate thechanges in electronic properties, DOS, and hence CQ of the MoS2-based heterostructure with Mosubstitution, Mo vacancy, and S substitution, simultaneously.For the case of doping, the two common approachesinclude Mo substitutionby transition metals or S atom replacement by group V  and group VII atoms (F and Cl). The maximum simulated 2 monolayer,showed high DOS near the Fermi level, and the highest simulated CQ obtained is 377 μF/cm2 at+0.19 V. It can be enhanced further by introducing materials, likemonolayer black phosphorus, underneath it via charge transfer fromblack phosphorus to VS2. As a result, the improved highest CQ obtained is 428 μF/cm2 at+0.17 V.88 It is important to note thatmonolayer black phosphorus does not have DOS near the Fermi level.Doping is another adoptable strategy for V-based dichalcogenides.However, beyond the 3% level, Co doping of 1T-VSe2 showsadverse effects on the quantum capacitance and gravimetric capacitance(panels B and C of 2 (4.60 F/g) > WS2 (3.50 F/g) > MoS2 (3.40 F/g) > MoSe2 (2.57 F/g) at a 10 mV/s scan rate in a 1 M Na2SO4 aqueous electrolyte. The MoS2 cell exhibitsthelowest phase constant of 60° at a low frequency compared to thatof TiS2 (75°). The higher capacitance value of TiS2 is attributed to the low density and higher electrical conductivity.86Another transition metal dichalcogenide, 1T-VSCQ of hexagonal FeSis estimated from first-principles calculations to be 408 F/g. Whenthe vacancy is introduced in the structure, CQ enhanced to 2280 F/g at a positive bias.89FeS is another emerging material thatcan be considered as an energystorage electrode. 690 The general formula for MXenes is Mn+1XnTx, whereM, X, and Tx stand for the transitionmetal, carbon and/or nitrogen, and surface terminations with n = 1–4, respectively. Some of the most researchedand significantly attracted MXenes are Ti3C2Tx, Ti2CTx, V, and Nb. Importantly, the volumetric capacitance of Ti3C2Tx MXene hydrogelobtained is 1500 F/cm3 with respect to Hg/HgSO4 at 2 mV/s in H2SO4, which is much higher thanthat of MoS2 or graphene.22MXenes have recently emergedas promising 2D materials of transitionmetal carbide/nitride/carbonitride in the field of energy storageand other suitable applications as a result of the features of metallicconductivity, large interlayer spacing, easy functionalization, andredox-active surface oxide-induced pseudocapacitive behavior.CQ. 91 summarizes the contribution from EDLC, redox capacitance, CQ, and total capacitance (CT) of Ti-, V-, Nb-, and Mo-based MXenes. To calculatetheoretically, a few assumptions made in ref  on the surface. On the basis of the synthesistechniques, Tx can be different. For example,Tx is O, OH, Cl, and F for chemical etching,92 O and OH for hydrothermal, and Cl or halideswith O-functional groups for molten salt techniques. Oxygen functionalgroups are considered unavoidable because of the chemical processinvolved in all techniques, and they are responsible for aiding thepseudocapacitance. Eventually, the theoretical calculations on CQ and surface charge density suggested V2CT2 MXene with mixed terminations as a suitableanode material of asymmetric supercapacitors in aqueous and ionic/organicsystems.93 The result obtained theoreticallyfor pristine and functionalized MXenes (91 (i) Ti2C has the highest EDLC and CT, even compared to Ti3C2, whereas V2C has a higher CQ at 0 and 1 V, and Nb2C has the highest CQ at 1 V among the studied pristine MXenes. (ii) O functionalizationlowered the EDLC, CQ, and CT for all MXenes.94 (iii) Amongthe functionalized MXenes, O-functionalized V2C has a higher CQ at 0 V and O-functionalized Mo2C has the highest CQ at 1 V. However,O-functionalized Nb2C has the highest total capacitanceat both 0 and 1 V.In contrast to the pristine carbon-based materials, MXenes generallyshow higher values of the DOS and d MXenes 14 can be3C2Tx MXene. It has been reported that O-doped MXene synthesis from theO-functionalized MAX phase is a more facile approach, called in situ oxygen doping.98 Fromthe O doping, the DOS near the Fermi level is improved, which is reflectedin the enhanced interfacial capacitance of O-doped Ti3C2Tx compared to its bare counterpart.98 In this way, one can decrease the valence stateof the inner Ti atoms, which promotes electronic transport, and increasethe valence state of outer Ti atoms, which is responsible for theenhanced pseudocapacitance.Instead of the O-functional group, the charge storagecapacitycan be enhanced with the replacement of carbon in a titanium octahedronby oxygen in Ti2C and Nb2C MXenes.96 As seen from CQ for Ti2C MXene.99 Despite the lower CQ values of V2C and Mo2C caused by the introduction of functional groups, the functionalizedMXenes still have a higher CQ comparedto the other electrode materials.96 Thereis also an exception for Sc2C MXene with other functionalgroups as well. The maximum differential CQ of Sc2CSi2 with T of P, Cl, Se, and Si ishigher than that of monolayer Sc2C in both aqueous andorganic electrolytes (95The above result 14A is batrolytes 14C.953C2Tx film exhibits higher gravimetric (volumetric)capacitance of 543 F/g (2063 F/cm3) at 1 A/g with98% capacitance retention after 8000 cycles, which is higher thanthe untreated Ti3C2Tx film (281 F/g).100 Among the post-annealingunder different environments , Ti2CTx MXene annealed at N2–H2 provides thebest storage properties compared to as-synthesized MXene.97 In both cases,97100 the improvement in performances is mainly attributedto the increased surface area, increased interplanar distance, increasedcrystalline order, highest carbon content, and removal of −Fand −OH terminal groups. On the contrary to F removal, the CQ value obtained theoretically from F-functionalizedMXene is quite impressive.93 Ca-adsorbedTi3C2F2 and Li-adsorbed Ti3C2F2 showed the highest CQ of 488.153 and 259.490 μF/cm2, respectively,among the all of possible combinations.99 We emphasize that the use of F is not recommended because it reducesthe electrochemical reactivity and electrical conductivity of MXene,while it is also hazardous and causes some safety issues.In reality, after thesynthesis, MXenes possess multiple terminationgroups, and these are unavoidable. Theoretical results suggest thatremoving the functional groups from the surface of electrode materialscould be a better option to obtain a high energy storage performance.From the experimental side, on the basis of testing in a two- or three-electrodeconfiguration, it is also observed that post-annealing as-synthesizedMXene has better performances. The alkalinized (by KOH treatment)and annealed (under Ar at 673 K) Ti+, Na+, K+, etc.). The (opto)electronic propertiesof the final structure obviously depend upon the vacancy type.101 It has been predicted that CQ of Ti2CO2 can be enhanced at apositive potential further by increasing the oxygen vacancy concentrationbecause a larger charge transfer takes place for neighboring O andTi atoms. It is also important to note from the theoretical studythat one oxygen vacancy is more effective compared to two or threeoxygen vacancies.102 Ti2CO2 with oxygen vacancy concentrations of 11.11 and 16.67% hasa lower maximum CQ of 3131.18 and 3573.14μF/cm2 at a positive potential, respectively. Apartfrom the O vacancy, the C or M vacancy also enhances the DOS at theFermi level. As predicted, Zr2CO2 MXenes withZr vacancy can be chosen as cathode materials, whereas Zr2CO2 MXenes with C and O vacancies can be a good choicefor anode materials.101Theharsh synthesis techniques of MXene from its parent structureleave an atomic vacancy in the MXene structure, which has a significantimpact on the diffusion behavior of electrolyte ions  atoms were doped, and the increased CQ was attributed to the increased DOS contribution from3d and 4s electrons of Co. N doping into carbide-based MXene couldbe another alternative approach to enhance CQ.Apart fromthe termination groups, doping is another approach forMXene as well to change the DOS and, hence, 2C MXene, niobium nitride MXene emerges as promisingelectrode material. We highlight that simulated CQ of NbN at negative and positive biases is found to be834.5 and 1683.7 