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Comparative study of correlation effects in CaVO3 and SrVO3

I.A. Nekrasov,1, 2 G. Keller,2 D.E. Kondakov,1, 2, 3 A.V. Kozhevnikov,1, 2, 3

Th. Pruschke∗,2 K. Held,4 D. Vollhardt,2 and V.I. Anisimov1, 2

1Institute of Metal Physics, Russian Academy of Sciences-Ural Division,

620219 Yekaterinburg GSP-170, Russia

2Theoretical Physics III, Center for Electronic Correlations and Magnetism,

University of Augsburg, 86135 Augsburg, Germany

3Department of Theoretical Physics and Applied Mathematics,

USTU, 620002 Yekaterinburg Mira 19, Russia

4Max Planck Institute for Solid State Research,

Heisenbergstr. 1, 70569 Stuttgart, Germany

Abstract

We present parameter-free LDA+DMFT (local density approximation + dynamical mean field

theory) results for the many-body spectra of cubic SrVO3 and orthorhombic CaVO3. Both systems

are found to be strongly correlated metals, but not on the verge of a metal-insulator transition.

In spite of the considerably smaller V-O-V bond angle in CaVO3 the LDA+DMFT spectra of the

two systems for energies E < EF are very similar, their quasiparticle parts being almost identical.

The calculated spectrum for E > EF shows more pronounced, albeit still small, differences. This is

in contrast to earlier theoretical and experimental conclusions, but in good agreement with recent

bulk-sensitive photoemission and x-ray absorption experiments.

PACS numbers: 71.27.+a, 71.30.+h

1

I. INTRODUCTION

Transition metal oxides are an ideal laboratory for the study of electronic correlations in

solids. In these materials, the 3d bands are comparatively narrow with width W ≈ 2−3 eV

so that electronic correlations, induced by the local Coulomb interaction U ≈ 3 − 5 eV,

are strong. For U/W ≪ 1, we have a weakly correlated metal and the local density

approximation (LDA) (see [1] for a review) works. In the opposite limit U/W ≫ 1 and for an

integer number of 3d electrons, we have a Mott insulator with two separate Hubbard bands as

described by Hubbard’s I and III approximations [2] or the LDA+U method [3]. Transition

metals are, however, in the “in-between” regime, U/W = O(1), where the metallic phase is

strongly correlated with coexisting quasiparticle peak at the Fermi level and Hubbard side

bands.

Dynamical mean-field theory (DMFT) [4, 5, 6, 7, 8], a modern, non-perturbative many-

body approach, is able to capture the physics in the whole range of parameters from

U/W ≪ 1 to U/W ≫ 1 for model Hamiltonians, like the one-band Hubbard model (for an

introduction into DMFT and its applications see [8]). And, with the recent merger [9, 10, 11]

of LDA and DMFT, we are now able to handle this kind of correlation physics within realistic

calculations for transition metal oxides.

A particularly simple transition metal oxide system is Ca1−xSrxVO3 with a 3d1 electronic

configuration and a cubic perovskite lattice structure, which is ideal for SrVO3 and or-

thorhombically distorted upon increasing the Ca-doping x. Fujimori et al. [12] initiated the

present interest in this 3d1 series, reporting a pronounced lower Hubbard band in the pho-

toemission spectra (PES) which cannot be explained by conventional LDA. Subsequently,

thermodynamic properties were studied, and the Sommerfeld coefficient, resistivity, and

paramagnetic susceptibility were found to be essentially independent of x [13].

On the other hand, PES [14], seemed to imply dramatic differences between CaVO3 and

SrVO3, with CaVO3 having (almost) no spectral weight at the Fermi energy. Rozenberg et

al. [15] interpreted these results in terms of the (DMFT) Mott-Hubbard transition in the

half-filled single-band Hubbard model. With the same theoretical ansatz, albeit different

parameters, the optical conductivity [16] and the PES experiments [17] for different dopings

x were reproduced.

