An enhanced Raman scattering from a thin layer of adenine molecules deposited on graphene substrate was detected. The value of enhancement depends on the photon energy of the exciting light. The benzene ring in the structure of adenine molecule suggests π-stacking of adenine molecule on top of graphene. So, it is proposed that the enhancement in the adenine Raman signal is explained by the resonance electron transfer from the Fermi level of graphene to the lowest unoccupied molecular orbital (LUMO) level of adenine. Non-invasive sensing of biological molecules, especially deoxyribonucleic acid (DNA) and its constituents, by means of label-free optical spectroscopy can open new prospects in biomedical analysis. Recently, we described a possibility for fluorescent detection of low concentrated DNA solution infiltrated into globular photonic crystal . Since tMaximal theoretical enhancement of the Raman signal caused by the surface of nanostructured noble metals can reach tens of orders of magnitude . Such siApplication of graphene as a substrate for SERS has renovated the interest in the use of surface-enhanced spectroscopy in optical sensing. It has been established that the Raman signal from some organic molecules deposited on graphene can be enhanced but usually less than in the abovementioned plasmonic case. The effect itself is quite novel for graphene and depends both on the type, spatial orientation of the tested molecules, strength of their interaction with graphene, molecular energy levels, and graphene properties , 9. GrapIn the present work, we report about up to 12 times enhancement of the Raman signal from an adenine layer on graphene in comparison with adenine deposited on quartz substrate and discuss the reasons for such effect.We used wide-area commercial graphene sheets prepared by chemical vapor deposition and transferred on a silicon substrate covered with a 200-nm-thick silica layer. The adenine was dissolved in distilled water at a low concentration (0.1 mg per ml). This solution was deposited on graphene samples as microliter droplets. Hydrophobicity of the graphene surface and the low concentration of adenine provided homogeneous drying of the small droplets in the form of thin films  energies of the adenine molecule with respect to the vacuum level taken as a reference point. Experimentally, it can be done, for example, by derivation of the real and imaginary values of the permittivity of solid adenine films in the deep ultraviolet spectral range. It is done, for example, in article [It can be speculated that the light with photon energy 2.41 eV (514 nm) fits better to the energy gap than the photons with energy of 2.54 eV (488 nm). The complication here is in the identification of the exact LUMO and highest occupied  article  by means article , 23. Sim article . There, If we suppose that the graphene Fermi level is situated near −4.6 eV , we can Voltage-dependent shift of the graphene’s Fermi level could be another way to control the resonance conditions for electron transfer to adenine on graphene. Our first attempts in this direction were not very successful because graphene suffers from hysteresis of electrical characteristics in atmospheric conditions . It compEnhanced Raman scattering from thin adenine layers deposited on graphene was detected. It was accompanied by quenching of the background fluorescence of adenine by the underlying graphene layer. The enhancement of the Raman signal depends on the photon energy of the exciting light in a manner which is in agreement with the assumption that a resonant electron transfer from the Fermi level of graphene to the LUMO level of adenine molecule takes place.


When multiple statistical tests are conducted, this procedure needs to be adjusted to compensate for the otherwise inflated Type I error. In some instances in tabletop gaming, sometimes it is desired to roll a 20-sided die (or 'd20') twice and take the greater outcome. Here I draw from probability theory and the case of a d20, where the probability of obtaining any specific outcome is Interestingly, this value coincides with the probability of obtaining a specific outcome on a 20-sided dice (or ‘d20’), as1.  This parallels the use of NHST without any correction for multiple comparisons, as it is more likely to get a significant effect due to chance  if many tests are conducted without a correction for multiple comparisons.In scientific research, it is important to consider the issue of conducting multiple statistical tests and the likelihood of spuriously obtaining a ‘significant’ effect. Within a null-hypothesis significance testing (NHST) framework, statistical tests are usually conducted withn die. This approach assumes that each statistical test is wholly independent from each other, and thus is likely to over-estimate the effect related to conducting multiple statistical tests using variations in how the measures are calculated or the use of different, but correlated, measures. Nonetheless, this exploration is based in probability theory and mathematical derivations, rather than computational simulations, and can serve as an comprehensible primer in understanding the relationship between repeated statistical tests and probability distributions.Here I wondered how much the probability of obtaining a 20, on a d20, would increase due to multiple tests–i.e., obtaining at least one 20 across2 and scientists4, have misconceptions about NHST. This is further compounded by critics of NHST, which often over-emphasize the limitations of the approach, e.g., see8—but rather to improve comprehension of the characteristics of NHST.Developing an intuition of statistics and probability distributions is of particular importance as most people, both laymenn die, each withd sides is:The probability that of a specific outcome occurring on each onn rolls of ad-sided die are listed inThe probability of obtaining a specific outcome acrossTo develop some intuition of the effect of multiple die rolls, several simple cases can be considered.d = 2, i.e., a coin, the probability of obtaining at a heads when flipping one coin (n = 1) isn = 2) isFord = 6, i.e., a ‘conventional’ six-sided die, the probability of obtaining any specific outcome isany of multiple dice, the complementary event should again be considered, i.e., the probability of not obtaining that outcome on any of the die. Forn = 1, the probability ofnot obtaining a specific outcome isn = 2, the probability of not obtaining a six on either of the dice isFord = 20, i.e., a 20-sided die, the probability of obtaining any specific outcome isn = 2 dice are rolled, the probability of obtaining at least one 20 isn = 10 dice are rolled, the probability of obtaining at least one 20 is ≈ .4013. Withn = 20 dice, this increases further to ≈ .6415.Foro or greater, on at least one ofn d-sided die:We can also consider a more general problem, the probability of obtaining an outcome ofo on ad = 20 die, acrossn dice.For instance, when rolling a six-sided die, the probability of obtaining a five or higher isWhile it is widely understood that multiple comparisons need to be corrected for, many would underestimate the degree of inflation in Type-I error associated with additional, uncorrected statistical tests. Critically, statistical procedures have been developed to correct for multiple comparisons , see I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. The author provides an excellent foundation for developing an intuitive understanding of null hypothesis significant testing. The concept of using a 20 sided die to assist graduate students and new researchers to better understand what exactly is meant by .05 and how multiple comparisons have a dramatic influence on interpretation is an interesting one — and I believe novel. This intuitive approach can also be used to improve understanding for the general public and overall science communication. Although this report includes a mathematical derivation, which may be too advanced for new scholars or science communication, it provides an excellent rationale for the use of 20 sided die. When can also easily imagine that this rationale can be used better understand robustness of the outcomes of studies that may be influenced by experiment-wise error rates, such as in the cases of multiple attempts at replication or multiple trials of a specific experiment. The 20 sided die provides a concrete and real world method of communicating the complexities of multiple comparisons that is far more user-friendly than random number generators and variations of Monte Carlo studies. I am curious as to whether the exactitude in engineering and manufacturing a 20 sided die will result in exactly equal probability of each number appearing. A six sided die is created with right angles and is relatively easy to create an equal probability of landing on each side. Obviously, this makes no difference or changes the point of the paper; yet, it may add error should anyone actually attempt to roll the 20 sided dice multiple times. Just a thought as I am unsure on this issue. I suppose should a 20 sided die found to contain significant error or even bias, then there would be scandal in the Dungeons & Dragons world. The author also deserves credit for establishing high levels of nerd credibility. When Dungeons & Dragons, mathematical derivations, and useful statistical communication methods are combined into a single published scientific paper; the trifecta of nerd credibility has been achieved. Overall, this is a well-written report and the mathematics is correct. I am hopeful that the author continues to elaborate on this concept and develops other uses of a 20 sided die for communication and lesson plans in courses on research design and basic applied statistics. This will also be helpful in explaining experiment wise error rate/multiple comparisons in the cases of science communication as well.I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. This short report provides a simple and concise illustration of some of the issues surrounding multiple comparisons in statistical testing. I see nothing wrong with the logic or the mathematics, and can see that this would make a valuable contribution as an assigned text on an introductory statistics course.1 The only suggestion I have for material that could be added would be to include a citation to additional material on the topic of multiple-comparisons correction for the interested reader. This would make the piece more valuable as a teaching aid. I'd suggest adding a couple of sentences to the discussion along those lines and citing a review paper on the topic, such as Curran-Everett, 2000The paragraph after table 1 starts 'For intuition,'. This seems an odd phrase to me. Maybe replace with 'Intuitively' or 'For the purposes of familiarity...' or something like that.Just before the general equation the phrase 'across n die' appears on its own, as a separate paragraph. An error? Or is this supposed to be a subtitle? Couple of minor points:I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. The author provides a novel demonstration of the increasing probability of spurious research results when performing multiple tests: noticing the equivalence of a p = .05 statistical threshold and a d20 die (as used in popular games), the author goes on to describe changes in probabilities when using multiple dice, or when allowing multiple sides of the die to count as a correct result. The aim of this article, as I understand it, is to demonstrate that these changes have a surprisingly large influence on statistical hypothesis testing, and at the same time to provide a hands-on example that many readers might be able to relate to (in the form of the d20 die). The article is well-written and in my opinion fulfills both of these goals. Its rationale and the mathematical derivations seem to be sound and correct. I can easily see this article being used by educators to teach the topic of spurious statistical results and to make the topic more accessible.When the game name "Dungeons & Dragons" is first mentioned in the introduction, it should be followed by a citation of the game's publisher, year of publication, and, if necessary/appropriate, copyright information.A d6 die is described as "regular" in the text. This term seems ambiguous to me and I recommend replacing it with a term such as "cube-shaped," "classical," or "conventional."The current version of the manuscript appears to contain a printing error: before the last paragraph of the "mathematical derivations" section, the sentence fragment "across n die." is printed without context. I recommend the indexing of this article after these minor issues have been addressed, and I hope the author will continue to produce research notes that highlight statistical issues in an approachable manner. I have some minor edits/recommendations to increase the overall clarity and readability of the article:I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard.