F/g compared to Nb4N and Nb5N6.104 The maximum CQ has been observed for Nb2N (1196.28μF/cm2 at −1 V and 844.8 μF/cm2 at 0.5 V) and Nb4N3 (174.86 μF/cm2).105 Remarkably, increasing thenumber of layers has profound effects on enhanced CQ for both Nb2N and Nb4N3.We stress that, apart from the carbide-based MXene,there are alsonitride-based MXenes. It could be interesting to evaluate the superioritybetween N-doped carbide and nitride MXenes. Eventually, in contrastto Nb7CQ of silicene is predicted to be 2 times higher than that of graphene,even at a low bias.106 To improve CQ of these materials, the strategy is similarto graphene, namely, doping, introducing defects, etc. Among these,silicene with a six vacancy-defected structure performed better atthe voltage of 0–0.5 V.108 It is reported onthe basis of the theoretical calculation that the co-doping with thetransition metal and nitrogen to silicene delivered higher chargestorage and CQ compared to the singledoping with the transition metal or N. The DOS contribution near theFermi level only comes from the 3d state of the transition metal atomand the 3p state of the Si atom, whereas N helps to stabilize thesystem. The higher the N concentration, the more stable the structure.109 Theoretical CQ ofgermanene (3.51 μF/cm2) is also found to be higherthan that of graphene at 0 V. Although doping can have a significanteffect on DOS, this is not always the case. For example, N-doped germaneneshowed a theoretical CQ of 45.32 μF/cm2 at 0.01 V, and Ti-doped germanene exhibited the highest CQ of 91.47 μF/cm2 at 0.2 Vcompared to Cr, Co, and Mn doping,108 whereasboron and aluminum doping does not show any significant enhancement.There are other 2D materials, like arsenene110 and δ-6 borophene,111 and theoreticalstudies have been conducted focusing on tailoring the electronic properties,DOS, and hence CQ by means of doping,defect, or heterostructure formations.There are many 2Dmaterials, apart from graphene, transition metalchalcogenides, and MXenes, in the pipeline, and they have remarkablefeatures. They are sometimes even found to be superior to graphenebased on the theoretical calculation. 112As seen from the aboveliterature analysis, the major issues ofthese 2D materials as an energy storage electrode include (i) mass-scaleproduction of these 2D materials and, in particular, synthesis ofthe freestanding film, which remains a challenge, (ii) material stability,and hence (iii) very limited studies on the applications because thereis a lack of experimental confirmation of theoretical predictions.8CQ of electrodes at varioustemperatures. Considering pristine graphene-based materials, structuresare theoretically found to be quite stable at elevated temperaturestheoretically. However, once functionalized or doped, structural propertieschange , as highlighted by the shadowed color in panels A, B, and Dof CQ of the electrode has an almost decreasingtrend with the temperature. We also emphasize the changes in the electrodeand/or device that happen in the performance from real test results,the improved electrical conductivity of the electrode at higher temperatures,which is, in turn, higher specific capacitance, better coulombic efficiency,and higher specific energy/power density of the electrode and thecell up to a certain temperature. There is also the possibility ofthe phase change of the SC electrodes made of metal-oxide-type materialswith the temperature operation, and sometimes, it cannot be reversible.This sectiondiscusses the temperature dependence of the quantumcapacitance. Most of the simulations and even experimental testingas supercapacitor electrodes are carried out at room temperature.However, supercapacitors should be capable of working in the rangefrom −100 °C (173 K) to 60 °C (343 K), with extremelylow failure rates. Because the quantum capacitance is an intrinsicproperty of electrode materials, it is interesting indeed to see whathappens to schange 7D.Eventperature 15, whichaphdiyne 15B.14 In9CQ upon specificelectrolytes. The expected answer is certainlynot because CQ is an inherent propertyof the electrode. First-principles calculations on the desolvationbehavior of Li+, Na+, and K+ at theedge plane pores and basal plane pores of porous carbon materialsconfirmed that there are no significant changes in the total DOS nearthe Fermi level.114 On the other hand,a recent theoretical study revealed that the maximum CQ was found for the B-doped CNT in the alkaline electrolyteat a positive bias, the B-doped CNT in the acidic electrolyte at anegative bias, and the N-doped CNT in the alkaline electrolyte ata negative bias .In this review, our concern is the estimation of CQ of the electrode when the electrochemical energy storagedevice testing is conducted under a defined electrolyte ,a common behavior of the quasi-metallic nature of carbons, correspondsto the quantum capacitance 17D. The tructure 17G.120 I in refs 17C to ob in refs 17H. To m1111.1CQ). CQ is connected in serieswith CEE (capacitance as a result of theelectrode/electrolyte interaction). In summary, we have discussedthe quantum capacitance of various electrode materials, namely, carbon,2D materials, and their composites, and hence, it has a significantimpact on the total capacitance. CQ of carbon and 2D materials. Besides the knowledgeof the surface engineering of the electrode, electrolyte modification,and electrode/electrolyte interaction improvements, the enhancementof CQ became equally important to obtainhigh storage performance from the fabricated supercapacitor device.By tuning the density of states by introducing defects, dopants, orother heterostructures, one can enhance the quantum capacitance ofthe electrode materials and the potential window of the energy storagedevice. Dependent upon the performance of the electrode and its quantumcapacitance behavior, one can choose the right material and the bestapproach for its potential applications, because all strategies maynot be leading to the enhanced CQ. Theelectrode material with a high CQ valuein the positive bias and a low CQ valuein the negative bias window is a suitable choice as an anode of anasymmetric supercapacitor. Meanwhile, the electrode materials withhigh and low CQ values in the negativebias and negative bias window, respectively, can be a choice as cathodematerials for asymmetric supercapacitors.68 One can also measure the surface charge density at positive bias(Qa) and negative bias (Qc). The value of Qa/Qc can be an indication of the choice of theelectrode.67 In generalCQ ofthe electrode also has a dependency upon the temperature of operationas the surface charge density, and DOS depends upon the temperature.It has also been seen that CQ of the electrodecan be tailored by the intercalation of different electrolyte ions;this result can guide experimentalists to choose the right electrolytefor the desired electrode materials.Supercapacitors or electrochemicalcapacitors are promising energy storage devices that provide morecharge storage capacity than conventional capacitors and higher cyclelife and higher power density than the battery. The electrode materialof the energy storage device plays a key role, and the total chargestorage capacitance contribution comes from the electrode/electrolyteinteractions and quantum capacitance of the electrode  and scanning tunneling microscopy (STM), canbe further refined for better control and optimization to study thequantum capacitance properties at the nanoscale. Furthermore, thesestudies are also essential to probe the reaction environments andthe changes within the electrodes.Advanced microscopy and microanalysis: The developmentof Explorationof novel 2D materials: We can explore andsynthesize new 2D materials, such as MXene, borophenes, phosphorene,germanene, etc., with tailored electronic properties for superiorquantum capacitance characteristics, leading to enhanced supercapacitorelectrodes.Quantum mechanical modeling:Advancements in theoreticalcomputational techniques, particularly quantum mechanical modeling, can be harnessed to predict thequantum capacitance of 2D materials accurately. This can guide experimentalefforts