The puzzling discrepancy between these spectroscopic and the thermodynamic measure-

2

ments, suggesting a Mott-Hubbard metal-insulator transition or not, were resolved recently

by bulk-sensitive PES obtained by Maiti et al. [17] and Sekiyama et al. [18, 19]. In the lat-

ter work it was shown that (i) the technique of preparing the sample surface (which should

preferably be done by fracturing) is very important, and that (ii) the energy of the X-ray

beam should be large enough to increase the photoelectron escape depth to achieve bulk-

sensitivity. Theoretically, pronounced differences between SrVO3 surface and bulk spectra

were reported by Liebsch [20]. Besides bulk-sensitivity, the beam should provide a high in-

strumental resolution (about 100 meV in [18, 19]). With these experimental improvements,

the PES of SrVO3 and CaVO3 were found to be almost identical [17, 18, 19], implying consis-

tency of spectroscopic and thermodynamic results at last. This is also in accord with earlier

1s x-ray absorption spectra (XAS) by Inoue et al. [21] which differ only slightly above the

Fermi energy, as well as with BIS data [14]. Parameterfree LDA+DMFT results by us [22],

reported in the joint experimental and theoretical Letter by Sekiyama et al. [19], showed

good agreement with the high-resolution bulk-sensitive PES. Independent LDA+DMFT cal-

culations for 3d1 vanadates, including SrVO3 and CaVO3 have been reported by Pavarini et

al. [23]. Most recently Anisimov et al. employed a full-orbital computational scheme based

on Wannier functions formalism for LDA+DMFT to calculate total densities of states for

SrVO3 which are in good agreement with new PES data. [24]

In this paper we present details of our LDA+DMFT calculation [22] which could not be

included in the joint Letter [19]. In particular, we discuss the crystal structure of SrVO3

and CaVO3, explain the origin of the surprisingly small change in bandwidth of these two

systems, and compare the calculated spectrum for energies E > EF with XAS data [21]. We

start with discussing the structural differences between SrVO3 and CaVO3 in Section IIA,

based on the most recent crystallographic data provided by Inoue [26]. How these differences

reflect in the LDA results is shown in Section IIB, before we turn to the LDA+DMFT

scheme in Sections IIIA and the effects of electronic correlations in Section IIIB. Section IV

concludes our presentation.

3

II. SRVO3 VS. CAVO3: STRUCTURAL DIFFERENCES AND LDA RESULTS

A. Structural differences

Both SrVO3 and CaVO3 are perovskites, with SrVO3 in the ideal cubic structure

Pm3m [27] (Fig. 1) and CaVO3 in the orthorhombicaly distorted (GdFeO3) Pbnm struc-

ture [26, 28] (Fig. 2). The ideal cubic structure of SrVO3 implies that the VO6 octahedra,

the main structural elements of the crystal, are not distorted: The V-Obasal and V-Oapex

distances are the same, the Oapex-V-Obasal and Obasal-V-Obasal angles are 90◦, and the V-O-V

bond angles are exactly 180◦. The substitution of the large Sr2+ ions by smaller Ca2+ ions

leads to a tilting, rotation, and distortion of the VO6 octahedra. Nonetheless, in CaVO3,

both the V-Obasal and the V-Oapex distances are practically the same. Therefore, the most

important feature of the distortion is the change of the V-Obasal-V and V-Oapex-V angles,

which determines the strength of the effective V3d-V3d hybridization and, hence, the band-

width. Due to the rotation and tilting of the octahedra both angles (one of them is marked

as ∠123 in Figs. 1 and 2) have the same value θ = 180◦ for SrVO3 and θbasal ≈ 161◦,

θplane ≈ 163◦for CaVO3.

B. LDA results

The valence states of SrVO3 and CaVO3 consist of completely occupied oxygen 2p bands

and partially occupied V 3d bands. Since the V ion has a formal oxidation of 4+, there is

one electron per V ion occupying the d-states (configuration d1). In Figs. 3 and 4 the LDA

density of states (DOS) are presented for both compounds, as calculated by the linearized

muffin-tin orbitals method (LMTO) [29] with an orthogonal basis set of Sr(5s, 5p, 4d, 4f),

Ca(4s, 4p, 3d), V(4s, 4p, 3d), and O(3s, 2p, 3d) orbitals [30]. These results are in agreement

with previous LDA calculations in the basis of augmented plane waves (APW) by Tagekahara

