Recent photoemission spectra of the perovskite series Sr$_x$Ca$_{1-x}$VO$_3$
revealed strong modifications associated with surface contributions. To study
the effect of Coulomb correlations in the bulk and at the surface the
quasi-particle spectra are evaluated using the dynamical mean field theory. It
is shown that as a result of the reduced coordination number of surface atoms
correlation effects are stronger at the surface than in the bulk, in agreement
with experiment.Comment: 4 pages 3 figure

A. Fukushima

A. Liebsch

D. Vollhardt

E. Müller-Hartmann

J. Zaanen

K. Held

K. Maiti

Th. Pruschke

English

arXiv

Crossref

Surface versus Bulk Coulomb Correlations in Photoemission Spectra of
                    
                      
                        
                          S

Recent photoemission spectra of the perovskite series CaxSr1-xVO3 revealed strong modifications associated with surface contributions. To study the effect of Coulomb correlations in the bulk and at the surface, the quasiparticle spectra are evaluated using the dynamical mean field theory. It is shown that as a result of the reduced coordination number of surface atoms correlation effects are stronger at the surface than in the bulk, in agreement with experiment

Liebsch, A.

Juelich Shared Electronic Resources

P H Y S I C A L R E V I E W L E T T E R S week ending7 MARCH 2003VOLUME 90, NUMBER 9Surface versus Bulk Coulomb Correlations in Photoemission Spectra of SrVO3 and CaVO3A. LiebschInstitut fu¨r Festko¨rperforschung, Forschungszentrum Ju¨lich, 52425 Ju¨lich, Germany(Received 13 September 2002; published 3 March 2003)096401-1Recent photoemission spectra of the perovskite series CaxSr1xVO3 revealed strong modificationsassociated with surface contributions. To study the effect of Coulomb correlations in the bulk and at thesurface, the quasiparticle spectra are evaluated using the dynamical mean field theory. It is shown thatas a result of the reduced coordination number of surface atoms correlation effects are stronger at thesurface than in the bulk, in agreement with experiment.DOI: 10.1103/PhysRevLett.90.096401 PACS numbers: 71.20.Be, 71.27.+a, 79.60.BmAlthough the electronic properties of strongly correlatedmaterials are currently a field of intense experimental andface, the t2g degeneracy is lifted since only the dxy bandexhibits strong dispersion within the surface plane (the zPhotoemission is a key spectroscopy for the investiga-tion of electronic properties of strongly correlated mate-rials. Because of its surface sensitivity, there is growingconcern to what extent the data are representative of bulkproperties and whether they need to be corrected forsurface effects influencing the one- and many-electronproperties. For instance, earlier photoemission data onCaxSr1xVO3 [1,2] indicated that SrVO3 is a stronglycorrelated metal and that CaVO3 is close to a metal-insulator transition with very little spectral weight atthe Fermi level. In contrast, low-frequency bulk probesfound metallic behavior regardless of Ca concentration[3]. In view of the relative simplicity of these perovskites,this discrepancy is indeed astonishing. For this reasonCaVO3 has been intensively investigated [4].To identify surface contributions in photoemissionfrom CaxSr1xVO3, Maiti et al. [5] and Sekiyama etal. [6] performed measurements using a wide range ofphoton energies. As a result of the frequency dependentescape depth of the photoelectron, the spectra revealstriking variations evidently associated with surfacemodifications of the electronic structure: Emission fromthe coherent peak near the Fermi level is reduced andcorrelation-induced satellites have larger weight than inthe bulk. On the other hand, the bulk emission fromSrVO3 and CaVO3 was found to be remarkably similar,in agreement with low-frequency bulk measurements.Strong spectral changes with photon energy were alsoobserved on SrRuO3 [7] and CaxLa1xVO3 [8]. Mostlikely, these are caused by surface contributions [9].Another example is Sr2RuO4 for which earlier photo-emission data appeared to be in conflict with de Haas–van Alphen measurements [10]. Recent experimental andtheoretical work proved