We have demonstrated that by tuning the ratio between organic solvents such as N-methyl-2-pyrrolidinone or ortho-dichlorobenzene, and n-octylbenzene molecules, the concentration of exfoliated graphene can be enhanced by 230% as a result of the high affinity of the latter molecules for the basal plane of graphene. The LPE processed graphene dispersions were further deposited onto solid substrates by exploiting a new deposition technique called spin-controlled drop casting, which was shown to produce uniform highly conductive and transparent graphene films.Due to a unique combination of electrical and thermal conductivity, mechanical stiffness, strength and elasticity, graphene became a rising star on the horizon of materials science. This two-dimensional material has found applications in many areas of science ranging from electronics to composites. Making use of different approaches, unfunctionalized and non-oxidized graphene sheets can be produced; among them an inexpensive and scalable method based on liquid-phase exfoliation of graphite (LPE) holds potential for applications in opto-electronics and nanocomposites. Here we have used  The former relies on the formation of covalent bonds between atoms or suitably designed small molecular building blocks to form 2D network by using chemical1921231728via Coulomb repulsion; this can be achieved upon addition of small molecules such as sodium dodecyl sulfate accompanied by alcohols36383940ortho-dichlorobenzene (o-DCB). In particular, we focus our attention on n-octylbenzene (NOTBZ) as dispersion-stabilizing agent due to its total miscibility in the selected solvents and its known capacity to promote the exfoliation yield of grapheneo-DCB during the LPE process on the quality and quantity of produced graphene flakes. We also describe a new deposition technique used for fabrication of uniform graphene films deposited from solution on flat solid surfaces. The set-up includes an integrated heating system to guarantee the fast evaporation of the solvent. More importantly, the as-obtained graphene film shows low sheet resistance and high optical transparency.Graphene, a 2D honeycomb lattice of carbon atoms, has been the subject of countless studies since its first experimental isolation by mechanical exfoliation in 20041367910121516o-DCB . To quantify the concentration of graphene after centrifugation, graphene dispersion was mixed with chloroform (CHCl3) and heated up to 50 °C for 30 min and then passed through polytetrafluoroethylene (PTFE) membrane filters (pore size 100 nm). The remaining solvent and NOTBZ molecules were washed several times with diethyl ether and CHCl3. As previously reportedIn order to cast light onto the role of the addition of NOTBZ in the graphene liquid-phase exfoliation, we first prepared dispersions by adding graphite powder in two different solvents most commonly employed for LPE, i.e. NMP and ions see  were chao-DCB. The average concentration of graphene amounted to 85 ± 5 μg mL−1 for NMP, and 100 ± 6 μg mL−1 for o-DCB as portrayed in 29The LPE studies started by analysing the result of two independent blank experiments performed using pure NMP and o-DCB. Among the four solvents used, upon addition of NOTBZ at specific percentage, we found that the concentration of graphene was more pronounced in NMP and o-DCB, and the highest yield was obtained for NMP as displayed in −1 was reached upon addition to the NMP dispersion of 15 volume % of NOTBZ. Surprisingly, at this percentage, the concentration of graphene in each of the solvents even TCB and DMF  is the highest. In the case of o-DCB, the maximum of graphene concentration is 190 μg mL−1 and is also observed upon addition of 15 volume % of NOTBZ. These concentrations correspond to an approximate increase of the exfoliation yield by 230% for NMP and 100% for o-DCB as compared to the blank experiments. It is worth noting that 15 volume % corresponds to a surface of graphene fully covered by NOTBZ molecules as detailed in Figure S2. Interestingly, the exfoliation at 100 volume % of NOTBZ, i.e. in pure NOTBZ, resulted in dramatic decrease of the exfoliation yield. In fact, no graphene was exfoliated, as revealed by TEM analysis. The exfoliation was successfull only when the amount of NOTBZ is below 40%. This phenomenon can be expained by the fact that NOTBZ itself is a bad solvent for liquid-phase exfoliation. While, recent reports have demonstrated that solvents with surface tensions of ca. 40 mJ m−2, e.g. NMP, o-DCB, are the best candidates for carying out LPE experiments, the relatively low surface tension of NOTBZ (ca. 30 mJ m−2) and notably high increase of the LPE yields in the case of NMP/NOTBZ and o-DCB/NOTBZ provided unambigous evidence that NOTBZ molecules can act as dispersion-stabilizing agent.We have then extended our LPE studies to the use of NOTBZ as dispersion-stabilizing agent. At room temperature and ambient pressure, NOTBZ is a liquid which is perfectly miscible with NMP and In order to characterize the exfoliated graphene sheets, qualitative analysis providing more relevant details such as the percentage of single-layer graphene (SLG) flakes, the lateral size of the flakes and the presence/absence of defects is needed. Currently, the most reliable method for the identification of the number of graphene layers in material produced by LPE is based on High-Resolution Transmission Electron Microscopy (HR-TEM). Typically, the analysis of the folded edges of the graphene sheets provides estimates of the number of layers composing the flakes. Moreover, from the TEM analysis, the average lateral size of the graphene sheets can be defined.First, we discuss dispersions prepared in NMP in the absence and/or the presence of NOTBZ molecules at the highest concentration obtained, i.e. the 15%. The TEM micrographs reveal that the majority of dispersions in NMP are composed of a large fraction of monolayer 15% and bilayer 18% graphene sheets folded over themselves with lateral size smaller then 500 nm. In the presence of NOTBZ, graphene flakes were found mainly in a monolayer 35% and in a bilayer 28% form . Also, to-DCB in the presence and/or absence of NOTBZ as dispersion-stabilizing agent at the highest concentration obtained, i.e. the 15%. The TEM micrographs reveal that the majority of dispersions in o-DCB are composed of a large fraction of monolayer 25% and bilayer 22% graphene sheets folded over themselves with lateral size smaller then 500 nm .To complement the characterization result by HR-TEM, Raman spectroscopy was used. In fact, Raman analysis is more qualitative and it has been shown that this technique is sensitive to the changes in thickness composition under different experimental conditions. It has been revealed that Raman spectroscopy offers a simple and fast analysis of graphene sheet thickness with the evolution of 2D peak shape43 for NMP . TherefoNoteworthy, the thickness analysis based on Raman spectroscopy is only quantitative and must be used in combination with HR-TEM results. Commonly, the results based on TEM are more reliable for liquid-phase exfoliated graphene, and the determination of number of layers based on Raman spectra is more suitable for graphene prepared by micromechanical exfoliation and CVD methods. Therefore, the small discrapancy in the flake thicknes analysis between the Raman and TEM is not surprising.2 and quartz) to form uniform films for applications in electronics remains a challenge. The solvents used for LPE have high boiling points, which results in a re-aggregation problem particularly when drop-casting method is used. Moreover, spin-coating of such dispersions is very challenging because as a results of the poor wetting, only few graphene sheets remains on the surface of the substrate, making it an unsuitable technique to form uniform films of graphene. Another well-known phenomenon observed when a drop of graphene dispersion is drying on a surface, is the coffee-ring effect45462 . AFM and SEM were used in order to investigate the change of morphology of these films, when different numbers of deposition (n) are applied. The graphene sheets are forming islands (as observed in n = 9) is needed in order to form a film with more than 95% of surface coverage. A correlation between the coverage and the number of deposition has been extracted from AFM analysis .Despite the increase of the exfoliation yield and the successful production of mono and few layers thick graphene sheets, the deposition of these graphene dispersions on commonly used substrates  regardless the type of solvent or the presence or absence of NOTBZ. In all cases and as expected, the transmittance decreases when the number of deposition or the surface coverage increases. For n = 9, where the sample is uniform with coverage exceeding 95%, the transmittance at 550 nm is lowered as compared to a single deposition and it decreases from ~93 to 72%.Optical transmittance and electrical resistance of graphene films are two important characteristics for many opto-electronic applications requiring transparent electrodes. Therefore, benefiting of the advantages offered by our developed set-up, we prepared on quartz substrates conductive graphene films from graphene dispersions in o-DCB, and were higher in the case of NMP (3200 to 2200 Ω/square) and in the presence of NOTBZ because of the low conductivity of the molecule. However, if more depositions are performed, the film resistance decreases (see o-DCB only) shows a surface coverage close to 100% for 9 depositions with 72% of transmittance and 680 Ω/square. With a surface coverage amounting 100%, the thickness of the graphene film times the sheet resistance value expressed in Ω/square is equal to the volume resistivity in Ω m of the graphene film. In our case the volume resistivity is as low as 1.6 × 10−5 Ω m. Also the sheet resistances and transparency reported in this manuscript are very close to those of graphene deposed by casting-dropping graphene/acetone suspension onto a polystyrene glass ride 3 (~400 Ω/square and 73% at 550 nm)3 (~30 Ω/square and 90% at 550 nm)The measured sheet resistances of the 24 nm thick graphene film led to very high values for films prepared from only three depositions see . This isases see  due to to-DCB. Careful analysis revealed a significant increase in the yield of exfoliation with the volume percentage of NOTBZ until a maximum. In particular, the most effective exfoliation was obtained with 15 volume % of NOTBZ in NMP as a solvent, with a concentration of