Anisotropic quasiparticle renormalization in Na0.73CoO2: role of
  inter-orbital interactions and magnetic correlations
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Anisotropic quasiparticle renormalization in Na0.73CoO2: role of
inter-orbital interactions and magnetic correlations
J. Geck1,2,∗, S.V. Borisenko1, H. Berger3, H. Eschrig1, J. Fink1, M. Knupfer1,
K. Koepernik1, A. Koitzsch1, A.A. Kordyuk1,4, V.B. Zabolotnyy1, and B. Büchner1
1IFW Dresden, P.O. Box 270116,D-01171 Dresden, Germany
2Department of Physics and Astronomy,
University of British Columbia, Vancouver, BC, V6T 1Z1, Canada
3Institut de physique de la matiére complex,
EPF Lausannne, 1015 Lausanne, Switzerland and
4Institute of Metal Physics of the National Academy
of Sciences of Ukraine, 03142 Kyiv, Ukraine
(Dated: Received: November 8, 2018)
Abstract
We report an angular resolved photoemission study of NaxCoO2 with x≃0.73 where it is found
that the renormalization of the quasiparticle dispersion changes dramatically upon a rotation from
ΓM to ΓK. The comparison of the experimental data to the calculated band structure reveals that
the quasiparticle renormalization is most pronounced along the ΓK-direction, while it is significantly
weaker along the ΓM-direction. We discuss the observed anisotropy in terms of multiorbital effects
and point out the relevance of magnetic correlations for the band structure of NaxCoO2 with
x ≃ 0.75.
PACS numbers: 71.27.+a, 71.18.+y,74.25.Jb,74.70.-b
∗ Email: geck@physics.ubc.ca
http://arxiv.org/abs/0704.1048v2
The unconventional behavior of correlated electrons in materials comprised of square lat-
tices has attracted a vast amount of attention [1, 2]. However, besides strong electronic
correlations, the topology of the underlying lattice structure itself constitutes another im-
portant ingredient that can produce exotic electronic ground states.
The CoO2-layers in the NaxCoO2 materials, which are built up from edge-sharing CoO6
octahedra, constitute a realization of a correlated electron system based on a triangular
lattice. More specifically, these compounds possess a layered hexagonal structure, where
strongly covalent CoO2- and ionic Na-layers (ab-planes) alternate along the perpendicular
c-axis [3]. Upon changing the Na content x, these materials can be doped with electrons and,
in addition, water molecules can be intercalated. Both changing x and water intercalation
drastically alter the electronic properties of NaxCoO2, leading most notably to the emergence
of superconductivity upon hydration [4, 5]. We will focus on the non-hydrated compounds
with x ≃ 0.7, where an anomalous metallic state with an extremely large and field dependent
thermoelectric power as well as a giant field dependent scattering rate was observed [6, 7].
There is also evidence for the seemingly paradoxical coexistence of electron itinerancy and
localized magnetic moments, as well as for unusual charge order CDW phenomena in these
macroscopically metallic compounds [8, 9, 10].
The unconventional electronic properties described above strongly motivate the study
of the electronic structure of NaxCoO2 by means of angular resolved photoemission spec-
troscopy (ARPES), which provides direct and unique experimental access to single-particle
excitations and, thus, to the many-body effects in these materials. Previous ARPES stud-
ies on NaxCoO2 [12, 13, 14, 15, 16, 17] showed pronounced deviations from the electronic
structure predicted by LDA calculations [11]. In addition, a strongly renormalized heavy
QP band, displaying a kink feature was reported [13, 14, 15].
In this ARPES study we focus on the momentum (k) dependent renormalization effects
in Na0.73CoO2, which is essential to unravel the relevant couplings that govern the low
energy physics. ARPES experiments were carried out using a lab-based system equipped
with a SCIENTA SES 200 analyser and a Gammadata He discharge lamp at an excitation
energy hν = 21.2 eV (energy resolution 30meV, angular resolution 0.3◦). The high-quality
Na0.73CoO2 single crystals examined in this study were grown by the sodium chloride flux
methods as described in Ref. [18].