that this discrepancy can beresolved by accounting for the surface reconstruction ofSr2RuO4 which leads to significant changes in photoemis-sion spectra [11].The understanding of surface effects in photoemissionfrom transition metal oxides is clearly important in orderto distinguish them from bulk correlation phenomena.0031-9007=03=90(9)=096401(4)$20.00 theoretical investigation [12–14] surface effects havethus far received little attention [15]. In the presentwork, we use the dynamical mean field theory (DMFT)[13,16,17] to evaluate the surface and bulk quasiparticlespectra of SrVO3. We show that because of the planarelectronic structure of perovskite systems and the con-comitant narrowing of the surface local density of states,correlation effects at the surface are more pronouncedthan in the bulk. In the perovskites, this enhancement isparticularly strong since the local Coulomb energy is notfar from the critical value for a metal-insulator transition.Such a trend had been predicted by Potthoff and Nolting[15] who studied the metal–insulator phase diagram for asemi-infinite simple cubic s band at half filling. Here wecalculate the self-energy for a multiband system using arealistic local density of states appropriate for SrVO3 andfind qualitative agreement with photoemission [5,6]. Wealso comment on surface photoemission from CaVO3.Electronic structure calculations for SrVO3 within thelocal density approximation (LDA) [18] show that theconduction bands near EF consist of degenerate t2g bandsderived from V4 (3d1) ions. The filled O 2p bands areseparated from the t2g levels by a gap of about 1 eV, and thecubic crystal field of the V-O octahedron shifts the egbands above the t2g bands. The t2g bands can be repre-sented via a tight-binding Hamiltonian with diagonal ele-ments of the form hxy;xyk  ed  t0cx  cy  t1cxcyt2  t3cx  cy  t4cxcycz, where ci  2 coskia, i x; y; z, and a is the lattice constant. The ti denote effectivehopping integrals representing the V-O-V hybridization,where t0;2, t1;3, and t4 specify the interaction between first,second, and third neighbors, respectively. Off-diagonalelements which vanish at high-symmetry points are verysmall and will be neglected.Figure 1(a) shows the t2g bulk bands of SrVO3.According to the planar electronic structure, the bulkdensity of states b! exhibits the characteristic asym-metric peak related to the Van Hove singularity at the Xpoint [see Fig. 1(b)]. The overall shape of the bulk densityof states agrees with LDA calculations [18]. At the sur-2003 The American Physical Society 096401-1-6-4-2024-3 -2 -1 0 1 Self-energy  Σi(ω)  (eV) Energy (eV) Re Σi(ω)Im Σi(ω)FIG. 2. Second-order self-energy of SrVO3. Solid curves:bulk t2g self-energy; dashed (dotted) curves: dxz;yz (dxy) self-energy for surface layer. For clarity, the real part is shifteddown by 3 eV. The straight line gives ! k for k  0:5 eV.-1-0.500.511.5 Energy (eV)   Γ                  X                   M                   L                   Γ  (a)00.511.5-1 -0.5 0 0.5 1 1.5 Density of states  (1/eV) Energy (eV) (b)bulk  t2g , surface  dxy surface  dxz,yzFIG. 1. (a) Tight-binding fit to LDA t2g bulk bands of SrVO3(EF  0). (b) Solid curve: isotropic bulk density of states;dashed and dotted curves: local density of dxz;yz and dxy statesin the first layer of SrVO3.P H Y S I C A L R E V I E W L E T T E R S week ending7 MARCH 2003VOLUME 90, NUMBER 9axis defines the surface normal). To evaluate the surfacedensity of states, we use a Green’s function formalism[19] for semi-infinite tight-binding systems. The tight-binding parameters are assumed to coincide with those inthe bulk, except for a small surface potential to ensurecharge neutrality.Figure 1(b) shows the local density of states s! ofthe dxz;yz bands for the surface layer of SrVO3. Its weightis reduced at low and high energies but enhanced atintermediate energies. Thus, the effective width ofs! is smaller than that of b! although their totalwidths are identical. The density of dxy states nearlycoincides with b!, reflecting the planar nature of t2gstates. It would be desirable to perform electronic struc-ture calculations for SrVO3 surfaces since they shouldprovide