and reduce the need for extensive trial-and-error experiments.Moreover, machine learning and artificial intelligence can also playa leading role in modeling quantum capacitance, allowing for the rapidscreening of materials and configurations.Multiscale modeling: Integrating multiscale modelingapproaches that bridge quantum mechanical calculations with meso-and macroscopic simulations  can providea comprehensive understanding of quantum capacitance effects in realsupercapacitor devices.Materials engineering:Future research may focus onengineering the band structures of 2D materials through doping, strainengineering, defect engineering, or heterostructure design to tailortheir quantum capacitance for specific applications.Device integration: Integration of 2D-material-basedsupercapacitor electrodes into practical devices from small flex devicesfor personal use to large-scale commercial energy storage, such aswearable electronics or energy storage systems used for hybrid electricvehicles, will be crucial. This involves addressing scalability, stability,and compatibility issues.Energy storagesystem optimization and measurement guidelines:Beyond materials, future research should focus on the holistic optimizationof supercapacitor systems, including electrolytes and device architectures,to maximize the benefits of high-quantum capacitance materials. Moreover,one has to pay attention to the electrochemical measurements at currentdensity, potential, and electrolyte concentrations. For example, reportingthe specific capacitance of the device and/or electrode equal or abovea 20 mV/s scan rate or a 2 A/g current density is more useful. Theinformation on self-discharge, leakage current, and cell voltage consideringthe potential drop is other important parameters that can be takeninto account.Standardization and benchmarking:Developing standardsand benchmarking protocols for measuring the quantum capacitance valueswill be important for ensuring consistency and reliability in thefield.Certainly,discussing potential future perspectives in research methodologies,both experimental and modeling, in the context of quantum capacitanceof 2D-material-based supercapacitor electrodes is essential for keepingpace with the evolving landscape of the field. The following are somekey areas to consider:Incorporating these future perspectives into researchmethodologies, both experimental and modeling, will contribute tothe continued advancement of 2D-material-based supercapacitor electrodesand their role in the evolving landscape of energy storage technology.


Questions are one of the most frequently used strategies in therapy. There is a body of theoretical work on the kinds of questions that are preferred in specific treatment approaches. However, research on the use of questions in general, how they are formed and what specific therapeutic work they do, is relatively scarce in the literature. In this study, we use the conceptual framework and methods of conversation analysis (CA) to examine how systemic questions soliciting clients' perspective on the partners' thoughts and intents  are realized interactively in actual clinical practice and the range of therapeutic work they perform in couples therapy. We identified 78 OPQs from archival data of videotaped time-limited couples therapies, a clinical population working with a professional therapist. From this set of 78 OPQs, five excerpts representing diverse use of OPQs were selected. These excerpts were transcribed in detail capturing not only the textual content but also the prosodic, gestural, and non-verbal aspects of these episodes. Using CA methodology, we identified four specific kinds of changes these questions can promote: progress toward relational optimism, support of positive aspects of the couple's relationship, promoting the concept that the couples' experiences and emotions are interlinked, and introducing new creative relational options. Detailed CA analyses of these clinical excerpts allowed us to identify how the OPQ sequences were built to realize these therapeutically useful moves using various conversational resources progressively and interactively. The conversational analysis of these sequences facilitated the exploration of relationships between the ways the questions are formed, timed, and delivered and the specific functions they perform to move the therapy forward. In conclusion, we make the general argument that examining important therapy events through a CA perspective provides a significant complementary vector to quantitative research on the therapy process. Dictionary definitions of “questions” often prioritize notions such as “interrogative sentences or clauses… which are designed to elicit information, defined by syntax or grammatical structure” ; these types of questions are designed to have the effect of encouraging exploration or elaboration on the topic. The second category is “closed questions”; these solicit relatively succinct concrete information or a yes/no answer. Some theories of therapy—e.g., client-centered and humanistic—avoid closed, interrogative questions and favor open-ended formulations , whereas others  are more welcoming to the use of questions and do not promote one type over the other  and some implementations of CBT, to clarify false and/or dysfunctional beliefs  questions to direct the clients” attention to specific, attainable, but previously neglected solutions  on questions is relatively sparse   of someone else belonging to their social network . According to Tomm , p. 5, Ons Tomm, . Interacns Tomm, . Althougns Tomm, , how sucThe excerpts analyzed in this project were selected from a prior study designed to examine change processes common to various forms of couples therapy . Some examples of this question type were as follows: “Where does he get the idea from that you have already made up your mind?”; “Does she know what's going on for you when this happens?”; “Is your going there a problem for her?”; “How does he let you know that your opinion doesn't count?” All sessions were transcribed in this step following the CA transcription conventions , drawing attention to other's relationship-fostering conduct (n = 37), facilitating awareness of other's knowledge (n = 10), and exploring barriers to productive ways of relating (n = 22). In the first type, hypothetical questions, therapists would solicit a spouse's view on how the relationship could become better if some aspect of the other spouse's experience were to change . “If/then” and “What if…” are common linguistic practices for getting this action underway. For the second category, drawing attention to other's relationship-fostering conduct, the therapist would get the spouse to focus on the other spouse's positive contributions to support the relationship in the here and now, rather than hypothetically. Commonly turn designs identified were “How does s/he show you Y?” or “Have you noticed her/him doing Y?”. The third category, facilitating awareness of other's knowledge, draws unique attention to what the other spouse might not be aware of (or even the spouse's lack of awareness of what the other knows…) and, furthermore, that helping the other spouse to gain this knowledge may produce relationship benefits. Common generic turn designs for this category were “What does s/he know/not know?” Finally, exploring barriers to productive ways of relating, this OPQ type gets the spouse to reflect on the reasons why the other spouse might be holding back with regard to conduct or emotions. Some common formats for accomplishing this action were “Why does s/he do/not do/stop doing Y?” Brief conversational extracts illustrating each of these actions are shown in the following subsections.A total of 78 examples of OPQ question sequences targeting other perspectives were identified in the data. From this corpus, we identified four distinct practices in which these questions performed interpersonal work: own personal relationships with family members . Melvin had mentioned how he valued conversations with his uncle, especially after the death of his father, and the importance he placed on his annual family trips (without Leyla) in order to connect with his family members. Melvin also complained about what he perceived as Leyla not respecting or understanding his need to be with his family.Hypothetical questions have been described as commonly having an “If/then” or “What if” action format . The question is also designed from what may be termed a “not-knowing position” , which not only indexes that what he is about to say may be controversial  but also seems to orient to Leyla's greater epistemic rights. Melvin is, after all, accounting for what Leyla thinks. In response, the therapist asks a hypothetical question that gets Melvin to consider how Leyla might have a different perspective on Melvin's situation if she understood how important certainly family matters were to Melvin. On the one hand, the question proposes an alternative scenario for the couple, one in which Leyla's thinking was more in line with Melvin's. On the other hand, the question generates agreement from Melvin concerning a more productive and positive relationship scenario: Leyla understands Melvin's needs. In line 17, Melvin initiates an other-repair sequence with “∧Saythatagain.