exfoliated graphene of 250 μg mL−1 corresponding nearly to 230% increase in exfoliation yield when compared to samples prepared in pure NMP (85 μg mL−1). In the case of o-DCB, the most effective exfoliation was observed using also 15 volume % of NOTBZ, which led to ca. 100% increase in the exfoliation yield. Furthermore, a remarkable increase of single-layer graphene (SLG) flakes was observed in some cases. Careful investigation made it possible to correlate the 15% NOTBZ volume to 100% of surface area estimated which was found to be accurate for all studied solvents. TEM analysis of dispersions produced in NMP revealed that the quantity of SLG is improved by 100% when using NOTBZ molecules. In the case of o-DCB, the quantity of SLG was found amounting 25% even after addition of NOTBZ molecules, although a qualitative Raman analysis showed an opposite trend between NMP and o-DCB after adding NOTBZ. Graphene ink produced with our approach was deposed uniformly on SiO2 or quartz substrate by using a new deposition technique relying on a spin-controlled drop casting. These graphene films exhibit sheet resistance as low as 1 kΩ/square and transparency of 70% at 550 nm. By controlling the number of depositions and the concentration of graphene dispersions, film resistance and transparency can be tuned. Our approach opens up new avenues for the technological applications of graphene ink as low-cost electrodes and conducting nanocomposite for electronics.We have demonstrated that it is possible to enhance the yield of graphite exfoliation by mastering a molecule-assisted LPE-based approach to produce high-quality graphene flakes from bulk graphite. To attain a fundamental understanding of the role of molecule-graphene interaction on the yield of graphene LPE, we have carried out a comparative study by using NOTBZ as dispersion-stabilizing agent upon increasing the volume ratio of NOTBZ in two organic solvents, i.e. NMP and p.n. 332461) and ortho-dichlorobenzene  were purchased from Sigma-Aldrich and used as solvent for the exfoliation. N-octylbenzene  and graphite powder (p.n. 332461) were also acquired from Sigma-Aldrich and used without further treatment.N-methyl-2-pyrrolidinone  in two different solvents, i.e. NMP and −1. The laser power was well below 1 mW to avoid damage. Around 50 flakes drop-cast on silicon substrates were analyzed and the shape of the 2D peak and intensity (as height) ratio between D and G peak, I(D)/I(G) were analyzed. In particular, the 2D peak was fitted with a Lorentzian lineshape and the coefficient of determination, R2, was used to discriminate between monolayer (symmetric peak), few-layers graphene (asymmetric 2D peak) and graphitic (2 peaks). Such an approach allowed us to gain qualitative information on the number of layers distribution and the amount of defects. Atomic Force Microscopy (AFM) characterization was carried out by using a Veeco Dimension 3100, running with a Nanoscope IV controller. The analysis of AFM images and the extraction of the topographical profiles, for measuring the thickness of the different films, were done using Gwyddion.The amount of exfoliated graphene was measured on a Cubis Ultramicro-Balance MSA2.7S-000DM using a membrane holder. The filters were weighed 5 times before and after the filtration process in order to average the mass of graphene. Dispersions were first transferred in 10 mm path length quartz cuvette and analyzed by means of UV-vis-IR absorption spectroscopy using a Jasco V670 spectrophotometer equipped with a Peltier thermostated cell holder at 20.00 ± 0.05 °C. Also the optical transmittance of graphene films was measured using the same spectrophotometer equipped with a transmittance holder. The number of layers of graphene flakes was determined by High-Resolution Transmission Electron Microscopy (HR-TEM) using a JEOL 2100 F microscope. TEM samples were prepared by drop-casting the graphene dispersions on standard Quantifoil® R 2/1 holey carbon copper grid, followed by solvent evaporation at 150 °C for 10 min. Micro Raman measurements were carried out with a Renishaw spectrometer in confocal mode and backscattering geometry with excitation energy of 488 nm, 514.5 nm and 633 nm. A 100X objective with a NA of 0.95 was used for the characterization. This ensured a small laser spot size of less than 400 nm. The spectral resolution of the spectrometer is 2–3 cmo-DCB or NMP were deposed on freshly cleaned quartz substrate using our spin-controlled drop-casting set-up. A custom high torque step motor, with 1.8°/step and 200 step/revolution was used. We explored different parameters, i.e. rotation angle (from 0 to 35 steps), speed (from 1 to 35 step/s) and temperature (from 20 to 80 °C). The best condition giving a homogeneous film was by setting the rotating angle and speed at 22 steps and 11 steps/s respectively while heating at 50 °C. One deposition corresponds to one cycle of drop-casting 70 μL of graphene dispersion, 30 minutes of rotation and 180 min of post annealing at 100 °C under vacuum. The numbers of deposition were varied between 1 and 9. Sheet resistances were measured with a four probes Jandel (RM3000) platform.Prior to use, quartz substrates were washed by applying 2 cycles of acetone and isopropanol and cleaned by UV ozone treatment. 70 μL of the as-prepared graphene dispersions in How to cite this article: Haar, S. et al. Enhancing the Liquid-Phase Exfoliation of Graphene in Organic Solvents upon Addition of n-Octylbenzene. Sci. Rep.5, 16684; doi: 10.1038/srep16684 (2015).


Experimental data are understood within density-functional theory approach and the observed effects are in good agreement with the theoretical data.Realization of a free-standing graphene is always a demanding task. Here we use scanning probe microscopy and spectroscopy to study the crystallographic structure and electronic properties of the uniform nearly free-standing graphene layers obtained by intercalation of oxygen monolayer in the “strongly” bonded graphene/Ru(0001) interface. Spectroscopic data show that such graphene layer is heavily  Analysis of the electronic structure of graphene, which can be accessed in ARPES experiments, is performed via unfolding of the graphene-related bands to the primitive (1 × 1) Brillouine zone of graphene.In the present work we demonstrate the possibility to form the graphene/O/Ru(0001) intercalation system at the relatively low partial oxygen gas pressure and the elevated temperature for the complete initial graphene coverage on Ru(0001). The formed system of very high quality demonstrate the weak moiré structure as clearly deduced in scanning tunnelling and atomic force microscopy (STM and AFM) experiments. These experiments combined with the respective density functional theory (DFT) results allow to discriminate between geometric and electronic contributions in the microscopy imaging of this system. Our spectroscopy (STS) and DFT results show that a graphene layer in the graphene/O/Ru(0001) system is electronically decoupled from the substrate and demonstrates the π and Ru Crystallographic and electronic structures of graphene/Ru(0001) and graphene/O/Ru(0001) were compared in local STM/STS and AFM experiments. 20on-the-fly in the middle of the scan that allows to carefully trace the imaging contrast between two modes and its relation to the geometric and electronic contributions. In our STM experiments for the bias voltages in the range of ±1 V, graphene/Ru(0001) is always imaged in the Relatively large real space corrugation of 1.27 Å of graphene on Ru(0001)  makes AFM measurements with atomic resolution quite demanding. The results of such experiments are compiled in C places .−4 mbar of oxygen measured by the ion-gauge placed in the UHV chamber. Oxygen was introduced via a stainless steel pipe, which end was placed 1 mm from the sample surface that allows to increase the local pressure drastically (approximately by two orders of magnitude). This preparation procedure was initially also verified by the independent XPS measurements confirming our STM/AFM findings for the oxygen-intercalation system, graphene/O/Ru(0001).The oxygen intercalation was performed for the full graphene monolayer on Ru(0001) at 200 °C and a partial pressure of 1.8 × 10As can be found from the large scale STM image of graphene/O/Ru(0001) , oxygen s ≈20 pm  comparedDecoupling of graphene from the substrate and its nearly free-standing behaviour can be also concluded from the STM imaging of graphene/O/Ru(0001) around the step edges . One canIntercalated oxygen layer underneath graphene forms an ordered (2 × 1) structure on Ru(0001) as can be deduced from the Fast-Fourier-Transformation (FFT) image of the STM data shown in on-the-fly in the middle of the scan. Both parts of this panel demonstrate the atomic resolution. Panel (b) of this figure shows the AFM scan of gr/O/Ru(0001) and the respective height profiles extracted from the similar places of STM and AFM are shown in panel (c). The extracted atomic and mean moiré lattice corrugations extracted from the STM data are ≈30 pm and ≈10 pm, respectively. The same values extracted from AFM images are ≈6 pm and ≈4 pm, respectively.Similar to gr/Ru(0001) we also employ the combined STM/AFM measurements to the gr/O/Ru(0001) system. This allows to trace the true crystallographic structure of the system via discrimination between electronic and structural contributions in STM and AFM imaging. T = 150 °C in UHV conditions After STM/AFM studies of gr/O/Ru(0001) the same sample was transferred through air (maximum exposure time was 1 min) in the other experimental station for low temperature STM/STS studies. Due to the protection properties of graphene and its extreme inertness242526T = 1 K) STM/STS studies of the graphene/O/Ru(0001) system. Panel (a) presents combined topographic K points of the Brillouine zone (BZ) of graphene2829K and E relative to K point of the graphene BZ. [The possible deviation of the shape of the later features from the circle (see lower inset (FFT-ii) in the panel (b) might be due to the trigonal warping of the scattering vector map at higher binding energies with respect to p-doped.Series of the topographic EF)n-doping of graphene in gr/O/Ru(0001) with In order to verify this result the single ) system . Our valweak and strong interaction between graphene and Ru substrate with the minimal distance between C and Ru of 2.24 Å  of 2.10 Å) [covalent-like bonds at the graphene-Ru interface for the strongly interacting places of the structure. These results are in very good agreement with previous works323334In order to justify our experimental findings we perform analysis of these data within the framework of DFT .  