[31]. For a combination of the LDA band structure with many-body techniques [9] however,

the atomic-like LMTO wave functions employed here are particularly convenient. As is

apparent from Figs. 3 and 4, the O-2p states lie between -7.5eV and -2.0eV in SrVO3 and

between -6.5eV and -1.5eV in CaVO3. The 3d states of V are located between -1.1eV and

6.5eV in SrVO3 and between -1.0eV and 6.5eV in CaVO3. These results are in agreement

with previous LDA calculations in the basis of augmented plane waves (APW) by Tagekahara

4

[31], but for our purposes LMTO is more appropriate.

In both compounds, the V ions are in a octahedral coordination of oxygen ions. The

octahedral crystal field splits the V-3d states into three t2g orbitals and two eg orbitals. In

the cubic symmetry of SrVO3, hybridization between t2g and eg states is forbidden, and

the orbitals within both subbands are degenerate. In contrast, the distorted orthorhombic

structure of CaVO3 allows them to mix and the degeneracy is lifted. In the lower part of

Figs. 3 and 4, we present these t2g and eg subbands of the V-3d band. For both Sr and

Ca compounds, the reader can see an admixture of these Vanadium t2g and eg states to

the oxygen 2p states in the energy region [-8 eV,-2 eV]. This is due to hybridization and

amounts to 12% and 15% of the total t2g weight for SrVO3 and CaVO3, respectively. The

main t2g (eg) weight lies in the energy region [-1.1 eV,1.5 eV] ([0.0 eV,6.5 eV]) in SrVO3 and

[-1.0 eV,1.5 eV] ([0.2 eV,6.5 eV]) in CaVO3. Since the energy difference between the centers

of gravities of the t2g and eg subbands is comparable with the bandwidth, t2g and eg states

can be considered as sufficiently separated in both compounds.

Let us now concentrate on the t2g orbitals crossing the Fermi energy and compare the

LDA t2g DOS of SrVO3 and CaVO3. Most importantly, the one-electron t2g LDA bandwidth

of CaVO3, defined as the energy interval where the t2g DOS in Figs. 3 and 4 is non-zero, is

found to be only 4% smaller than that of SrVO3 (WCaVO3= 2.5 eV, WSrVO3

= 2.6 eV); in

general agreement with other LDA calculations [23]. This is in contrast to the expectation

that the strong lattice distortion with a decrease of the V-O-V bond angle from 180◦ to 162◦

affects the t2g bandwidth much more strongly. Such a larger effect indeed occurs in the eg

bands for which the bandwidth is reduced by 10%. To physically understand the smallness

of the narrowing of the t2g bands we have investigated a larger Hamiltonian consisting of eg,

t2g, and oxygen p orbitals. We calculated the overall direct d−d and the indirect d−p−d hopping

for this larger Hamiltonian. The predominant contribution to the eg-eg hopping is through

a d−p−d hybridization, which is considerably decreasing with the lattice distortion. This is

also the case for the t2g orbitals. However, for the t2g orbitals, the direct d−d hybridization

is also important. This hybridization increases with the distortion since the t2g orbital lobes

point more directly towards each other in the distorted structure. Hopping parameters for

individual orbitals change rather substantially from SrVO3 to CaVO3. But, altogether, a

decreasing d−p−d hybridization and an increasing d−d hybridization results in a very small

change of the t2g bandwidth.

5

III. CORRELATION EFFECTS IN SRVO3 AND CAVO3

A. Dynamical Mean-Field Theory

As is well-known, LDA does not treat the effects of strong local Coulomb correlations ad-

equately. To overcome this drawback, we use LDA+DMFT as a non-perturbative approach

to study strongly correlated systems [9, 10, 11]. It combines the strength of the LDA in

describing weakly correlated electrons in the s- and p-orbitals, with the DMFT treatment

of the dynamics due to local Coulomb interactions. In the present paper we will discuss the

relevant parts of the LDA+DMFT approach only briefly, refering the reader to Ref. [10, 11]

for details.