∧” (Itdoes/sucks)°]. In line 13, the therapist picks up on Colin's incipient emotional display by asking whether he still feels the hurt, thus highlighting Colin's pain in the present moment of therapy for Anna to witness. Then, following minimal client confirmation, he launches into his OPQ (lines 15–18). The question does various kinds of interactional work. First, it shifts the topic from “Anna hurts Colin” to the more emotionally supportive “how does Anna now show you that she cares/wants to repair the trust”; second, it tries to get Colin to consider more prosocial motives on Anna's part . Although this move could be seen as turning Colin's attention to Anna's positive force in the relationship, rather than focusing on how she has hurt Colin, it may be that the therapist worked to shift the topic too quickly. There is a 1-s pause in line 20, and Colin evinces difficulty in answering by claiming a lack of knowledge  and by speaking even more softly. Moreover, rather than orient to Colin's displayed emotion, the therapist continues to focus on Anna's possible prosocial motives in lines 23–28 . After receiving minimal confirmation from Colin, he then uses another OPQ to get Colin to name additional prosocial motives Anna might have, independently from what the therapist had already proposed. It also speaks to Colin's hurt without actually directly confronting Anna with this, allowing Anna to “see” Colin's hurt without her being requested to take a position—and maybe become defensive.Colin begins this extract by recounting the disappointment he felt when Anna slept with another man. In line 08, T affiliates with Colin's turn by Take yourtime,°”. These responses, known as take-your-times or TYTs, have been shown to occur in other institutional settings such as caller helplines and police interviews  but also by asserting that there must be ways in which she demonstrates her caring and trust.The therapist's repeated attempts at topicalizing Anna's positive intentions and getting Colin to contemplate this perspective may, however, have been done too quickly and may not have appropriately attended to Colin's mounting distress at having to confront this painful episode, that is, he may not yet be ready to consider Anna's actions from an alternative, non-hurtful perspective. This is shown in the 2-s pause in line 34 and from the therapist's subsequent “°therapeutic project of getting Colin to recognize Anna's prosocial motivesAre are you saying that because(.) Anna's here?). This leads Colin to become defensive and deny avoidance and instead claim knowledge of Anna's intentions, while not being able to name them.As this extract unfolded, Colin displayed mounting distress and tearfulness on numerous occasions. One option from the therapist could have been to affiliate with his distress by formulating and/or engaging with the distress to some appropriate degree, inviting Colin to continue exploring his hurt Muntigl, . InsteadTo conclude, by choosing to stay with the optimistic/positive thread, the therapist consistently supports the foreword movement in the narrative, going from empathizing and validating the “hurt” to noting the possibility that Anna may be participating in the dynamic of emotion by trying to help repair the relationship. Thus, Colin's pain is recast as not just a “private affair” for him to resolve but an interpersonal one in which Anna is an important participant. It also creates a shift from the past to the present, allowing Anna to witness Colin's engagement with his pain.OPQs may also solicit a spouse's knowledge about other's knowledge, and these questions often appear in the following turn formats: “What does s/he (not) know about X” and “Does s/he know about X?”, where X generally references other's feelings or important relationship matters.knowledge role,  and then proposes what Leyla is unaware of (>shedoesn't<s::ee the visible importance of uh (.) the interaction,). From line 16, Melvin then goes into significant detail to explain how the interaction between him and his family members is important for Leyla to understand. He first mentions his cousin, recounting that “there's mo::re going on” when he enters the room relationship-wise than is perhaps perceptible to others. He provides another example with his cousin Sarah (line 24). He claims that they have “a lotta history” and that even though they might not see each other frequently or for longer durations of time, “there'sintensity, there's feelings,”. To sum up, the therapist's OPQ led Melvin to elaborate not only on his view of Leyla's perspective concerning her lack of knowledge about Melvin's relationship with his family but also occasioned a detailed account of how his relationships with his cousins are very important. Thus, by targeting Leyla's knowledge, the OPQ allowed Leyla to witness Marvin's beliefs about what she is not aware of but also what is important to him and how his family relations are deeply meaningful.The therapist continues the prior conversation from  by produOPQs that target other spouses' knowledge may also work to get a spouse to reflect on what s/he believes that s/he knows about other's knowledge. These questions tend to be used in a context in which the spouse does not yet realize that his or her spouse already possesses the requisite knowledge. An example is shown in tryingto get beyond the affair”, and offers an optimistic assessment that she wants to stay. In line 06, the use of “me” seems to offer a “first person” option to Colin. Colin, however, is still hearable upset, as evidenced by his snorty sniff in line 03 . He does, however, concede that her anger has subsided.As can be recalled from Stivers, .8 Colin There was angerth↓ere, and there's a lot less of that. so). Colin is also displaying low intensity upset during his turn  keep it to myself”. Thus, Anna cannot access Colin's feelings because he does not reveal them to her. Thereafter, in lines 34–37, the therapist produces another OPQ that again targets what Colin thinks Leyla knows: >Does she seethe hurt, <. In doing so, the therapist again shifts the topic, but this time from Colin's “anger” to his “hurt”. After receiving visual confirmation from Leyla that she does ), he takes this as a “go ahead” to focus on Colin's hurt emotions in the here and now, which implies that Colin's hurt is not a “private affair” but something that has a legitimate place in the present conversational moment. This focus on the present moment is linguistically accomplished throughout the rest of the therapist's turn with the following expressions: “now”, “you started to experience” and “just a few minutesago”. Colin confirms the therapist's question, which is followed by the therapist's return confirmation, thus producing an empathic moment , which leads the therapist to assert Anna's knowledge of his anger and sadness. In lines 30–31, however, Colin counters the therapist's assertion by stating that she is not aware of his anger and accounts for