2.10 Å) . The ori 2.10 Å) . This cap-doped systems.According to the previous13p-doping of graphene and formation of the localized dipole moment at the graphene-O-Ru interface.The side view of gr/0.5 ML-O-(2 × 1)/Ru(0001) is overlaid with the difference charge density , which sinterface states are formed in the energy range n-doped.The electronic structure of graphene (DOS) on Ru(0001) and on 0.5 ML-O-(2 × 1)/Ru(0001) is shown in   eV see . The dopσ and π states at the Γ and M points of BZ, respectively, and therefore their energy positions and intensities might be affected, for such big system , by the slight variation of the k-points sampling in BZ during integration.Oxygen intercalation (0.5 ML) in graphene/Ru(0001) leads to the almost complete recovering of the free-standing character of the graphene-derived electronic states. Comparing DOS for this system with the one for free-standing graphene, the position of Dirac point is strongly interacting system with the formation of several interface states at the K-point of BZ as a result of hybridisation between graphene and valence band states leading to the complete destruction of the Dirac cone. Thus, as it was already postulated in ref. weakly and strongly interacting regions within the graphene/Ru(0001) system, due to the metallic character of graphene in this system, the electronic structure of graphene in its original BZ is defined by the bonding strength and the electronic structure at the most perturbed graphene places. Upon the oxygen intercalation hybridisation between graphene and metal valence band states is absent (see π (as well as σ) branches are clearly recognisable in the electronic structure of graphene/0.5 ML-O-(2 × 1)/Ru(0001) [Similar conclusion regarding effective electronic decoupling of graphene from metal via oxygen intercalation can be made when comparing the results of band structure calculations performed for the studied systems . For grasent see . The maiRu(0001)  and theyIn order to prove our results we also perform simulations of STM images in the framework of the Tersoff-Hamann formalismstrongly interacting graphene layer from the Ru(0001) substrate via intercalation of an oxygen layer. The modifications of the crystallographic structure before and after intercalation are traced by the combined STM/AFM measurements. Strong variation of the imaging contrast is found in STM, reflecting the electronic structure of the system, whereas the corrugation obtained in AFM experiments is very close to the one deduced from DFT calculations. Decoupling of graphene via oxygen intercalation leads to the strong p-doping of a graphene layer with the Dirac point located at In our work we successfully decouple a Graphene/Ru(0001) system was prepared in ultrahigh vacuum system via cracking of ethylene: in situ via Ar+ -sputtering. In presented STM images the tunnelling bias voltage, The STM and AFM measurements were performed in constant current or constant frequency shift modes, respectively. In this case the topography of sample, et al.k-meshes for sampling the supercell Brillouin zone are chosen to be as dense as 6 × 6 and 3 × 3, respectively, and centred at the Γ-point. The STM images are calculated using the Tersoff-Hamann formalismThe DFT calculations were carried out using the projector augmented wave (PAW) methodHow to cite this article: Voloshina, E. et al. Restoring a nearly free-standing character of graphene on Ru(0001) by oxygen intercalation. Sci. Rep.6, 20285; doi: 10.1038/srep20285 (2016).


Moiré superlattices in graphene supported on various substrates have opened a new avenue to engineer graphene’s electronic properties. Yet, the exact crystallographic structure on which their band structure depends remains highly debated. In this scanning tunneling microscopy and density functional theory study, we have analysed graphene samples grown on multilayer graphene prepared onto SiC and on the close-packed surfaces of Re and Ir with ultra-high precision. We resolve small-angle twists and shears in graphene, and identify large unit cells comprising more than 1,000 carbon atoms and exhibiting non-trivial nanopatterns for moiré superlattices, which are commensurate to the graphene lattice. Finally, a general formalism applicable to any hexagonal moiré is presented to classify all reported structures. K and K′ corners of the Brillouin zone, giving rise to a linear energy dispersion of its quasiparticles close to the Fermi levelK and K′ points of the Brillouin zone are called Dirac cones.Graphene (gr) is a two-dimensional crystal with honeycomb structure, whose peculiar electronic properties have raised considerable interest in the past few years. Indeed, its electronic bands cross at the Such exotic electronic properties are predicted for pristine graphene, but are altered when graphene is supported by a substrate. Indeed, due to the structural mismatch between graphene and its support, graphene has periodically varying stacking configurations with its substrate45678101112131720212221222420252628Other surfaces interact more strongly with graphene, and are prone to exchange electrons with it, establishing partially covalent bonds. Graphene-substrate bonding then implies both van der Waals forces (physisorption) and partial covalent bonding (chemisorption), and is modulated along the moiré periodicity111230313436383541The usual structural model used to describe moirés assumes  top that47474951There are many ways the above assumption for commensurability can be fulfilled, as can be shown by considering strains and rotation of the graphene with respect to its substrate43Here we present the straightforward extension of Hermann’s formalism to the latter case. Besides, we derive the relationships that establish the consistency between this formalism, and another one, recently presented by Zeller and Günther to describe the number of beatings a moiré can compriseWe apply this description to resolve the structure of the moiré superlattices in graphene on multilayer graphene prepared on SiC, and in monolayer graphene on Re(0001) and Ir(111). For this purpose, we resort to scanning tunneling microscopy (STM) in both direct and reciprocal (Fourier) space, in the latter case achieving better than 0.1 pm precision on the lattice parameter determination, owing to distortion-less imaging with atomic resolution across several 10 nm fields of view. We find rotated and sheared moiré superlattices. Similarly to the rotation, shear appears more obviously in the moiré than in the graphene, as confirmed by our density functional theory (DFT) calculations. Some of these moirés comprise several moiré beatings in the case of metal substrates. Strikingly, commensurability between graphene and moiré superlattices provides a fine description of even very large moiré supercells, comprising above 1,000 carbon atoms.am is an integer number times graphene’s (agr) or the support’s (as) lattice parameters: am = i agr = m as, with i and m two coprime integers.In most cases, supported graphene and its substrate do not share the same lattice parameter and/or graphene lies twisted by some angle with respect to its support. Assuming commensurability between the two lattices, a supercell can be defined which comprises the smallest integer numbers of unit cells of both graphene and the support. This supercell defines the moiré superlattice. Formally, in a one-dimensional picture, the moiré superlattice parameter km), of graphene (kgr) and of the support (ks) hence fulfil i km = kgr and m km = ks. We stress that these two equations constitute the general definition of a moiré superlattice. On the contrary, the definition usually proposed in the literature, km = kgr − ks, does not require commensurability. It can be obtained in the particular case of a commensurate system, with i − m = 1, i.e. with i and m two consecutive integer numbers. This particular case is sketched in i − m = 2. Strikingly, at first sight the two moirés in i − m = 1 moiré  described as a i − m = 1 moiré. In fact it has a richer Fourier spectrum than the latter, as can be seen on i − m = 2 moiré is km = (kgr − ks)/(i − m) = (kgr − ks)/2, and not (kgr − ks) as is the case for the i − m = 1 moiré. The predominant intensity of the second harmonic (kgr − ks) translates nothing else than the close (but not exact) lattice coincidence observed at half the moiré period  space unit vectors of the moiré superlattice , uniaxial strain in a given direction εu (2 and 3), and a rotation (4) of the graphene layer. It can be noted that the so far overlooked shearing contribution is taken into account by combining a rotation, biaxial and uniaxial strains. The impact of such a combination on a moiré has only been predictedIn the most general case, graphene is twisted, strained and sheared with respect to its substrate. The combination of all these contributions can be separated into four elementary geometrical transformations represented on i, j, k, l, m, n, q, r), which are determined through atomically-resolved microscopy, is then necessary :On the other hand, one can equivalently describe the graphene-substrate relation by explicitly writing the commensurate relation defining the moiré superlattice. In order to account for its structural complexity in two dimensions, a set of eight integers :i, j, k, l, m, n, q, r) integers used here correspond to the decomposition of the superstructure lattice vectors i, j, k, l), and the supporting material lattice vectors , as sketched on The . The extended Wood’s notation reads as (p1Rφ1 × p2Rφ2). This notation gives the reader the ability to easily capture the graphene-substrate relation, and imagine how sheared it is by comparing p1 and p2, and φ1 and φ2. Once again, these quantities relate to the  integers, as explained in the P1RΦ1 × P2RΦ2), with:Although using a set of eight integers is efficient to describe a moiré superlattice, it is a relatively cumbersome notation that does not give an immediate picture of the structure. A clearer formulation of such sheared structures is then desirable. In the simple case of graphene experiencing only deformations preserving its pristine with i, j, k, l, m, n, q, r) integers is here discussed to justify this necessity.The geometrical formalism developed so far proves necessary to properly interpret the refined twist angles and shearings observed