The LDA+DMFT Hamiltonian can be written as

H = H0LDA + U

∑m

∑i

nim↑nim↓ +∑

i m6=m′ σσ′

(U ′− δσσ′J) nimσnim′σ′ . (1)

Here, the index i enumerates the V sites, m the individual t2g orbitals and σ the spin. H0LDA

is the one-particle Hamiltonian generated from the LDA band structure with an averaged

Coulomb interaction subtracted to account for double counting [9]; U and U ′ denote the

local intra-orbital and inter-orbital Coulomb repulsions, and J is the exchange interaction.

We calculated these interaction strengths by means of the constrained LDA method [32]

for SrVO3, allowing the eg states to participate in screening [33]. The resulting value of

the averaged Coulomb interaction is U = 3.55 eV (U = U ′ for t2g orbitals [10, 34]) and

J = 1.0 eV. The intra-orbital Coulomb repulsion U is then fixed by rotational invariance to

U = U ′ +2J = 5.55 eV. We did not calculate U for CaVO3 because the standard procedure

to calculate the Coulomb interaction parameter between two t2g electrons, screened by eg

states, is not applicable for the distorted crystal structure where the eg and t2g orbitals are

not separated by symmetry. On the other hand, it is well-known that the change of the

local Coulomb interaction is typically much smaller than the change in the DOS, which was

found to depend only very weakly on the bond angle. That means that U for CaVO3 should

be nearly the same as for SrVO3. Therefore we used U = 3.55 eV and J = 1.0 eV for

both SrVO3 and CaVO3. This is also in agreement with previous calculations of vanadium

systems [33] and experiments [16].

DMFT maps the lattice problem Eq. (1) onto a self-consistent auxiliary impurity prob-

lem, which is here solved numerically by the quantum Monte-Carlo (QMC) technique [35].

6

Combined with the maximum entropy method [36], this technique allows us to calculate

spectral functions [37, 38, 39, 40].

A computationally important simplification is due to the fact that, in ideal cubic per-

ovskites, the (degenerate) t2g states do not mix with the (degenerate) eg states. In this

particular case, the self-energy matrix Σ(z) is diagonal with respect to the orbital indices.

Under this condition, the Green functions Gm(z) of the lattice problem can be expressed in

the DMFT self-consistency equation by the Hilbert transform of the non-interacting DOS

N(0)m (ω):

Gm(z) =

∫dǫ

N0m(ǫ)

z − Σm(z)− ǫ. (2)

This procedure avoids the rather cumbersome and problematic k-integration over the Bril-

louin zone by the analytical tetrahedron method [41]. We obtain N(0)m (ǫ) for SrVO3 and

CaVO3 from the t2g-projected DOS of Figs. 3 and 4 by truncating the contribution in the

oxygen range below -1.5 eV and multiplying by a renormalization factor (to have maximally

one electron per site and orbital). This procedure is employed as it resembles the three

effective bands of t2g character which cross the Fermi energy and are, hence, responsible for

the low-energy physics.

B. LDA+DMFT(QMC) results and discussion

The calculated LDA+DMFT(QMC) spectra for SrVO3 (right panel) and CaVO3 (left

panel) are presented in Fig. 5 for different temperatures. Due to genuine correlation effects,

a lower Hubbard band at about −1.5 eV and an upper Hubbard band at about 2.5 eV is

formed, with a well pronounced quasiparticle peak at the Fermi energy. The 4% difference

in the LDA bandwidth between SrVO3 and CaVO3 is only reflected in some additional

transfer of spectral weight from the quasiparticle peak to the Hubbard bands, and minor

differences in the positions of the Hubbard bands. Clearly, the two systems are not on the

verge of a Mott-Hubbard metal-insulator transition. Both, SrVO3 and CaVO3, are strongly

correlated metals, though SrVO3 is slightly less correlated than CaVO3 with somewhat more

quasiparticle weight, in accord with their different LDA bandwidth. As one can see from

Fig. 5, the effect of temperature on the spectrum is small for T . 700 K.