a more accurate density of states. Nevertheless,the key effect discussed here, i.e., the narrowing of thelocal density of dxz;yz states, should hold quite generally.To interpret the experimental photoemission data, weevaluate the quasiparticle spectra by accounting for localCoulomb correlations. According to the one-electronproperties discussed above, we are dealing with a non-isotropic system where two narrow bands interact with awider band. This situation is reminiscent of the layerperovskite Sr2RuO4, which essentially consists of Rusheets containing two narrow dxz;yz bands interactingwith a wide intraplanar dxy band. The peculiar featureof this system is the fact the on-site Coulomb energy lies096401-2between the single-particle widths of the nondegeneratet2g bands: Wxz;yz < U <Wxy [20]. In the present case, thedifference between dxz;yz and dxy bands at the surface isless pronounced so that Wi < U for all three bands.Nevertheless, since in the first layer the effective widthof dxz;yz states is reduced, the influence of Coulomb cor-relations on the surface bands should be stronger than onthe wider bulk bands.The key quantity characterizing the effect of Coulombcorrelations is the complex self-energy. Since we neglectthe weak hybridization between t2g bands, ! is diago-nal in orbital space. Despite this simplification, a fulldescription of correlations near the surface would be ex-ceedingly complicated since, in principle, it would re-quire a mixed momentum/real space approach in order tohandle the loss of translational symmetry normal to thesurface. This could be accomplished using a cluster for-malism where the semi-infinite system is representedvia a slab of finite thickness. Unfortunately, the planarcharacter of t2g orbitals leads to a slowly convergentlocal density of dxz;yz states, with many spurious 1=!pVan Hove singularities stemming from the quasi-one-dimensional hopping parallel to the surface. On the otherhand, a cluster generalization of the DMFT is feasibletoday only for very small cluster size. We therefore ignorethe momentum variation of the self-energy and assumethat, for a given layer, it depends only on the local densityof states within that layer. Additional coupling of thequantum impurity problems represented by the layers isprobably small [15] and is neglected for computationalreasons. The reduced dimensionality at the surface there-fore enters the many-body calculation via the layer-dependent density of states. In view of the localCoulomb interaction, this assumption seems justified forqualitative purposes.Before discussing the quasiparticle spectra derivedwithin the DMFT, it is useful to compare the frequencydependence of the self-energy in the bulk and at the096401-200.20.40.6-3 -2 -1 0 1 2 3 4Nb (ω)  (1/eV)Energy  (eV)(a)  bulk t2g00.20.40.6-3 -2 -1 0 1 2 3 4Ns (ω)  (1/eV)Energy  (eV)(b)  surface dxz,yz00.20.40.6-3 -2 -1 0 1 2 3 4Ns (ω)  (1/eV)Energy  (eV)(c)  surface dxyFIG. 3. Quasiparticle density of states of SrVO3 derivedfrom DMFT. (a) Bulk t2g states, (b) surface dxz;yz states, and(c) surface dxy states. Solid curves: U  4:3 eV; dot-dashedcurves: U  4:0 eV; dashed curves: bare densities as in Fig. 1.P H Y S I C A L R E V I E W L E T T E R S week ending7 MARCH 2003VOLUME 90, NUMBER 9surface. For convenience, we give here the results ob-tained within non-self-consistent second-order perturba-tion theory since this provides a clear identification of thevarious orbital contributions to the diagonal elementsi! [20]. Figure 2 illustrates the second-order self-energy for U  4:3 eV and J  0:7 eV. The effectiveband narrowing at the surface yields a narrower distribu-tion of Imxz;yz! compared to Imb! for the iso-tropic bulk. Because of the orbital mixing via the on-siteCoulomb interaction Imxy! lies between these twodistributions. From the Kramers-Kronig relations, it thenfollows that Rexz;yz! exhibits a more pronouncedminimum below the band bottom than Reb!. Thus,as indicated by the line ! k for a typical band energyk, the surface satellite appears at a lower value of U thanin the bulk. This qualitative picture is fully supported bythe more accurate DMFT results discussed below.In the DMFT, the