A typical Fermi level (EF ) crossing observed at T=25K is shown in Fig. 1, where the
image on the left hand side shows the photoelectron intensity as a function of momentum k
and binding energy EB. A single and well defined QP band, which crosses the Fermi energy
at EB = 0 eV can be observed. On the right hand side of Fig. 1 an energy distribution
curve (EDC) and a momentum distribution curve (MDC) are shown. By mapping the EF
crossings over a large area of k-space, a cut through the Fermi surface (FS) of Na0.73CoO2
parallel to the CoO2 planes was measured. The data allows for a precise calibration of the
k-scale, because dispersions from the first into the second Brillouin zone were captured.
In Figs. 2 (a),(b) the k-dependent photoelectron intensity for two fixed binding energies of
EB = 0 eV and 0.132 eV are shown. Focussing on the cut at EB = 0 eV in Fig. 2 (a), a large
hole-pocket centered around the Brillouin zone center Γ is observed. The FS displays a clear
hexagonal topology. The intensity variations along the FS, leading to a seemingly lower
symmetry, are caused by matrix element effects. The size of the observed FS agrees well
with the doping level, provided that only one of the two a1g-bands (cf. Fig. 2 (c)) crosses
EF . This agrees with the data shown in Fig. 1, where a single QP-band crosses EF .
In accordance with previous studies, the hole-pockets along ΓK are not observed for
EB = 0 eV. It can be seen in Fig. 2 (b) that the corresponding e
g-band (cf. Fig. 2 (c)) lies
well below EF , as reported earlier [15]. This can also be observed in Fig. 2 (c), where the
measured band structure along ΓK and ΓM is compared to the band structure obtained by
LDA [11]. There is a fair agreement of the ARPES data and LDA at higher binding energies
above 1.5 eV. However, close to EF deviations occur which are particularly pronounced along
In Fig. 3 two cuts of the data set shown in Fig. 2 along the ΓK- (left) and ΓM-direction
(right) are shown. Focussing on the cut along ΓK, two prominent features can be observed.
First, there is a band crossing EF that forms the FS. Second, there is another band at higher
binding energies, which can be identified as the e′g-band. The data indicates that the top of
the e′g-band is at about 85meV.
By tracking the maximum of the MDCs for different EB, the QP-dispersion (E(k)) in-
dicated by black symbols is obtained. Close to EF the dispersion can be well described by
a linear behavior, yielding the Fermi velocity vF = (0.3 ± 0.05) eV Å along ΓK. However,
at slightly higher EB, the measured dispersion is bent and thus deviates from the linear
behavior close to EF . We define the energy where this deviation becomes significant as Ed,
resulting in Ed = (26 ± 8)meV for the ΓK-direction. The second bend in the dispersion
around 80meV is related to the crossing of the two bands [17]. Applying the same analysis
to the cut along ΓM leads to vF = (0.6± 0.08) eV Å and Ed = (66 ± 5)meV. Clearly, both
vF and Ed depend on the direction in k-space.
The observed bending of the dispersion that sets in around Ed could be due to a coupling
of the QP to bosonic excitations. In fact, consistent with this interpretation, we observe an
enhanced increase of the scattering rate around Ed. It has to be noted, however, that the
feature in the dispersion observed here is not as well defined as the kink in the cuprates,
for example. This means that the values of Ed cannot be identified straightforwardly with
a specific mode energy and, moreover, a coupling to several different bosonic excitations is
possible.
In the following we will focus on vF , which is a well defined quantity: Cuts for different
ψ-values (cf. Fig. 1 (b)) were systematically analyzed in the same way as described above.
The obtained variation of vF as determined from the ARPES data is shown in Fig. 4 (a).
Upon rotating the direction of the cut from ΓM to ΓK, vF decreases by about a factor of 2.
Using the function kF (ψ) that was determined from the data in Fig. 2 (a) together with the
obtained values of vF , the variation of the effective mass m
∗ with ψ can be calculated. The
result is given in Fig. 4 (c). Remarkably, the QP along the ΓK direction is about twice as
heavy as the QP along ΓM. This pronounced anisotropy of m∗ is expected to have a strong
impact on the in-plane electronic properties of Na0.73CoO2.