this with “To conclude, we argue that the OPQs work to break a relationship pattern in which Colin suffers privately” and Anna feels guilty for Colin's guilt but also privately.OPQs may also be used to explore the reasons and motives of other's conduct. Questions such as “why do you think he does that?” or “why does he stop doing it?” are typical examples of such questions. she treats with contempt(0.2) you:r need,). The therapist adopts an epistemic frame (whatIdon'tunderstand) that not only makes explicit his downgraded knowledge about this issue but also signals Melvin's greater knowledge and entitlement to speak about Leyla's possible reasons for disrespecting his needs and that his knowledge about her motives is relevant here. Melvin then takes up this opportunity in line 13 by beginning with a story preface  and after, by launching into a storytelling episode about his fishing trip. During Melvin's story, in line 16, T takes up a turn that does important discursive work. It underscores that this is not a first-time telling  and makes salient the affectual nature of this issue .At the beginning of the Extract, the therapist directs a question to Melvin, asking him to explain how Leyla does not respect Melvin's needs try'en hurt.”) and then states how Leyla's actions had affected him emotionally  reallybothered me). It should also be noted that, in lines 48–51, the delivery of Melvin's talk also changes in terms of the length and frequency of his pauses but also, more importantly, his softened and quieter voice. In line 52, the therapist seems to pick up on this change by producing a noticing that calls attention to Melvin's displayed emotion in the here and now (its choking you up °rightnow eh?°), thus moving the focus toward how this event that happened in the past is having a significant impact on him in the present moment of therapy. With this move, the therapist is able to confirm, and convey empathy with, Melvin's feelings of distress  but then proceeds to discuss how Leyla's phone call could have created a rift in the relationship between him and his cousin Sarah (myrelationship with mycousin I don't wanna change it.). This is because his cousin had planned to visit Melvin and berate him for his actions . Thus, Leyla's phone call is portrayed as potentially creating multiple lines of disaffiliation, not only between him and his wife but also between him and his cousin as well. This may explain Leyla's response in line 61, in which she expresses surprise at Sarah's action (↑Sarahtold you this?) and, therefore, that she did not know about Sarah's plans. By implying that it was not her intention to get Sarah to berate Melvin, Leyla displays an attempt to repair (at least part of) the mounting disaffiliation between her and Melvin. By way of response, however, Melvin continues to criticize Leyla's actions as “lousy” and to assert his own innocence in the matter  an onmy annual fishing trip.…”).Research has shown that noticings tend to implicate a subsequent affiliative response from the client such as confirmation or even more elaborate “feelings talk” , it presupposes that something had “stopped” her from doing that, and, finally, it frames these presuppositions as a question in which Melvin may himself provide the answer. The OPQ, therefore, marks an abrupt shift in the way in which the events told by Melvin have thus far been constructed and conceptualized. In line 78, Melvin seems to orient to this “radical shift” by expressing a lack of understanding or incredulity by producing what in CA parlance is termed an other-initiated repair  and T, in lines 81–83, offers a repair by repeating his question but this time by incorporating Melvin's present tense use of “stops”. In this subtle move, the focus of attention moves from what may have stopped Leyla in that specific situation to what may generally stop her from talking to Melvin both in the past and present. What then follows is a long pause in which Melvin makes verbal signs of contemplation . After Leyla makes a remark in line 85 that jokingly suggests that she should take up the turn and answer, Melvin provides a response that is prefaced by some hesitation and possibly some degree of distress . But now rather than continuing to complain about Leyla, he offers up his own behavior as an obstacle to communication between them (“be' she thinksI'm not gonna be receptive to her.”). Thus, with this seemingly subtle questioning move, the therapist is able to extend Melvin's complaint about Leyla as the principal wrongdoer toward a more reflective mode in which both persons' actions are made accountable for co-constructing a certain relationship pattern.Faced with this complaint story in which Melvin provides a detailed account of Leyla's misconduct and his own innocence, the therapist could respond with an affiliative and empathic move—such as a formulation—that validates Melvin's emotional experience. The risk in doing so, however, would be to deepen and support Melvin's portrayal of Leyla as the wrongdoer and as Melvin as the victim. Instead, the therapist poses a question to Melvin that does not affiliate with Melvin's complaint but rather provides an alternative perspective and explanation of the story events. T's question—“kindagetsinthatwayofyourrelationship;itmakesLeylathinkaboutyouinwaysthatmaynotbe(0.5)fairtoyou.). Melvin's next responses are not only strongly confirmatory, but they also underscore the magnitude in which reservation may be acting as a negative force in the relationship. First, the relevance of “being reserved” is treated as highly significant (its probably the s::martest thingI've heard in about (0.6) three years.); second, reservation is characterized as a new perspective on the relationship or a “leap forward” in thinking (“I'v-have never thought of it that way.”); and third, they convey strong affiliation with the therapist's view that reservation could be a relationship problem. Melvin's responses, therefore, seem to index alliance building between him and the therapist both in terms of strengthening the therapeutic relationship and also in terms of being mutually aligned in the joint task of how productive couples therapy may now proceed.Melvin's reservation continues to be a topic in the remainder of this Extract. In lines 90–97, the therapist seeks confirmation from Melvin about the negative impact of reservation (other-perspective questioning in unique ways. Thus, our study extends past studies, for example (Peräkylä, Our goal in this study was 2-fold: to explore some of the different ways in which OPQs can be used to generate forward movement in CT and to explicate some of the important relational functions of OPQs and how these are realized in sequence. Our CA focus on the turn design features of these questions revealed that different linguistic practices may be employed to implement the action of Our CA analyses allowed us to highlight how these OPQs are produced in sequence, yielding a more positive conceptualization of the “others” included or implied in the question (e.g., partner's knowledge, feelings of motives, which were often followed by a positive hypothesis of the partner's intent. For example, in whatdo you think stopped Leyla from coming and talking to youdirectly°” Crafted this way, the preferred response to a “wh” question would address the part “whatstopped” but also invite Melvin to take a position on the relationally positive/optimistic proposition that follows: “coming to you directly”.OPQs often included an offer displaying one's knowledge to the client and, consistent with Peräkylä  findingsAs Peräkylä and Vehviläinen  study onThe original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.The studies involving human participants were reviewed and approved by Simon Fraser University Research Ethics Board. The patients/participants provided their written informed consent to participate in this study.PM: designed the study, performed data analysis, supervised data analysis, and wrote the article. AH: performed data analysis and wrote the article. All authors contributed to the article and approved the submitted version.