in atomically-resolved microscopy images. The experimental uncertainty on the identification of the  can be lowered by precisely determining 2. The latter effect translates into an uncertainty as low as km and kgr is ~1%. For , this precision translates through propagation of uncertainty into 2%.Quantitatively, the uncertainty on  is liable to put shears in evidence. At first thought, atomic resolution imaging can artificially produce sheared images. Such shears may result from imaging artefacts, for instance, in the case of scanning probe microscopy, thermal drift of the piezoelectric scanners or inequivalent calibration of these scanners along the two scan directions. However, these artefacts have no influence on the decomposition of The above described determination of . For a N = 1 moiré, First, the case of multilayer graphene on the C-rich  in  see . Here, ti, j, k, l, m, n, q, r) = . Using Equation (4a–d), such a structure can be analysed as two graphene layers sharing the same lattice parameter p1 = p2 = 1), and rotated by This commensurability relation gives a complete structural description, by decomposing the moiré lattice vectors in the basis of each graphene layer, using the set of integers  through a self-limiting processN = 1 moiré superlattice with 10 graphene cells on 9 Re cellsThe case of multilayer graphene on C-face SiC has shown a situation where a moiré superlattice is related to a single structural parameter: the twisting angle A direct analysis of the STM topograph along the same lines as for pz-like orbital of a C atom in atop position with the d-like orbitals of the underlying metal atom is then maximal. Consequently, the local electronic density of states is modified, making it appear low in STMFirst, depending on the position within the beatings, the apparent height accessed by STM shows a varying number of visible C: in a valley, only 3 atoms out of a 6-C ring are seen, whereas on a hill, all 6 are observed. This is due to the sites occupied by the C atoms on the terminal metallic layer, which fall into three typical configurations: a C on top of a metal atom (atop), or on top of a hollow site. Two kinds of hollow site can be distinguished, depending on the presence (hcp) or absence (fcc) of another metal atom of the second terminal metallic layer below the hollow site. In a valley, the sites occupied by the C atoms are either atop and hcp, or atop and fcc. The overlap of the Second, the apparent atomic rows of C oscillate with the same periodicity as the beatings. This phenomenon has been reported and discussed in the case of gr/Ru see ref. , and obs6364N = 1 moiré superlattice of gr/Re, comprising a sufficiently small number of atoms to be treated numerically. This moiré is characterized by the set  = . On Using DFT calculations, these two effects have been reproduced in the case of a sheared and twisted On N = 1 superlattice  = . As a signature of the anisotropy, the moiré cell contains a different number of beatings N1 = 1 and N2 = 2 in each of its main directions, as can be deduced from The corresponding set of integers therefore is (P1RΦ1 × P2RΦ2) extended Wood’s notation, with N = 1 superlattice, comprising 308 carbon atoms, as well as a sizeable shear. The corresponding shear of the graphene lattice is obvious in the corresponding extended Wood’s notation (p1Rφ1 × p2Rφ2). Using Equation (4a–d), one gets R0.73 × 0.886 R0.36). This structure is close but different from the previously reported assignment of a (7 × 7)R0, N = 1 moiré  in the case of gr/Re, graphene is biaxally compressed by e.g. in the case of gr/Ir. Similarly to gr/Re, the FFT-image of N > 1). In addition, the position of the graphene spots with respect to the moiré reciprocal lattice is not the same in each main direction, which means the structure is sheared. Actually, along the close-to-horizontal direction in reciprocal space  = , as interpreted in P1RΦ1 × P2RΦ2), with R0° structurep1Rφ1 × p2Rφ2), with This description of the superlattice can be summarized with . Shear and strain of such extents have already been reported beforeUsing Equation , this shearing translates into a combination of biaxial compression Using an extended Wood’s notation for a pictorial description using two scaling factors and two angles,In more physical terms with rotation angles, and uniaxial and biaxial strains,With eight integers that decompose independently the two moiré lattice vectors onto those of graphene and of its support.Three support lattices have been considered so far, revealing that a moiré structure can be rotated, strained and sheared. It also demonstrates that moiré superlattices comprising more than one beating are commonly encountered. Three equivalent ways have been presented to describe moiré superlattices with ease:N > 1 beatings superlattices, and of sheared superlattices, which both display specific properties. N > 1 beatings superlattices indeed exhibit inequivalent moiré hills12 cm−2 , hence with shifted Dirac conesi.e. by considering two sets of four integers,  and , which obey the same equations. Below, we introduce these equations in the case of  from The notation relying on eight integers enables to enumerate all the possible structures by combining every possible value for each integer. The system can also be treated by addressing two independent directions separately, as, one can express the moiré lattice constant am, the biaxial strain ε (assuming the lattice parameter of HOPG as a zero-strain situation), and the twist angle φ between graphene and its support  Rφ can be established straightforwardly , it is then possible to enumerate every possible structure. Using a limited set of parameters such as those defined by Nkm = kgr − ks. The representation of these curves is given by:With increasing values of (N the number of beatings given by N1 = N2.where N (see This series of parametrized curves highlights moiré superlattices with increasing numbers of beatings N see . The aboε = 2.51% (11), ε = −1.73% (19) and ε = 3.45% (20), and ε = −2.38% (21). Higher number of beatings are in fact probable for such structures. Such a high number of beatings was determined in the case of the so-called R30 phase of gr/Ir (see ref. μ-LEED) and STM study showed that within a moiré unit cell of ~3.02 nm lattice parameter, N = 37 beatings separated by ~0.47 nm occur N = 37 moiré is described with  =   =   = , ε = −0.02%  = , ε = −2.73% , even in growth conditions quite far from thermodynamic equilibrium. Presumably, the strong bonds of covalent character between carbon and metal atoms inside the growing flake are not readily broken, as would be required for twisting.Gr/Ir and gr/Pt are typical of the first situation. Numerous moiré phases have been reported for them, as shown on φ ~ 0° can be grown, as observed in STMμ-LEED61N = 4 (N1 = N2 = 2) superlattice  = ) using surface x-ray diffractionAlthough large-angle graphene twists are almost prohibited for gr/Re, slightly twisted graphene phases of gr/Re coexist. These numerous very similar structures can be assumed to be local minima in the energy landscape of gr/Re. Their coexistence then implies a high activation energy between each of them, so the formation of a large-scale uniform graphene phase is kinetically limited. In other words, graphene needs to be heated to high enough temperature to rearrange into the most stable phase of gr/Re. However, at high temperature, graphene growth competes with bulk dissolution and carbide formation, so the growth is performed by annealing cyclesi, j), such that  = . For instance,  =  in the present work, and  =  in ref. Graphene on C-face SiC grows with rotational disorder between the adjacent graphene layersN > 1 number of beatings will produce rich electronic modulations in graphene.In conclusion, different supported graphene systems have been studied with STM. A consistent analysis of moiré superlattices involving both direct and FFT STM images has been presented. The geometry of the superlattices, as apparent in STM images, has been rationalized by calculating electronic density maps derived from DFT calculations. A spatial precision of a tenth of 1 pm is achieved, revealing that graphene lying on a substrate is actually twisted, strained and sheared, which breaks its rotational symmetry. A geometrical model enables to classify all moiré superlattices. This model gives a global picture assuming commensurability between graphene and its substrate , yielding various numbers of beatings. While a very large number of structures is possible, only a few have actually been reported. In the case of strong graphene-substrate interaction, it is unlikely that all predicted superlattices are discovered, since for instance phases corresponding to a substantial rotation of graphene with respect to the substrate do not tend to form. For low interaction graphene-substrate systems, the complexity of the moiré superlattices has been undetected or overlooked, leading to possibly simplified interpretations. We anticipate that moiré superlattices with 2 pieces. The growth has been performed in a RF-furnace following the recipe in ref. 2 and Ar atmosphere at 1,560 °C, and subsequently annealed in Ar atmosphere at the same temperature.Graphene has been grown on undoped double-polished 4H-SiC−10 mbar) by cycles of Ar+ ion bombardment at 2 keV at 750 °C and subsequent annealing at ~1,300 °C. The gr/Re was prepared following the recipe presented in ref. 2H4 at room temperature (introduced with a 3 · 10−8 mbar pressure), and two subsequent cycles of flash-annealing/cooling at 750 °C with a 5 · 10−7 mbar C2H4 pressure.Re single crystal cut in the (0001) surface purchased from Surface Preparation Laboratory was cleaned in a ultrahigh vacuum (UHV) chamber  surface purchased from Surface Preparation Laboratory was cleaned in the same UHV chamber as for gr/Re, by cycles of ArFor multilayer gr/SiC, STM measurements were performed at 4 K in a home-made He-cooled STM, using a commercial Pt/Ir tip bought from Bruker. For gr/Re and gr/Ir, STM measurements were performed at room temperature under UHV, using a commercial Omicron UHV-STM 1, with a W chemically etched tip. Before analysing STM images, thermal drift and miscalibrations have been corrected.DFT calculations were performed using the VASP code, with the projector augmented wave (PAW) approach78How to cite this article: Artaud, A. et al. Universal classification of twisted, strained and sheared graphene moiré superlattices. Sci. Rep.6, 25670; doi: 10.1038/srep25670 (2016).