In the left panel of Fig. 6, we compare our LDA+DMFT spectra (300K), which were mul-

tiplied with the Fermi function at the experimental temperature (20K) and Gauss broadened

7

with the experimental resolution of 0.1 eV [18] with the experimental PES data obtained by

subtracting the experimentally estimated surface and oxygen contributions. Due to the high

photon energy (several hundred eV) [18], the PES transition matrix elements will have no

strong energy dependence in the energy interval of a few eV studied here, which justifyies

that we do not take such matrix elements into account.

The quasiparticle peaks in theory and experiment are seen to be in very good agreement.

In particular, their heights and widths are almost identical for both SrVO3 and CaVO3.

The difference in the positions of the lower Hubbard bands may be partly due to (i) the

subtraction of the (estimated) oxygen contribution which might also remove some 3d spectral

weight below −2 eV, and (ii) uncertainties in the ab-initio calculation of U .

Since inverse photoemission spectroscopy (IPES) data for SrVO3 and CaVO3 are not yet

available we compare [44] the calculated spectrum for energies E > EF with XAS data by

Inoue et al. [21] (right panel of Fig. 6). We consider core-hole life time effects by Lorentz

broadening the spectrum with 0.2 eV [42], multiply with the inverse Fermi function (80K),

and apply Gauss broadening given by the experimental resolution of 0.36 eV [26]. Again, the

overall agreement of the weights and positions of the quasiparticle and upper t2g Hubbard

band is good, including the tendencies when going from SrVO3 to CaVO3. For CaVO3

(Ca0.9Sr0.1VO3 in the experiment), the LDA+DMFT quasiparticle weight is somewhat lower

than in experiment.

In contrast to one-band Hubbard model calculations, our material specific results repro-

duce the strong asymmetry around the Fermi energy w.r.t. weights and bandwidths. Our

results also give a different interpretation of the XAS than in [21] where the maximum at

about 2.5 eV was attributed solely to the eg band. We find that also the t2g upper Hubbard

band contributes in this energy range.

The slight differences in the quasiparticle peaks (see Fig. 5) lead to different effective

masses, namely m∗/m0 = 2.1 for SrVO3 and m∗/m0 = 2.4 for CaVO3. These theoretical

values agree with m∗/m0 = 2 − 3 for SrVO3 and CaVO3 as obtained from de Haas-van

Alphen experiments and thermodynamics [13, 43]. We note that the effective mass of CaVO3

obtained from optical experiments is somewhat larger, i.e., m∗/m0=3.9 [16].

8

IV. CONCLUSION

In summary, we investigated the spectral properties of the correlated 3d1 systems SrVO3

and CaVO3 within the LDA+DMFT(QMC) approach. Constrained LDA was used to de-

termine the average Coulomb interaction as U = 3.55 eV and the exchange coupling as

J=1.0 eV. With this input we calculated the spectra of the two systems in a parameter-free

way. Both systems are found to be strongly correlated metals, with a transfer of the ma-

jority of the spectral weight from the quasiparticle peak to the incoherent upper and lower

Hubbard bands. The calculated DMFT spectra of SrVO3 and CaVO3, and in particular the

quasiparticle parts, are found to be very similar, differences being slightly more pronounced

at energies above the Fermi energy. Our calculated spectra agree very well with recent

bulk-sensitive high-resolution PES [18] and XAS [21] data, i.e., with the experimental spec-

trum below and above the Fermi energy. Both compounds are similarly strongly correlated

metals; CaVO3 is not on the verge of a Mott-Hubbard transition.

Our results are in contrast to previous theories and the expectation that the strong

lattice distortion leads to a strong narrowing of the CaVO3 bandwidth and, hence, to much

stronger correlation effects in CaVO3. While the eg bands indeed narrow considerably, the

competition between decreasing d−p−d and increasing d−d hybridization leads to a rather

insignificant narrowing of the t2g bands at the Fermi energy. This explains why the k-

integrated spectral functions of CaVO3 and SrVO3 are so similar. With our theoretical

results confirming the new PES and XAS experiments, we conclude that the insulating-like

behavior observed in earlier PES and BIS experiments on CaVO3 must be attributed to

surface effects [20].