To determine the renormalization effects in Na0.73CoO2, we use the LDA band structure
as a reference and compare the ARPES Fermi velocities (vPESF ) to the corresponding LDA
values (vLDAF ). As it can be observed in Figs. 4 (a),(b), these two quantities show exactly
the opposite behavior: vPESF decreases and v
F increases upon rotation from ΓM to ΓK.
In order to check whether the deviation between ARPES and LDA is related to a lattice
distortion at the surface, LDA calculations were performed for structures where the distance
between the oxygen and the cobalt layers, i.e. the Co–O–Co bond angle, was changed. In
agreement with previous calculations, we observe that the top of the e′g band is shifted to
higher binding energies upon increasing the Co–O–Co bond angle. At the same time the
anisotropy of vLDAF is slightly reduced, but unchanged qualitatively. This strongly suggests
that the measured anisotropy of vPESF is not caused by a lattice distortion at the surface.
The comparison of LDA and ARPES therefore shows that the deviation of the LDA band-
structure from the measured QP-dispersion increases dramatically close to the ΓK-direction
(cf. inset of Fig. 3). In the following we will refer to this deviation as QP-renormalization
(QPR). This QPR can be characterized using a constant κ defined by (1+ κ) vPESF = v
The ψ- or, in other words, k-dependence of κ is shown in Fig. 4 (d), revealing the strong
anisotropy of the QPR in Na0.73CoO2. We note that, although the photoelectron intensity
in Fig. 2 (a) at kF is also influenced by matrix element effects, it is always significantly lower
in the ΓK- than in the ΓM-direction, in agreement with enhanced renormalization effects
along ΓK.
We find ∂kE
≃ ∂kE
LDA/2 along ΓK in the whole energy range up to EB = 85meV
(inset of Fig. 3). At the same time it is remarkable that the QPR gets stronger the closer
the so-called e′g-band gets to the Fermi level (c.f. Fig.2 (b)). This points to an effect related
to coupling between the a1g- and the e
g-bands. In fact, a strong interaction between these
bands is manifested by a large hybridization gap at higher binding energies and the polar-
ization dependence along ΓK found in a recent ARPES study [17]. Hence, the k-dependent
QPR at EF is most likely caused by multiorbital effects, i.e. interactions between the states
of e′g and a1g symmetry. In this case, the QP-states along ΓM and ΓK display different prop-
erties: Along ΓM the QP-states have largely a1g symmetry, while they display pronounced
multiorbital properties along ΓK. This is of crucial importance for the many-body effects
in these materials, since the coupling of the QP to bosonic excitations depends critically on
the symmetry of the QP-states [21]. To conclude so far, the observed anisotropies clearly
indicate that multiorbital effects play an important role for the QP-dynamics at EF .
Furthermore, our DFT studies –details will be provided in a forthcoming publication–
show that magnetic correlations play an important role for the QP-dynamics as well: Accord-
ing to non-magnetic LDA calculations the band structure of Na0.75CoO2 displays a strong 3D
character. In agreement with a previous DFT study [22], we obtain a sizeable kz-dispersion
parallel to the c-axis that leads to additional caps of the FS as shown in Figs. 5 (a),(b). Such
a strong 3D character is not in agreement with ARPES data: (i) in general, the QP peaks
at EF are expected to be considerably broadened in a 3D system, in particular because the
short life time of the final states becomes important [19]. This is not the case (Fig. 1). (ii)
ARPES measurements at various excitation energies do not show any evidence for a strong
dispersion along c [17].
However, magnetic LSDA calculations yield an AFM ground state, where ferromagnetic
ab-planes are coupled antiferromagnetically along c. This agrees well with neutron data [23].