The inversion symmetry preserved antidot would then further split the πa (πz) bands into πa1 (πz1) and πa2 (πz2) bands with an energy interval Ed, which accounts for the bandgap opening in a kind of superlattices with Dirac cone being folded to Γ point. However, such antidot would not affect the semimetal nature of the other superlattices, showing a novel mechanism for bandstructure engineering as compared to the sublattice-equivalence breaking. For a superlattice with bandgap of ~Ed opened at Γ point, the Es could be increased by strengthening strain to close the bandgap, suggesting a reversible switch between the high velocity properties of massless Fermions attributed to the linear dispersion relation around Dirac cone and the high on/off ratio properties associated with the sizable bandgap. Moreover, the gap width actually could be continuously tuned by controlling the strain, showing attractive application potentials.Using the density functional theory with generalized gradient approximation, we have studied in detail the cooperative effects of degenerate perturbation and uniaxial strain on bandgap opening in graphene. The uniaxial strain could split π bands into π The linear energy dispersion relation around Dirac point brings us many unique and amazing properties, showing fascinating application potentials. The charge carriers, which could be tuned continuously between electrons and holes, have the group velocity as high as 106 m/s being close to that of light. Therefore, the graphene-based nanostructures are believed to be promising materials for next-generation high-performance nanoelectronic devices12356789101112131415161718Graphene consisting of hexagonally arranged carbon atoms has attracted tremendous research interests on both theory and experiment. Attributed to the etc. have been proved to be efficient for synthesizing graphene nanomesheset al. reported the nicely patterned graphene nanomesh fabricated by using the block copolymer lithographyet al. reported the CVD growth of large area smooth-edged graphene nanomesh by nanosphere lithographyet al. These progresses in fabricating advanced nanomaterials suggest the possibilities in preparing graphene nanomeshes in experiment with nice precision. In fact, this could be regarded as to pattern graphene into superlattice with carbon vacancies, which would modulate the corresponding Born-von Karman boundary conditions24252021222 surface2 surface folds the Dirac cone to Γ point. So, to shed light on the experimental studies, we have carried out detailed studies of hexagonal-antidot-patterned graphene superlattice in which the inversion symmetry remains. The novel mechanism differing with the sublattice-equivalence breaking for bandstructure engineering and the effects of uniaxial strain on electronic properties are carefully discussed. Most interesting, for a kind of graphene superlattices whose bandgaps are opened at Γ point, the gap width could be continuously tuned by applying uniaxial strain until it is closed. So, for such superlattices, one could reversibly switch between the massless Fermion properties attributed to the linear dispersion relation around Dirac cone and the high on/off ratio properties associated with the sizable bandgap.In the field of bandstructure engineering of graphene, an issue needs to be addressed. Along with the bandgap opening, the linear energy dispersion relationship around Dirac cone would be usually destroyed, which in turn would obviously reduce the charge carrier mobility. Usually, the wider bandgap opened in graphene to gain higher on/off ratio would lower the carrier mobility much more. Hence, it would be interesting if the bandgap could be switched on/off for a specific graphene-based nanomaterial toward different application demands. Interestingly, the advanced nanotechnologies have been successfully used in fabricating antidot-patterned graphene nanostructures–the graphene nanomeshes. The block copolymer lithography, nanoparticles local catalytic hydrogenation, nanosphere lithography, nanoimprint lithography, D6h high symmetry antidots in this paper for: (1) it could shed light on the circular mesh hole of the synthesized graphene nanomesh, and (2) it preserves the inversion symmetry. This kind of antidots in fact do not break the sublattice equivalence, which however could still open bandgap of some graphene superlattices, showing a novel mechanism for bandstructure engineering.The studied graphene superlattice is schematically illustrated in A × B periodic unit as shown in A and B are along the armchair and zigzag edges, respectively. The smallest rectangle unit cell defined by A1 = a + b and B1 = −a + b is illustrated in a × b primitive unit cell of graphene. As compared to the graphene studied with primitive unit cell, we would like to hereafter refer the pristine graphene studied with supercell A × B as pseudo graphene superlattice (PGS). If a perturbation such as an antidot was introduced in the A × B unit cell, the PGS would turn to be a real superlattice. In order to facilitate discussion, we would like to use the notation  to account for the lattice A × B with A = AP1 and B = BQ1. Therefore, the  stands for the smallest rectangle lattice A1 × B1. In h-BZ) and the rectangle one (r-BZ) corresponding to the primitive unit cell and the  PGS are shown, respectively. One can see that the K point in h-BZ would be folded to the T1r-BZ. The energy bandstructure of  PGS is presented in 1 point, confirming the above band-folding analysis. Based on our detailed analysis for the  PGSes with different P, we could conclude that the Dirac point would be always folded onto r-BZ. Interestingly, the Dirac point could be folded to Γ point when Q = 3m (m is an integer). In r-BZ is presented in h-BZ of primitive unit cell is equivalent to the Γ2 point in r-BZ of  lattice. The energy bandstructure shown in 2.Firstly, we start the discussion of electronic properties with the energy band-folding analysis. In this paper, the orthogonal superlattice with the P,Q) (Q = 3m) PGS by introducing an inversion symmetry preserved defect, such as the D6h hexagonal antidot, which does not coincide with the sublattice-equivalence breaking mechanism. For illustration, we have studied the electronic properties of , , and  superlattices. According to our energy band folding analysis, the ,  PGSes should have Dirac points at r-BZs while the  PGS should have Γ as Dirac point in its r-BZ. After introducing a C12 hexagonal antidot in the unit cell , their bandstructures are studied and shown in Aany × Bany, the lattice vectors could be expressed as Aany = N11a + N12b and Bany = N21a + N22b (a and b are the basis vectors of primitive unit cell of graphene). If the coefficients satisfy the conditions of 2N11 + N12 = 3m1 and 2N21 + N22 = 3m2 or N11 + 2N12 = 3m3 and N21 + 2N22 = 3m4 , the Dirac cone would be folded to Γ point and the introduced inversion symmetry preserved defect in the repeated unit cell would then open a bandgap in such superlattice.A bandgap can be opened in the  superlattice with Q = 3m could be closed by moving Dirac cone away Γ point ? Hence, in this subsection, we would like firstly to concentrate on discussing the effects of uniaxial strain on the Dirac cone move.In the above discussion, the hexagonal antidot acts differently on bandgap engineering of the free-standing graphene superlattice, which strongly depends on the position of the Dirac point. Only for the lattice with A1 lattice) and zigzag (B1 lattice) edges, respectively. In our studies, the Dirac cone was found to move along the 1 point in a applied along the armchair edge would move Dirac cone away T1 point with z along the zigzag edge would move it toward Γ point In D6h-defect-patterned superlattice, the  PGS lattice is adopt as a prototype example. As shown in a and σz are investigated in detail. Both of them could shift the Dirac cone away Γ. In z are illustrated. The band closing point at Γ is degenerate in z as shown in z and πa respectively. The charge densities of the πz and πa bands are plotted in z band accounts for the orbitals along zigzag edge while the πa is for the orbitals along armchair edge. This suggests that the Dirac point move could be attributed to the splitting between the energy degenerate bands πz and πa. Interesting it is that the density distributions of πa and πz bands show anisotropic characters. However, due to the fact that they would cross with each other at Fermi level in the neighborhood of Γ point, the anisotropic characters could not be observed in the conducting property studies. But, as to be discussed, the peculiar phenomena may be obtained in the strain engineered defect-patterned suplattice. For the  PGS without strain, the bond lengths of πz and πa bonds are exactly the same, which are around 1.425 Å. By applying the 5% σz strain along zigzag edge, the πz bond is elongated by ~3% while the πa bond remains almost unchanged. The tight binding (TB) method is well known in treating π bands of graphene, which could help to understand the physical origin of the electronic properties of graphene-based nanostructures. By considering only the nearest neighbor atoms, the related energy Enna could be obtained through28ti is the transfer integral, ki is the component of wavevector k, ai is the corresponding lattice constant, and z and πa orbitals at Fermi level make two separated Dirac points adjacent to Γ. In the spirit of the concept of pseudospin, two valleys with different chiralities of the corresponding electrons are located at K and K′ points in the h-BZ of primitive unit cell of graphene. In the pseudo superlattice , the valleys are folded onto Γ point in the corresponding r-BZ. The effects of the uniaxial strain are to split the degenerate valleys by shifting them away Γ in opposite directions, which would still keep them equivalent in energy with the apexes of corresponding Dirac cones being located at Fermi level.In order to investigate the effects of Dirac cone move on the bandgap opening of the D6h-antidot-patterned superlattice studied in this paper may be a potential candidate. In  (Q = 3m) PGS, the Dirac point would be folded to Γ point. Then, the high symmetry D6h antidot can open a bandgap in the corresponding graphene superlattice, which however could not change the semimetal nature of the other superlattices with Q≠3m (the Dirac point is not at Γ). Interestingly, by controlling strain, one can manipulate whether the Dirac point is located at Γ point or not of the  (Q = 3m) PGS, which suggests the possibilities in switching on/off bandgap of such superlattice.On a hand, due to the linear dispersion relationship around Dirac cone, the charge carriers gain high group velocity, which could also be tuned between the holes and electrons. On the other hand, the semimetal nature of graphene does not favor its usage as for high-performance nano-transistors, which requires high on/off ratio. In order to obtain high on/off ratio, a bandgap needs to be opened for the graphene-based nanostructure. However, along with the bandgap opening, the linear dispersion relation of graphene crystal would be destroyed also, which in turn harms the velocity properties of the charge carriers. So, it would be interesting to explore the possibilities in switching between the high velocity properties of massless Fermions and the high on/off ratio properties. The 6 hexagon  PGS, the introduced defect could open a bandgap at Γ point according to the discussion of the bandgap opening mechanism. Applying a strain σz of ~5%, we have then studied its electronic