V. ACKNOWLEDGMENTS

This work was supported by Russian Basic Research Foundation grant RFFI-GFEN-

03-02-39024 a (VA,IN,DK), RFFI-04-02-16096 (VA,IN,DK) and the Deutsche Forschungs-

gemeinschaft through Sonderforschungsbereich 484 (DV,GK,IN) and in part by the joint

UrO-SO project N22 (VA,IN), the Emmy-Noether program (KH), by Grant of President

of Russian Federation for young scientists MK-95.2003.02 (IN), Dynasty Foundation and

International Center for Fundamental Physics in Moscow program for young scientists 2004

9

(IN), Russian Science Support Foundation program for young PhD of Russian Academy of

Science 2004 (IN).

∗New permanent address: Institut fur Theoretische Physik, Universitat Gottingen,

Friedrich-Hund-Platz 1, D-37077 Gottingen, Germany.

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[37] A. Liebsch and A. Lichtenstein, Phys. Rev. Lett. 84, 1591 (2000).

[38] I. A. Nekrasov, K. Held, N. Blumer, A. I. Poteryaev, V. I. Anisimov, and D. Vollhardt, Euro.

Phys. J. B 18, 55 (2000).

[39] K. Held, G. Keller, V. Eyert, V. I. Anisimov, and D. Vollhardt, Phys. Rev. Lett. 86, 5345

(2001).

[40] I.A. Nekrasov, Z.V. Pchelkina, G. Keller, Th. Pruschke, K. Held, A. Krimmel, D. Vollhardt,

and V.I. Anisimov, Phys. Rev. B 67, 085111 (2003).

[41] Ph. Lambin and J. P. Vigneron, Phys. Rev. B 29, 3430 (1984).

[42] M. O. Krause and J. H. Oliver, J. Phys. Chem Ref. Data 8, 329 (1979).

[43] I. H. Inoue, C. Bergemann, I. Hase, and S. R. Julian, Phys. Rev. Lett. 88, 236403 (2002).

[44] It should be noted that the XAS measurements were taken at the Oxygen K-edge. Hence there

is no symmetry breaking of the Vanadium 2p shell in the final state. In this case the XAS

data can be taken as a good substitute for presently unavailable IPES data.

12

FIG. 1: SrVO3, an ideal cubic perovskite, with V-O-V angle θ=∠123=180◦; V: large ions, Obasal:

small bright ions, Oapex: small dark ions.

FIG. 2: CaVO3, an orthorhombicaly distorted perovskite, with V-O-V angles θbasal ≈ 161◦, θplane ≈

163◦; V: large ions, Obasal: small bright ions, Oapex: small dark ions. The local c-axis, later used

for the definition of the orbitals, is directed along the tilted V-Oapex direction.

13

−8 −6 −4 −2 0 2 4 6 8

Energy (eV)

0

1

2

3

4

5

6D

OS

(st

ates

/ato

m/e

V)

V−3d(t2g

)

V−3d(eg)

0

1

2

3

4

5

6

7

V−3dO−2p

SrVO3

FIG. 3: DOS of SrVO3 as calculated by LDA(LMTO). Upper panel: V-3d (full line) and O-2p

(dashed line) DOS; lower panel: partial DOS of V-3d (t2g) (full line) and V-3d(eg) (dashed line)

orbitals. The Fermi level corresponds to 0 eV.

-8 -6 -4 -2 0 2 4 6 8

Energy (eV)

0

1

2

3

4

5

6

DO

S (s

tate

s/at

om/e

V)

V-3d(t2g

)

V-3d(eg)

0

1

2

3

4

5

6

7

V-3dO-2p

CaVO3

FIG. 4: DOS of CaVO3 as calculated by LDA(LMTO). Upper panel: V-3d (full line) and O-2p

(dashed line) DOS; lower panel: partial DOS of V-3d (t2g) (full line) and V-3d(eg) (dashed line)

orbitals. The Fermi level corresponds to 0 eV.

14

-2 0 2 4 6Energy (eV)

0

0.5

1

1.5

DO

S (s

tate

s/eV

/orb

ital)

T~300 KT~700 KT~1100 K

-2 0 2 4 6Energy (eV)

U=3.55 eV, J=1.0 eV

V3d(t2g

) orbitalsLDA+DMFT(QMC) results

CaVO3

SrVO3

FIG. 5: LDA+DMFT(QMC) spectrum of SrVO3 (right panel) and CaVO3 (left panel) calculated

at T≈300 K (solid lines), T≈700 K (dashed lines), and T≈1100 K) (doted lines).