Graphene-based optical modulators have been extensively studied owing to the high mobility and tunable permittivity of graphene. However, weak graphene-light interactions make it difficult to achieve a high modulation depth with low energy consumption. Here, we propose a high-performance graphene-based optical modulator consisting of a photonic crystal structure and a waveguide with graphene that exhibits an electromagnetically-induced-transparency-like (EIT-like) transmission spectrum at terahertz frequency. The high quality-factor guiding mode to generate the EIT-like transmission enhances light-graphene interaction, and the designed modulator achieves a high modulation depth of 98% with a significantly small Fermi level shift of 0.05 eV. The proposed scheme can be utilized in active optical devices that require low power consumption. Over the past two decades, THz source generation and detection have achieved substantial progress and revitalized the development of THz technologies4. Recently, there has been a rapid development in the THz metamaterial devices8. However, more research on advanced components in the THz regime is still required. In particular, THz optical modulators, which are key devices for actively controlling THz signals, are crucial in THz communications and imaging12. Although types of THz optical modulators based on semiconductor materials have been suggested14, their modulation depths are not sufficient high.The terahertz (THz) spectral range of 0.1–10 THz is an important frequency band owing to its potential applications in various fields, such as security imaging, wireless high-speed communications, and biomedical diagnostics17. In particular, the optical property of graphene can be easily controlled by the gate-voltage18. This tunability enables the application of graphene in optical modulators as an active layer. The high carrier mobility on the order of 106 cm/Vs allows fast responses to electromagnetic fields. In addition, cost-effective graphene-based modulators can be realized using the chemical vapor deposition (CVD) method. In recent, a high-quality large-area graphene single layer grown by CVD have been reported in several studies 22. However, suspended single-layer graphene has a negligible absorption of 2.3% for normal incidence, and the tunable effect is not sufficiently strong for drastic variations in absorption, transmission, or reflection owing to the low light-graphene interaction, which is a significant obstacle in achieving high modulation performance.Recently, graphene has garnered significant attention owing to its several exceptional properties, such as high thermal conductivity, remarkable carrier mobility, and wide optical bandwidth24. In the THz and mid-infrared regions, graphene supports surface plasmons, and the properties of the plasmonic modes can be tuned by adjusting the Fermi level. Several types of optical modulators that utilize graphene plasmons and metamaterials have been reported and they exhibit high modulation depth33. However, high-quality (high-mobility) graphene is required to induce high quality factor (Q-factor) plasmonic resonance. In addition, high Fermi level graphene doping (> 0.4 eV) is required to achieve high modulation performance, which increases the power consumption. Another approach to increasing the light-graphene interaction is adopting the epsilon-near-zero (ENZ) effect35. When the permittivity of graphene is approximately zero, the electric field is highly confined within the graphene layer, thereby increasing absorption. However, the ENZ effect in graphene is yet to be experimentally demonstrated and is highly debated36. Inserting a graphene layer in a resonator supporting a high Q-factor can enhance the light-graphene interaction40. For example, optical modulators with the graphene layer placed in photonic crystal (PC) structures or ring resonators that support high Q-factor resonance have been suggested for the optical communication wavelength region. However, studies on optical modulators combining graphene and high Q-factor resonators in the THz frequency band are insufficient.To improve light-graphene interaction, graphene plasmons have been introduced41. Although realizing EIT is difficult owing to strict experimental conditions, an EIT-like spectral response can be obtained by coupling two resonators44. We demonstrate that the high Q-factor guiding mode to generate EIT-like transmission enhances the light-graphene interaction, and the transmission can be drastically modified by a negligible Fermi level shift. The proposed modulator achieves a high modulation depth of ~ 98.2% with a Fermi level shift of 0.05 eV. Therefore, we infer that the proposed modulator is highly desirable in many fields, such as in THz imaging and communications. All simulations were conducted using the finite-element-method (COMSOL Multiphysics software).Here, we numerically demonstrate a low-voltage, high-modulation depth optical modulator by inserting two graphene layers in a structure supporting electromagnetically induced transparency (EIT)-like transmission. EIT is a transmission phenomenon with a very narrow band due to destructive quantum interferenceWtop and Wbot) with a gap. The PC comprising square-shaped pillars of width wpc and height tpc is placed on the top waveguide. The refractive indices of SiO2 and the background material are assumed to be nSiO2 = 2 and nb = 1, respectively. The refractive index of SiO2 varies from 1.953 to 2.108 in the THz region, depending on the deposition method46. The imaginary part of the refractive index of SiO2 is negligible because it is much smaller than that of the refractive index of graphene. Two single-layer graphene sheets are placed on the bottom waveguide with a 10 nm SiO2 gap. The electrical doping level  of graphene is controlled by the tuning of the gate-voltage. So, if the doping level of the top graphene layer is adjusted to EF = E0 eV, that of the bottom graphene layer is adjusted to EF = −E0 eV. Therefore, since the two graphene layers act as active layers, the structure can enhance the effect of graphene. In the parallel-plate capacitor model, the required gate-voltage to adjust a certain EF decreases as the distance between the graphene layers decreases.Figure 47. It is well known that the EIT-like transmission spectrum can be obtained by coupling high and low Q-factor resonant modes. The proposed photonic crystal structure (without graphene and SiO2 layers) excites high and low Q-factor modes simultaneously in the top and bottom waveguides, respectively. We note that the low- and high-Q modes in the proposed photonic structure correspond to the |2⟩ and |3⟩ states in the atomic structure, respectively. Our previous works reported the details in the phase matching condition to generate EIT-like transmission and related dispersion relation of the proposed structure47. By utilizing the high-Q modes that enable strong light-matter interactions, the modulation efficiency of the transmitted THz wave can be improved.Figure EF = 0–0.01 eV when a THz wave is normally incident to the structure. The period, width, and thickness of the PC are assumed to be a = 218 μm, wpc = 0.7a, and tpc = 0.2a, respectively. The thicknesses of the top and bottom waveguides are t1 = 0.25a and t2 = 0.361a, respectively, and the gap size is g = 0.8a.Figure f = 1.002 THz, and the transmission peak decreases remarkably as the Fermi level increases at this frequency owing to the strong light-graphene interaction from the high Q-factor. In contrast, the transmission variation for the Fermi level variation is negligible at the frequency outside the transmission peak region owing to the weak light-graphene interaction.It is observed that the EIT-like transmission peak with a high Q-factor (~ 544) occurs at f = 1.002 THz) are presented in Fig. The transmission, reflection, and absorption curves at the EIT frequency (β)) of the bottom waveguide for the Fermi level variation, which is calculated by the numerical analysis of the one-dimensional waveguide by solving Maxwell’s equations. β is the wave vector of the high-Q guided mode in the bottom waveguide comprising a five-layer structure (air–SiO2 (t2)–graphene–SiO2 (10 m)–graphene–air). As the Fermi level increases, the PL decreases because the imaginary part of graphene’s permittivity increases as the Fermi level increases. In addition, the PL decreases abruptly from EF = 0–0.007 eV. This implies that the loss by graphene increases rapidly in this Fermi level range.Figure EF = 0 eV, most of the light is coupled to the bottom waveguide, and the electric field is highly confined in the bottom waveguide. In contrast, as the Fermi level increases, less incident light is coupled to the bottom waveguide, and the electric field becomes confined within