self-energy elements i! are func-tionals of the bath Green’s functions G1i  G1i i.On-site Coulomb correlations are treated using the self-consistent multiband Quantum Monte Carlo (QMC)method (for a review, see Ref. [13]). The temperature ofthe simulation is 125 meV with 64 imaginary time slicesand several runs using 105 Monte Carlo sweeps. Thequasiparticle density of states is obtained via maximumentropy reconstruction [21].Figure 3(a) shows the bulk quasiparticle spectrum ofSrVO3 for two Coulomb energies in the critical region forthe formation of incoherent Hubbard bands which areseen as satellites in the photoemission spectra [5,6]. Theexchange energy is J  0:7 eV [22]. These results showthat U must be larger than 4 eV to obtain the satellite. Thepeak near 2 eV above EF corresponds to the upper Hub-bard band and agrees with inverse photoemission data [2].Although for U  4 eV there is considerable correlation-induced band narrowing and an emerging satelliteshoulder, a larger U yields an even narrower coherentfeature near EF, with the missing weight shifted to thelower and upper Hubbard bands. Note that NbEF bEF which follows from the local approximation im-plicit in the DMFT for isotropic systems [23]. The mostrecent photoemission data [6] confirm this result.The surface quasiparticle spectra for SrVO3 are shownin Figs. 3(b) and 3(c). The lower Hubbard peak of thedxz;yz states is clearly visible already for U  4 eV be-cause of the narrower local density of states in the firstlayer. A larger U shifts the satellite to higher bindingenergies. The comparison with the spectra shown inFig. 3(a) demonstrates that correlation effects for a fixedvalue of U are stronger at the surface than in the bulk:The coherent peak near EF is narrower at the surface andthe incoherent satellite feature is more pronounced than inthe bulk, in agreement with experiment [5,6].The surface quasiparticle density of dxy states inFig. 3(c) is intermediate between Nb! and Ns! fordxz;yz. Although there is little single-electron hybridiza-096401-3tion between t2g bands, the local Coulomb interactionmixes them so that the dxy surface spectrum involves con-tributions arising from the more strongly correlated dxz;yzstates. Another consequence of the anisotropic surfaceself-energy is the correlation-induced charge transferbetween subbands [20]. Here, we find that 0.06 elec-trons are shifted from the dxy to the dxz;yz bands. Thecoupling between narrow and wide bands is a genuinemultiband effect and underlines the fact that single-particle bands in the presence of local Coulomb interac-tions cannot be considered independently.Note that the many-body reduction of the quasiparticleband width is much larger than the surface-induced one-electron band narrowing. On the other hand, since the on-site Coulomb energy is not far from the critical value for ametal-insulator transition, the band narrowing substan-tially enhances the influence of correlations at the surface.096401-3P H Y S I C A L R E V I E W L E T T E R S week ending7 MARCH 2003VOLUME 90, NUMBER 9It would be interesting to perform angle-resolved pho-toemission measurements to determine the correlation-induced band narrowing of the SrVO3 t2g bands. Forinstance, the energy at  should be only a few tenths ofan eV below EF instead of 1 eV as predicted by the LDA.Accordingly, the true t2g bands should be considerablyflatter than the single-particle bands. Also, measurementsusing polarized light could help to separate correlationeffects in the dxy and dxz;yz bands.We finally comment on the difference between CaVO3and SrVO3. According to bulk LDA calculations forCaRuO3 [24], orthorhombic distortions cause a slightnarrowing of the t2g bands and a broadening of the VanHove singularity above EF. The same trend is foundin CaVO3 [25]. Assuming the same on-site Coulombenergy for the V4 ions in CaVO3 and SrVO3, this effectimplies a weak transfer of spectral weight from thecoherent to the incoherent peak, in agreement with therecent photoemission data [5,6] and DMFT calculations[25]. At the surface, however, such a shift of spectralweight should be more pronounced because of the bandnarrowing discussed above, in