properties again. The corresponding bandstructure along Y′-Γ-Y path is shown in As to the  PGS, in order to facilitate discussion, we would like to first study the effects of a defect in the unit cell by contracting a Cz strain, where the strain makes the splitting between πz and πa orbitals, the D6h defect also induce band splitting. As shown in a1, πa2, πz1, and πz2, respectively, for which the corresponding band-decomposed charge densities are studied in D6h defect breaks the equivalence among πa (πz) orbitals, resulting in different bonding strengthes between πa1 (πz1) and πa2 (πz2) bonds. As compared to the corresponding C-C bonds of  PGS studied in 6 hexagon induces about 0.8% elongation of πa1 bonds and 0.6% contraction of πa2 bonds, respectively. As to the πz1 and πz2 bonds, the corresponding elongation and contraction are about 1.0% and 0.7%, respectively. In the spirit of the TB methoda2 and πz1 bands are lower in energy compared to the corresponding πa1 and πz2 bands, accounting for the splitting of πa and πz bands. Actually, the herein discussed splitting could also be understood by the intervalley scattering. The periodically arranged defects could be approximately treated as introducing a periodic potential Vd(r) to the pristine grephene. If the wavervectors of the opposite K and K ′ valleys differ with each other by a reciprocal lattice G, the intervalley scattering would induce band splitting. The energy interval Ed would be proportional to the integration K and K ′ pointsCompared to the electronic properties shown in a and πz bands and (2) the defect could break the equivalence among the armchair edge bonds (zigzag edge bonds) inducing the band splitting also. In fact, the competition between the band-split interval Es induced by the uniaxial strain and the Ed induced by the introduced defect dominates whether the bandgap could be switched on or off. Actually, we have also examined the free-standing defect-patterned  superlattice. The studied D6h defect also induces the band split Ed between πa1 (πz1) and πa2 (πz2) orbitals. For there is no strain applied to the lattice, the corresponding Es equals to zero. So, an obvious bandgap could be opened at Γ point. However, for the  superlattice studied in s is larger than the Ed, which makes the πa1 and πz1 to cross to form new Dirac cone.Now, one can see that (1) the strain along either armchair or zigzag edges could make the degenerate π bands to split into πD6h-antidot-patterned graphene superlattice by applying strain. In z = 0 in s increases as the strain σz enhances from 0% to 5%. As shown in 12 antidot patterned superlattice has been studied. Besides of the experimental fact of the successful fabrication of vacancy hole patterned graphene superlattice, we have performed the molecular dynamics simulations to evaluate the stability of the C12 patterned superlattice. We find that it can withstand the temperature of 1,500 K, implying that this superlattice structure is separated by high-energy barriers from other local minima on the potential energy surface. In this superlattice, the C12 antidot further splits the πa and πz orbitals, which brings the Ed ≈ 0.28 eV energy interval. For the studied  superlattice, the Ed remains almost the same as the applied strain increases. For the σz = 2% strain, the Es is smaller than the Ed. This still keeps the bandgap opening though the bandgap becomes narrower. An interesting point needs to be addressed. Now, the conduction band minimum (CBM) and the valence band maximum (VBM) consist of only πa- and πz-type bands, respectively, hinting the possibilities in obtaining anisotropic conducting properties. The electron and hole charge carriers may respectively transport along armchair and zigzag directions. However, for the case of the σz = 3% strain, the split energy interval Es gets larger than the Ed. The Dirac cone starts to form. For the condition with σz = 5% strain, the formation of the Dirac cone is obvious. So, for the energy interval Ed induced by the defect keeps almost constant, one could then switch on/off the bandgap by manipulating the energy interval Es through controlling uniaxial strain. This would be interesting for that the high velocity properties of massless Fermions attributed to the linear energy dispersion around Dirac cone and the high on/off ratio properties associated with the sizable bandgap could be switched with each other in the same material. For comparison, the superlattice patterned with (BN)6 flake (patching the C12-antidot hole with this nanoflake) has also been studied. For the graphene and BN sheet materials, the atoms are correspondingly hexagonally arranged in a plane to form the honeycomb structures. The calculated lattice constants of graphene and BN sheets are 2.47 and 2.51 Å, respectively. By using (BN)6 nanoflake to patch the vacancy hole in graphene, the local strain around the nanoflake should stand due to the lattice mismatch. Considering the fact that the ratio of the area of nanoflake against the one for the graphene is only around 0.04, the local strain would probably be released to some sense at the aid of the structural relaxation of graphene, which would help to stabilize the patched superlattice structure. In order to evaluate the structural stability, we have also carried out the MD simulations of the (BN)6 patched  superlattice, which suggest the stability at temperature of 1,500 K.In order to benefit experimental studies of patterning graphene nanomesh with circular antidots, we have also studied the bandgap on/off switching of the 12-antidot-patterned superlattice. The (BN)6 flake breaks the inversion symmetry by destroying the sublattice equivalence, opening ~0.13 eV bandgap. This bandgap seems unaffected in gap width by the uniaixal strain in our studies. Also, the deformed bandstructures induced by the uniaxial strain presented in 6 patched superlattice may have topological semiconducting properties due to the anticrossing bands shown in the neighborhood of Γ point, which are worthy of further investigations on both theory and experiment. As discussed the above, the uniaxial stretching strain would modify the electronic properties accordingly. Because of the linear dispersion relation around Dirac cone, the group velocity of massless Fermions could be estimated by the band energy gradient (k and E(k) are the wave vector and dispersion relation, respectively. For the fact that the mobilities of the charge carrier electrons and holes are almost same, we would like to concentrate on discussing their average values, with the purpose to illustrate the effects of strain. The average velocities of the PGSes studied in 5 m/s for the corresponding graphene superlattices under 0%, 2%, 3% and 5% strains, agreeing with the experimentally measured Fermi velocity of ~106 m/s for graphene228In 12-antidot-patterned  superlattice, the opened bandgap would be continuously reduced by enhancing strain, and the corresponding effective mass would be decreased also. According to the simple relationship μ) and effective mass (m) (τ is the scattering time of charge carrier)−13 s for scattering time, we have also estimated the carrier mobilities of the semiconducting superlattices to be ~103 cm2V−1s−1. Once the bandgap starts to close, the band energy dispersion would gain linear relationship again, resulting in high charge carrier mobility. For the case studied in z = 5% strain, the group velocity of the massless Fermions has been calculated to be ~6.12 × 105 m/s.In z and σa, the degeneracy between πa and πz bands would be removed, resulting in an energy interval Es to make the Dirac cone to move. The free-standing  (Q = 3m) PGS should have Dirac cone at Γ point according to the energy band folding analysis. Upon introducing a hexagonal antidot in the unit cell, the patterned superlattice would open a bandgap, showing a novel mechanism for bandstructure engineering as compared to the sublattice-equivalence breaking. In comparison with the defect-free PGS, the πa orbitals are split. The studied D6h defect has different effects on πa1- and πa2-type C-C bonds, making the former to contract and the latter to elongate. Similar effects are also observed for the πz-type C-C bonds. The energy interval between πa1 and πa2 energy bands and the value between πz1 and πz2 energy bands are same, which is referred as Ed. For the hexagonal-antidot-patterned  (Q = 3m) superlattice under uniaxial strain, the competition between Es and Ed dominates whether the bandgap remains open or not. For a given superlattice, the Ed keeps almost unchanged while the Es could be increased by enhancing the strain. Starting from the free-standing  (Q = 3m) superlattice, which has a bandgap opened by the energy split between πa1 (πz1) and πa2 (πz2) oribitals, the bandgap decreases along with the increase of the applied uniaxial strain until it closes. Upon this critical point, the energy bands πa1 and πz1 start to cross to form new Dirac cone. So, the electronic properties of  (Q = 3m) superlattice have been switched from the high on/off ratio properties to the high carrier velocity properties. Also, the transformation is reversible along with the strain releasing. Besides, the gap width could be continuously tuned by controlling strain, showing attractive application potentials.In conclusion, the possibilities, for switching between the high velocity properties of massless Fermions attributed to the linear dispersion relation around Dirac cone and the high on/off ratio properties associated with the sizable bandgap for a specific graphene superlattice, are carefully investigated. Upon applying uniaxial strain, such as the strains σab initio simulation package22pn with n = 1–3, respectively; for H, the configuration was 1sk-point sampling was performed with the Monkhorst-Pack techniquek-mesh. The structural parameters of the primitive unit cell of pristine graphene were firstly optimized, which were then used to construct superlattice. In our studies, the in plane lattices of the hexagonal primitive unit cell were calculated to be 2.466 Å, which is in good agreement with the previous datak-meshes of 7 × 9 × 1 and 3 × 5 × 1 were used for studying their electronic properties, respectively. Correspondingly, the charge densities and the local potentials were respectively calculated by using the 128 × 72 × 160 and 336 × 224 × 160 grid meshes. The convergence of the electronic properties was set to 10−5 eV. In the structural optimization, all the atoms were fully relaxed until the force acting on each atom converged to 0.01 eV/Å. As to the superlattice, we have also carefully checked the effects of antidot on lattice vectors of the repeated unit. The regularly arranged antidots in fact would not change the angle between lattice vectors, which would only affect the lattice constant. Thus, the symmetry of the superlattice could be preserved, which plays an important role in determining the position of Dirac cone in reciprocal space. For the superlattices simulated in our studies, the lattice constants were carefully optimized. As for testing the accuracy of the method, we also studied the lattice constant of diamond, which was calculated to be 3.571 Å in good agreement with the experimental value of 3.567 ÅWe have carried out spin-polarized first-principles calculations within the framework of density functional theory with a plane wave basis set as implemented in the Vienna How to cite this article: Jia, T.-T. et al. Dirac cone move and bandgap on/off switching of graphene superlattice. Sci. Rep. 6, 18869; doi: 10.1038/srep18869 (2016).