the top waveguide, which originates from the increase in the wave vector and mode mismatches. Hence the propagation loss decreases as the Fermi level increases. The absorption has a maximum value at EF = 0.0064 eV. Below this Fermi level, the propagation loss is the dominant factor for absorption, while the coupling efficiency is the main determinant of absorption at higher Fermi levels.Furthermore, we illustrate the field distributions for the Fermi level variation in Fig. MD = (Ton–Toff)/Ton. If we assume the on- and off-states to be EF = 0 and 0.1 eV, respectively, the proposed modulator achieves a high modulation depth of ~ 99.3% and an insertion loss of 16.5% with a small Fermi level shift of 0.1 eV. In addition, if we assume the off-state to be 0.05 eV, a modulation of ~ 98.2% can be achieved with a negligible Fermi level shift of 0.05 eV. Note that graphene-based modulators reported in Ref.33 require a minimum Fermi level shift of 0.2 eV. In addition, the maximum modulation depth among them is 87%. Compared to these modulators, the proposed modulator achieves significantly low energy consumption and high modulation depth simultaneously. In addition, the proposed modulator exhibits polarization-independent spectral response, which may be beneficial in practical applications.Figure 249. The proposed structure can be manufactured by a similar fabrication process. A graphene sheet on a copper film grown by CVD is transferred onto the SiO2 substrate using the standard wet-transfer technique50. Then, thermal evaporation is used to deposit metal for the electrode. Subsequently, a 10 nm SiO2 layer is deposited on the graphene layer using plasma-enhanced chemical vapor deposition (PECVD). The top graphene layer is transferred onto the SiO2 layer using the same process applied to the bottom graphene layer, followed by metal deposition for the electrode. Hence, the proposed highly efficient THz modulator structure can be realized by current fabrication technologies.It is important to discuss that fabrication process of the proposed structure. The 2D PC with a period of approximately 200 μm can be fabricated by conventional lithography techniques. Previous studies have reported that two graphene layers with a distance of a few nanometers can be realized on SiO2 can be realized by current fabrication technologies. A graphene sheet on a copper film grown by CVD is transferred onto the SiO2 substrate using the standard wet-transfer technique. Thermal evaporation is used to deposit metal for the electrode. In subsequent, a 10 nm SiO2 layer is deposited on the graphene layer using PECVD. The top graphene layer and the electrode are realized by using the same process applied to the bottom graphene layer. A standard THz-time domain spectroscopy system can be employed in observing the tunable EIT-like transmission through the proposed structure.We proposed a high-modulation depth, low-energy-consumption graphene-based modulator using the EIT-like transmission. The high Q-factor of the EIT transmission peak intensified the graphene absorption. The designed modulator achieved a significantly high modulation depth of 99.3% and a low insertion loss of 16.5% with a Fermi level shift of 0.1 eV. Furthermore, a modulation depth of 98.2% was achieved with a negligible Fermi level shift of 0.05 eV. In the proposed structure, the top waveguide with a 2D PC can be fabricated by conventional lithography techniques. In the bottom waveguide, the two-single layer graphene with a gap of 10 nm-SiO53:e, kB, T, ħ, ω, and EF denote the electron’s charge, Boltzmann’s constant, temperature, Planck’s constant, angular frequency, and Fermi level of graphene, respectively. The quantity of τ is the relaxation time defined as τ = μEF/eνF2, where νF represents the Fermi velocity (νF = 106 m/s) and μ denotes the carrier mobility . From the conductivity of graphene, the permittivity of graphene can be obtained byε0 and dG represent the vacuum permittivity and thickness of graphene (dG = 0.34 nm), respectively.The conductivity of graphene was calculated using the Kubo formula expressed asx- and y-directions. In addition, we adopted a transition boundary condition (TBC) to model the graphene layer as a 2D plane in the geometrical domain. TBC represents a discontinuity in the tangential electric field due to the surface current density. Note that the identical transmission spectra can be obtained when the graphene layer is treated as the 2D sheet using the surface current density boundary condition. The 10 nm-SiO2 layer sandwiched with two graphene layers was divided by a 2.5 nm grid size in the calculations.To calculate the transmission spectra, we adopted the periodic boundary condition for the


Magnons and plasmons are different collective modes,involvingthe spin and charge degrees of freedom, respectively. Formation ofhybrid plasmon–magnon polaritons in heterostructures of plasmonicand magnetic systems faces two challenges, the small interaction ofthe electromagnetic field of the plasmon with the spins, and the energymismatch, as in most systems plasmons have energies orders of magnitudelarger than those of magnons. We show that graphene plasmons formpolaritons with the magnons of two-dimensional ferromagnetic insulators,placed up to to half a micrometer apart, with Rabi splittings in therange of 100 GHz . Thisis facilitated both by the small energy of graphene plasmons and thecooperative super-radiant nature of the plasmon–magnon couplingafforded by phase matching. We show that the coupling can be modulatedboth electrically and mechanically, and we propose a ferromagneticresonance experiment implemented with a two-dimensional ferromagnetdriven by graphene plasmons. Theycan transport spin currents for applications in nondissipative spintronics,8 prevents long-range order. Thus, most prominent examplesof 2D ferromagnets (2DFM), such as VI3,9 CrI3,10 and Fe3GeTe2, have a sizable gap in the magnon energyspectrum. Experimental techniques that are very successful in producingand probing magnons in bulk ferromagnets are not easily adaptableto 2D systems due to the intrinsically small sample volume. For instance,the sensitivity of the ferromagnetic resonance is limited by the ratiobetween sample and detector sizes. Recent proposals, such as ferromagneticresonance force spectroscopy,11 addressthe challenge of probing submicrometer-size samples but are a longway from monolayer van der Waals magnets. Cavity magnonics12 has also emerged as a way of enhancing the couplingbetween exciting/probing fields and the magnetic sample. Rabi splittingson the order of 100 MHz have been obtained for micrometer-sized sphereson resonant microwave cavities.13 Furtherenhancement in coupling strength, leading to Rabi splittings of afew GHz, has been achieved for macroscopic-sized ferromagnets in optical14 and superconducting cavities.15Magnonsplay a particularly important role in two-dimensional (2D)magnets, as their uncontrolled thermal proliferation16 This stems from a combination of the scarcity of microwave sourcesof higher frequencies and the need to match the resonance frequencyof a cavity. This brings forward the second challenge, the strengthof the photon–magnon coupling. The interaction of the magneticfield of light with matter is notoriously much weaker than that ofthe electric field.17 Placing the ferromagneticsample in a resonant cavity enhances the coupling between the magnonand the cavity modes.12 The frequenciesof those modes, however, decrease as the cavity volume increases,whereas the enhancement factor goes in the opposite direction. Thereis, thus, a compromise between enhancement factor and resonance frequencythat limits the sensitivity of setups of this kind. This links tothe third challenge, which is detector sensitivity. Again, this islimited by the smallness of light’s coupling to magnetic dipolesand puts a constraint on the minimum enhancement factor needed.In this context, exciting and probing magnons efficientlyin 2Dferromagnets remain a challenge. There are three main bottlenecksfor the existing techniques. One is having a driving field of theright frequency: magnons in 2DFM have frequencies in the range ∼0.25–1THz, whereas the highest frequencies achieved in ferromagnetic resonance(FMR) experiments are ∼700 GHz.20 Coupling to grapheneplasmons has been proposed recently as a way to probe collective excitationsin superconductor surfaces,21 2D superconductors,22 and excitons in insulators.23 The common theme of those works is the coupling betweenthe strongly confined electric field associated with the grapheneplasmon and the charges of the electrons in the nearby system. Thecoupling to spins is more subtle, since it relies on the much smallermagnetic-dipolar nature. It is known, however, that momentum and frequencymatching can enhance