particular, since U=W israther large. This effect is indeed observed in the photo-emission spectra [5,6]. For a more detailed analysis, itwould be important to carry out electronic structurecalculations for CaVO3 surfaces to investigate ortho-rhombic distortions and possible reconstructions. Thelatter presumably would reduce hopping also within thedxy band, thereby enhancing surface correlations. Also,studies of incomplete screening of U at surfaces wouldbe useful.In summary, we have performed DMFT quasiparticlecalculations for SrVO3 in the bulk and at the surface. As aresult of the planar nature of the t2g states and the surfacenarrowing of the local density of states on-site correlationeffects are more pronounced at the surface than in thebulk, in agreement with photoemission data. The two-dimensional character of d states near EF is one of thehallmarks of transition metal oxides. The surface-induced enhancement of correlation effects discussed inthe present work should therefore be a phenomenon ob-servable in many materials.I thank A. Bringer for useful discussions and A. I.Lichtenstein for the QMC-DMFT code. I also thankS. Biermann for comments and for bringing Ref. [6] tomy attention.Note added.—After completion of this work, analo-gous QMC-DMFT calculations were reported for bulkSrVO3 and CaVO3 [25], demonstrating the similarity ofthese isoelectronic perovskite materials.096401-4[1] A. Fujimori et al., Phys. Rev. Lett. 69, 1796 (1992).[2] K. Morikawa et al., Phys. Rev. B 52, 13 711 (1995); I. H.Inoue et al., Phys. Rev. Lett. 74, 2539 (1995).[3] M. Onada, H. Ohta, and H. Nagasawa, Solid StateCommun. 79, 281 (1991).[4] A. Fukushima et al., J. Phys. Soc. Jpn. 63, 409 (1994);N. Shirakawa et al., J. Phys. Soc. Jpn. 64, 4824 (1995);I. H. Inoue et al., Phys. Rev. Lett. 88, 236403 (2002).[5] K. Maiti, D. D. Sarma, M. J. Rozenberg, I. H. Inoue,H. Makino, O. Goto, M. Pedio, and R. Cimino,Europhys. Lett. 55, 246 (2001).[6] A. Sekiyama, H. Fujiwara, S. Imada, H. Eisaki, S. I.Uchida, K. Takegahara, H. Harima, Y. Saitoh, andS. Suga, cond-mat/0206471.[7] K. Fujioka et al., Phys. Rev. B 56, 6380 (1997).[8] K. Maiti and D. D. Sarma, Phys. Rev. B 61, 2525 (2000);K. Maiti, P. Mahadevan, and D. D. Sarma, Phys. Rev.Lett. 80, 2885 (1998).[9] A. Liebsch (to be published).[10] A. P. Mackenzie et al., Phys. Rev. Lett. 78, 2271 (1997);T. Yokoya et al., Phys. Rev. Lett. 78, 2272 (1997), andreferences herein.[11] K. M. Shen et al., Phys. Rev. B 64, 180502(R) (2001);A. Liebsch, Phys. Rev. Lett. 87, 239701 (2001);R. Matzdorf et al., Science 289, 746 (2000); Phys.Rev. B 65, 085404 (2002).[12] M. Imada, A. Fujimori, and Y. Tokura, Rev. Mod. Phys.70, 1039 (1998).[13] A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg,Rev. Mod. Phys. 68, 13 (1996).[14] K. Held et al., in Quantum Simulations of ComplexMany-Body Systems: From Theory to Algorithms, editedby J. Grotendorst, D. Marks, and A. Muramatsu, NICSeries (John von Neumann Institute for Computing,Julich, Germany, 2002), Vol. 10, p. 175.[15] M. Potthoff and W. Nolting, Phys. Rev. B 60, 7834(1999); Z. Phys. B 104, 265 (1997).[16] D. Vollhardt, in Correlated Electron Systems, edited byV. J. Emery (World Scientific, Singapore, 1993).[17] Th. Pruschke, M. Jarrell, and J. K. Freericks, Adv. Phys.44, 187 (1995).[18] K. Takegahara, J. Electron Spectrosc. Relat. Phenom. 66,303 (1994).[19] D. Kalkstein and P. Soven, Surf. Sci. 26, 85 (1971).[20] A. Liebsch and A. Lichtenstein, Phys. Rev. Lett. 84, 1591(2001).[21] M. Jarrell and J. E. Gubernatis, Phys. Rep. 269, 133(1996).[22] J. Zaanen and G. A. Sawatzky, J. Solid State Chem. 88, 8(1990); T. Mizokawa and A. Fujimori, Phys. Rev. B 54,5368 (1996).[23] E. Mu¨ller-Hartmann, Z. Phys. 74, 507 (1989).[24] I. I. Mazin and D. J. Singh, Phys. Rev. B 56, 2556 (1997).[25] I. A. Nekrasov et al., cond-mat/0211508.096401-4

Surface versus Bulk Coulomb Correlations in photoemission spectra of SrVO3 and CaVO3

Surface vs. bulk Coulomb correlations in photoemission spectra of
  perovskites

Surface vs. bulk Coulomb correlations in photoemission spectra of perovskites

Abstract

Similar works

Full text

Available Versions

Crossref

Juelich Shared Electronic Resources