Directed self-assembly of block copolymers is a scalable method to fabricate well-ordered patterns over the wafer scale with feature sizes below the resolution of conventional lithography. Typically, lithographically-defined prepatterns with varying chemical contrast are used to rationally guide the assembly of block copolymers. The directed self-assembly to obtain accurate registration and alignment is largely influenced by the assembly kinetics. Furthermore, a considerably broad processing window is favored for industrial manufacturing. Using an atomically-thin layer of graphene on germanium, after two simple processing steps, we create a novel chemical pattern to direct the assembly of polystyrene-block-poly(methyl methacrylate). Faster assembly kinetics are observed on graphene/germanium chemical patterns than on conventional chemical patterns based on polymer mats and brushes. This new chemical pattern allows for assembly on a wide range of guiding periods and along designed 90° bending structures. We also achieve density multiplication by a factor of 10, greatly enhancing the pattern resolution. The rapid assembly kinetics, minimal topography, and broad processing window demonstrate the advantages of inorganic chemical patterns composed of hard surfaces. The self-assembly of block copolymers through microphase separation yields patterns with various morphologies and feature sizes ranging from 3 to 100 nm123467910111213b-PMMA) system20The Liu-Nealey (LiNe) flow is a paradigm of chemoepitaxy, as it seamlessly integrates with state-of-the-art 193 nm immersion lithography17Alternatively, if a material that wets PS or PMMA is patterned on a neutral surface, only lithography and plasma etching are needed to prepare the chemical contrast pattern. Here, monolayer graphene grown on a germanium wafer is proposed as an appealing template to perform directed self-assembly. Graphene has similar wetting behavior as an X-PS mat23282931In this work, we demonstrate that atomically-thin graphene stripe arrays can be used as chemical patterns for directed assembly of block copolymers, resulting in well-registered lamellae patterns with complex architectures. The graphene/germanium chemical patterns enable block copolymer assembly on templates with incommensurate periods and in 90° bending structures. Faster assembly dynamics are observed on graphene/germanium templates than on conventional patterns based on polymer mats and brushes. Density multiplication by a factor of 10 is also demonstrated, which means that the period of the assembled block copolymer is one-tenth the template periodicity. These results indicate that graphene/germanium chemical patterns enable robust, reproducible directed self-assembly of block copolymers.2  are used to ensure that the germanium surface is not etched and that the single-atom step height of the graphene stripes is preserved  (PMMA) mask over the continuous graphene monolayer films using electron-beam lithography . The expreserved . The sampe array  indicateb-PMMA is directed to assemble on the graphene/germanium chemical patterns via thermal annealing  of 78 nm. The graphene ribbon arrays are spin-coated with ~60 nm of PS-b-PMMA and the sample is annealed at 250 °C for 5–10 min in an inert N2 environment (O2 < 1 ppm and H2O < 1 ppm). b-PMMA assembles into lamellae that closely follow the underlying graphene chemical pattern and are not disrupted by the germanium terracing. In Ls, is chosen to be equivalent to L0 = 78 nm to ensure that the PS-b-PMMA assembles under optimum conditions.Finally, PS-nnealing . PS-b-PMb-PMMA on graphene/germanium templates and conventional chemical patterns based on X-PS (2) substrate. The graphene and X-PS films are patterned into similar line-space arrays with Ls = L0. The samples are spin-coated with PS-b-PMMA and annealed at 250 °C for 2–30 min to reach equilibrium. Directed assembly occurs more rapidly on the graphene-based chemical pattern than on the X-PS-based chemical pattern. Within 2 min, the block copolymer is largely ordered, following the underlying graphene template on >65% of the surface area . The line width of the graphene guiding stripes is chosen to be 1.5 L0 for n > 1 to clearly identify the underlying graphene stripes with SEM after directed assembly. The PS-b-PMMA is spin-coated onto the graphene ribbon array and the sample is annealed at 250 °C for 5–10 min to induce assembly. Despite the lack of guiding stripes for n periods of L0, the block copolymer segregates into regular domains between the graphene ribbons. On the wide graphene stripes, the PS and PMMA domains assemble into lamellae in which the bottom domains are nearly parallel to the surface, creating a U-shaped cross-section; this likely occurs because the PS preferentially wets the graphene surface when the width of a stripe is greater than L0, as previously reported on X-PS based chemical patternsb-PMMA is further characterized, below. Density multiplication by a factor of 10 is achieved using the graphene chemical pattern  film is determined to provide an indirect measurement of their surface affinity towards each of the domains in PS-b-PMMA. The water contact angle on a continuous monolayer graphene film (81°) is similar to that of the PS film (91°). Furthermore, the contact angle on a bare germanium surface after plasma treatment (72°) is similar to that of the PMMA film (68°). These results suggest that PS and PMMA preferentially wet the graphene and germanium regions, respectively, during assembly.Investigations of water contact angles and the wetting behavior of block copolymer filmsb-PMMA (molecular weight of 22k-b-22 k g mol−1) thin films with thicknesses of 1.5 L0, 1.75 L0 and 2.0 L0 are spin-coated onto continuous graphene films after growth on germanium, and onto bare germanium surfaces after being treated with an oxygen plasma to etch the graphene. The samples are annealed at 190 °C for 1 h to induce self-assembly and AFM is used to resolve the equilibrium morphology of the block copolymer films. At 190 °C, PS has lower surface energy than PMMA, so it is energetically favored to wet the free surface. Thus, from the morphology of the self-assembled films, the surface affinity of graphene and germanium toward each block copolymer domain can be determined.The wetting behavior of the block copolymer domains on graphene and germanium is further verified with a hole/island experimentb-PMMA films are shown in L0 and 1.75 L0 have featureless terraces with step heights of 1.0 L0, whereas films with thickness of 2.0 L0 are flat and featureless. These results are consistent with symmetric wetting of the PS-b-PMMA, as shown in the assembly schematics in L0, which is consistent with assembly on a nearly neutral surfaceL0 and 2.0 L0. The film is flat for the 1.5 L0 case, whereas the featureless regions are higher than the fingerprint regions for the 2.0 L0 case. As shown in the schematic of the assembled block copolymer domains in The morphologies of the assembled PS-0LS that deviates from L0The difference in surface energy between the graphene and the germanium likely provides the chemical contrast needed for directed assembly; the PS and PMMA preferentially wet the graphene and germanium regions, respectively. This chemical contrast also provides a favorable template for directed self-assembly with density multiplication, as both the PS and PMMA domains can wet the nearly neutral germanium substrate to form well-ordered patterns, despite the lack of guiding stripes every LThe above results were obtained using graphene guiding stripes that are grown directly on germanium. The direct synthesis of the graphene chemical pattern on a target substrate is desirable for wafer-scale assembly of block copolymers because (1) CVD is an inherently scalable process, yielding uniform continuous graphene films over large areas that are only limited in extent by the size of the substrate or the size of the reaction chamber422 is chosen as the target substrate because it is preferential to the PMMA domains over the PS domains, and thus provides suitable chemical contrast and surface energetics with respect to graphene to direct the assembly of PS-b-PMMA. After transfer onto SiO2, the continuous graphene films are patterned into guiding stripes using electron-beam lithography and reactive ion etching, as described above. The 85k-b-91k PS-b-PMMA is directed to assemble into aligned lamellae on the graphene guiding stripes on SiO2 wafers with Ls of 78 nm  by patterning the guiding stripes using extreme ultraviolet (EUV) lithography. After directed assembly, the PS-b-PMMA is well-ordered over the entire patterned region, demonstrating that our approach is compatible with state-of-the-art planar lithographic techniques used for high-throughput patterning  provide faster assembly kinetics, (2) enable assembly on patterns with high degree of incommensurability, (3) allow assembly on irregular and complex templates, and (4) provide density multiplication by a factor of 10, even for relatively high molecular weight block copolymers. In future work, chemical contrast may be alternatively patterned by exposing the sample to chemical or plasma treatment, by forming a self-assembled monolayer, or by depositing a second two-dimensional atomic layer . These graphene-based chemical patterns may enable the directed self-assembly of ultranarrow block copolymer domains for manufacturing of high resolution features, both in the semiconductor electronics industry and in high density magnetic media. This work also opens the door for directed assembly studies on chemical patterns based on the large library of two-dimensional materials.In conclusion, we demonstrate that an atomically-thin monolayer graphene/germanium chemical pattern can be easily prepared and successfully used to direct the assembly of PS-−5 torr. The chamber is filled to atmospheric pressure with a flow of 200 sccm of Ar (99.999%) and 100 sccm of H2 (99.999%). The samples are annealed for 30 min at 910 °C before introducing 4.6 sccm of CH4 (99.99%), which serves as the carbon precursor, to start the graphene synthesis. Growth occurs for 12 h to ensure complete graphene coverage on the germanium surface. The samples are rapidly cooled by sliding the furnace away from the growth region, which terminates growth.Ge(111)  and Ge(110) (University Wafer) substrates are used to catalyze graphene growth, as described previously42b-PMMA. The quality and thickness of graphene after growth and after patterning is assessed via Raman spectroscopy (Thermo Scientific DXRxi) using an excitation wavelength of 532 nm, power of 10 mW, and spot size of 0.6 μm. Contact angle measurements (Dataphysics OCA 15) are conducted using deionized water.AFM (Veeco MultiMode SPM) in tapping mode and SEM (Zeiss LEO 1530) are used to characterize the samples after graphene growth, after patterning of graphene into guiding stripes, and after directed assembly of PS-How to cite this article: Chang, T.-H. et al. Directed self-assembly of block copolymer films on atomically-thin graphene chemical patterns. Sci. Rep.6, 31407; doi: 10.1038/srep31407 (2016).