In the AFM state, the kz-dispersion is strongly reduced, which removes the aforementioned
FS-caps and yields the FS shown in Fig. 5 (c). In other words, according to LSDA, 3D
AFM correlations render the electronic structure of Na0.75CoO2 effectively 2D. The top of
the e′g-band at EB ≃ 70meV as well as the topology and size of the FS obtained in LSDA
are in good agreement with the ARPES data as demonstrated in 5 (d). The above results
together with the neutron data indicate that AFM correlations have a strong influence on
the electronic structure of NaxCoO2 with x ≃ 0.75.
In conclusion, we have shown that the QPR in Na0.73CoO2 is strongly anisotropic and
provided clear evidence for the relevance of multiorbital effects for the QP dynamics in this
material. In addition, detailed DFT studies highlight the impact of magnetic correlations on
the QP-states near EF , which is expected to be directly related to the unusual temperature
as well as the field dependencies of the thermopower and the QP scattering rates [6, 7, 14].
Hence, both the interactions between the a1g and e
g states as well as magnetic correlations
have to be taken into account in order to obtain a realistic description of these materials.
Acknowledgements: We thank Dr. Bussy (Univ. of Lausanne) for the micro probe
analysis and I. Elfimov, K.M. Shen, D.G. Hawthorn and G.A. Sawatzky for helpful discus-
sions. This work was supported by the Swiss NCCR research pool MaNEP of the Swiss NSF,
the DFG (FOR 538 research unit, Grant 51195121) and the BMBF (Grant 05KS4OD2/8).
J.G. gratefully acknowledges the support by the DFG.
Figure captions
FIG. 1: Left: Typical Fermi level crossing observed along a cut close to ΓM (ψ =
173◦, cf. Fig. 2 (b)) Right: Corresponding energy distribution curve (EDC) and momentum
distribution curve (MDC) at k = kF and EB = 0 eV, respectively.
FIG. 2: ARPES data for Na0.73CoO2 (excitation energy hν = 21.2 eV). (a), (b): Momen-
tum distribution maps of the photoelectron intensity integrated over a small energy interval
(EB ± 3meV) at EB = 0 eV and 0.132 eV measured at T=25K. The measured k-region is
indicated by the black dotted line in (a). The other regions in k-space have be obtained by
rotating this data set by 120◦ and 240◦. The broken white lines show the two-dimensional
Brillouin zone. High-symmetry points Γ, K, and M are indicated in (a) and the definition
of ψ is given in (b). A fit to kF = kF (ψ) is shown as a solid black line. (c): Comparison
of the measured band structure and the LDA calculation by Singh (black lines) [11]. The
crystal field split e′g- and a1g-manifolds are indicated.
FIG. 3: Cuts through the map data shown in Fig. 2 (a) and (b). The data is normalized to
binding energies above 0.25 eV. Black symbols: QP-dispersion determined by fitting MDCs
at different EB. Broken lines indicate the fitted linear dispersions (see text). The inset
shows the ARPES- (symbols) and LDA- (lines) dispersions as a function of k−kF (ψ). LDA
for x = 0.73 in the rigid band approximation (cf. Fig. 4).
FIG. 4: (a),(b): vPESF and v
F as a function of ψ. The experimental v
F values at a
given value of ψ were obtained by averaging over two equivalent cuts (e.g. ψ = 150◦, 210◦).
The LDA calculations were performed in the rigid band approximation for the low temper-
ature lattice structure using Wien2K. The same behavior was also found by LDA/LSDA
calculations in the virtual crystal approximation (cf. Fig. 5). (c): Effective mass of the QP.
(a)-(c): hν = 21.2 eV. Solid curves are fits to a sinus-function intended to serve as guides to
the eye. (d): κ = vLDAF /v
F − 1 characterizing the QPR.
FIG. 5: FS obtained for x = 0.75 by LDA in the virtual crystal approximation (VCA),
revealing a three-dimensional band structure. (c): FS for the AFM ground state obtained
by LSDA in the VCA where the band structure retains its pronounced two-dimensionality.
The color scale in (a)-(c) indicates vF . (d) Comparison of the measured and LSDA FS. The
DFT calculations have been performed using the FPLO code [20].
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	References