dramatically the coupling between light and anensemble of quantum objects.24 With thisin mind, we have studied the coupling between graphene plasmons and2D magnons in a van der Waals heterostructure.With regard to the frequency of the driving field, graphene plasmonscome to mind as prime candidates. Their frequencies can be tuned essentiallycontinuously, by gating graphene away from charge neutrality. Currentexperimental limits on such control set the spectral range of grapheneplasmons to a few THz within the wavelength range of interest to us.Graphene plasmons have been shown to form various kinds of polaritonsin van der Waals heterostructures.25 Spin–orbit coupling breaks spin rotation symmetry, stabilizeslong-range magnetic order, and opens up a gap in the magnon spectrumat zero wave vector, q = 0. In many cases of interest,the magnon gap in 2D ferromagnets is much larger than typical valuesin 3D. For instance, the magnon gap of CrI3 monolayers,one of the most prominent 2D magnents, has been reported to be inthe 0.3–1.0 meV range.26 For some materialsthis value can exceed 5 meV,28 putting the lowestenergy magnon in the terahertz region. On the other hand, the energyand wave vector of graphene plasmons may be tuned to match those ofmagnons in a 2DFM by adjusting the charge density of the graphenesheet. Thus, van der Waals heterostructures composed of 2DFM and plasmonicmaterials, such as graphene, may provide a platform to bridge theterahertz gap in optoelectronics. Previous attempts in this directionhave been aimed at the coupling between light and the orbital magneticmoments of electrons in conducting materials,29 but here we focus on the spin magnetic moment, which is associatedwith quantum magnetism.Long-range ferromagneticorder in 2D is only possible in the presenceof magnetic anisotropy, on account of the Mermin–Wagner theorem.z and relative dielectric constant ε.We consider a van der Waals heterostructure,depicted schematicallyin 30 The in-planemagnetic field of the plasmon is coupled to the local spins of theferromagnet via a Zeeman interactionR⃗l is the 2D vector marking the position of unit cell l in the 2D ferromagnet, z is the verticaldistance between the graphene sheet and the 2D ferromagnet, and σ⃗are the dimensionless Pauli spin matrices that relate to the spinangular momentum through The 2D ferromagnet is described with a spin Hamiltonianin thelinear spin wave approximation.aq⃗† is the creation operator for a plasmon with wave vector q⃗ parallel to the graphene sheet. We note that theplasmon magnetic field lies in-plane, so that it generates a torqueon the static magnetization. At the microscopic level, this entailsthe creation of magnons. The coupling strength F is given bypl(q) is the energy of a plasmon with wave vector q⃗, q) is the modelength of the plasmon (see the Supporting Information), and A is the area of the graphene sheet. Theplasmon field decays exponentially, but for the range of wave vectorsrelevant to this work the decay length is of the order of severalmicrometers, thus presenting no practical concern.Using the expression for the quantizedfield of the graphene plasmongiven in ref ,the Zeeq with an atomic spin S⃗l is vanishingly small, as it scaleswith the inverse of √A. In contrast, for collectiveexcitations such as magnons, it makes sense to transform the spinsto a plane-wave basisk⃗ is a wavevector in the Brillouin zone of the 2DFM and N isthe number of unit cells. After applying this transformation to N, where N is the number of spins, resultingin a Rabi coupling that no longer depends on system size, as N ∝ A. Thus, magnon–plasmoncoupling is enhanced due to the phase-matching of the plasmon fieldto a macroscopic number of phase-locked precessing spins.We note thatthe coupling strength of a plasmon mode with wavevector 32EF is graphene’sFermi energy, ε is the average dielectric constant of the twomedia surrounding the graphene sheet, α is the fine structureconstant, c is the speed of light, and q is the plasmon’s (in-plane) wave vector.Thequantized Hamiltonian for plasmons in graphene reads33+,– arethe ladder operators acting on the spin located at site l; their magnitude S is assumed to be the same throughoutthe whole material. The operators bl† and bl respectively create and annihilatea localized spin flip excitation at site l. Assumingtranslation symmetry in the 2D ferromagnet, we can rewrite the HPbosons in reciprocal space. Then, the Hamiltonian for bare magnonshas the formk⃗ span the Brillouin zone of the 2D ferromagnet. The function ℏωmag(k⃗) is the dispersion relationfor the bare magnons. For small momenta, we have ℏω ≃ℏω0 + ρk2, where the first term is the magnon gap and the second providesthe dispersion due to the exchange-driven spin stiffness ρ.To study theeffect of plasmon–magnon coupling, we adopta description of magnons in terms of linearized Holstein–Primakoff(HP) bosonspl ≈1 meV  andtypical graphene doping levels (EF ≈100 meV), q ≲ 0.1 μm–1. This is tiny compared to the linear dimensions of the magnon Brillouinzone (∼104 μm–1), so thatthe dispersion of the magnon states is negligible in that wave-vectorwindow.For plasmons with energies ℏωz is the distance betweenthe graphene sheet and the 2DFM, N is the numberof spins in the 2DFM, and k(+) ≡ kx + iky. The function F has been defined in k⃗ couples only to magnonswith the same wave vector. We notice in passing that the quantizedtreatment of both plasmons and magnons that we adopt here can be usedto model intrinsically quantum phenomena, such as spontaneous emissionof a plasmons due to a spin flip, or the dynamics of non-Glauber states,which are relevant for cavity quantum magnonics. These are out ofreach of the classical description adopted in previous works.18After transforming the Zeeman Hamiltonian to the HPrepresentationin reciprocal space, it readsbk⃗–ak⃗ and bk⃗†ak⃗† in k⃗(z) at the crossing frequency where the plasmon–magnondetuning ω– vanishes.If the terms proportional to ba and a†b†, by analyzing the plasmon Green function (see the Supporting Information for details), which can be probed innear-field optical experiments. Since the plasmon–magnon couplingis linear, the equations of motion for all Green functions can besolved analytically. Their explicit expressions are given in the Supporting Information. Here we will highlightthe most relevant features by plotting the plasmon spectral density, In the followingwe treat the complete magnon–plasmon Hamiltonian,including the nonconserving terms mag(0) = 3 meV, corresponding to a 2DFM such as Fe3GeTe2.35 In that figure we also show thedispersion curves for the bare plasmon and magnon. The formation ofa plasmon–magnon polariton with a Rabi splitting larger than100 GHz, dramatically larger than the values reported in cavity magnonics,12 is apparent.In z, as we show in Interestingly, the magnitude of the Rabi couplingΩ can betuned mechanically, by controlling the graphene–ferromagnetdistance EF with a backgate, as we show in EF that maximizes the Rabi coupling strength, as we show The Rabi couplingcan be further tuned electrically, controllingthe graphene Fermi energy 32 By placing a prism of a high dielectricconstant material on top of the hBN layer, it is possible to generateevanescent waves within the hBN that will excite the surface polaritonsof the heterostructure. Whenever the in-plane component of the wavevector of light matches that of a polariton with the same frequency,there is a dip in the reflected intensity. The in-plane wave vectorcan be controlled via the incidence angle. With this setup, it ispossible to excite polaritons whose wave vectors and frequencies liebetween the light cones inside hBN and the dielectric of which theprism is made. Germanium, for instance, would be a convenient materialto use for the prism. It is transparent to electromagnetic radiationsof frequencies below 1 THz and its relative dielectric constant withinthe same frequency range is εGe ≈ 16.39We now propose to take advantage of the magnon–plasmoncouplingto carry out ferromagnetic resonance of monolayers using an attenuatedtotal reflection setup see 3a. Excit0 = 3 meV and graphene gating voltage corresponding to EF = 500 meV. The dispersions for light insidehBN and germanium are plotted as dashed lines, to mark the spectralregion probed by the experiment. The black dot in 37 indicate that graphene plasmon-polaritons canhave lifetimes in the vicinity of 40 ps at a temperature of 60 K.Magnons in bulk CrI3, on the other hand, can have lifetimesof up to 2 ns for temperatures below the ferromagnetic transition(∼60 K).38 To assess the impactof finite excitation lifetime on our results, we introduced a phenomenologicalbroadening to the bare plasmon and magnon Green functions, to mimicthe experimentally estimated lifetimes. The result is shown in In