-3 -2 -1 0Energy (eV)

Inte

nsity

(ar

bitr

ary

units

) SrVO3, LDA+DMFT(QMC)

CaVO3, LDA+DMFT(QMC)

SrVO3 (Sekiyama et al.)

CaVO3 (Sekiyama et al.)

0 1 2 3 4Energy (eV)

SrVO3, LDA+DMFT(QMC)

CaVO3, LDA+DMFT(QMC)

SrVO3 (Inoue et al.)

Ca0.9

Sr0.1

VO3 (Inoue et al.)

FIG. 6: Comparison of the parameter-free LDA+DMFT(QMC) spectra of SrVO3 (solid line)

and CaVO3 (dashed line) with experiments below and above the Fermi energy. Left panel: high-

resolution PES for SrVO3 (circles) and CaVO3 (rectangles) [18, 19]. Right panel: 1s XAS for

SrVO3 (diamonds) and Ca0.9Sr0.1VO3 (triangles) [21]. Horizontal line: experimental subtraction

of the background intensity.

15

arX

iv:c

ond-

mat

/050

1240

v1

11

Jan

2005

Comparative study of orrelation e�e ts in CaVO

3

and SrVO

3

I.A. Nekrasov,

1,2

G. Keller,

2

D.E. Kondakov,

1, 2, 3

A.V. Kozhevnikov,

1,2, 3

Th. Prus hke

�

,

2

K. Held,

4

D. Vollhardt,

2

and V.I. Anisimov

1,2

1

Institute of Metal Physi s, Russian A ademy of S ien es-Ural Division,

620219 Yekaterinburg GSP-170, Russia

2

Theoreti al Physi s III, Center for Ele troni Correlations and Magnetism,

University of Augsburg, 86135 Augsburg, Germany

3

Department of Theoreti al Physi s and Applied Mathemati s,

USTU, 620002 Yekaterinburg Mira 19, Russia

4

Max Plan k Institute for Solid State Resear h,

Heisenbergstr. 1, 70569 Stuttgart, Germany

Abstra t

We present parameter-free LDA+DMFT (lo al density approximation + dynami al mean �eld

theory) results for the many-body spe tra of ubi SrVO

3

and orthorhombi CaVO

3

. Both systems

are found to be strongly orrelated metals, but not on the verge of a metal-insulator transition.

In spite of the onsiderably smaller V-O-V bond angle in CaVO

3

the LDA+DMFT spe tra of the

two systems for energies E < E

F

are very similar, their quasiparti le parts being almost identi al.

The al ulated spe trum for E > E

F

shows more pronoun ed, albeit still small, di�eren es. This is

in ontrast to earlier theoreti al and experimental on lusions, but in good agreement with re ent

bulk-sensitive photoemission and x-ray absorption experiments.

PACS numbers: 71.27.+a, 71.30.+h

1

I. INTRODUCTION

Transition metal oxides are an ideal laboratory for the study of ele troni orrelations in

solids. In these materials, the 3d bands are omparatively narrow with widthW � 2�3 eV

so that ele troni orrelations, indu ed by the lo al Coulomb intera tion

�

U � 3 � 5 eV,

are strong. For

�

U=W � 1, we have a weakly orrelated metal and the lo al density

approximation (LDA) (see [1℄ for a review) works. In the opposite limit

�

U=W � 1 and for an

integer number of 3d ele trons, we have a Mott insulator with two separate Hubbard bands as

des ribed by Hubbard's I and III approximations [2℄ or the LDA+U method [3℄. Transition

metals are, however, in the \in-between" regime,

�

U=W = O(1), where the metalli phase is

strongly orrelated with oexisting quasiparti le peak at the Fermi level and Hubbard side

bands.

Dynami al mean-�eld theory (DMFT) [4, 5, 6, 7, 8℄, a modern, non-perturbative many-

body approa h, is able to apture the physi s in the whole range of parameters from

�

U=W � 1 to

�

U=W � 1 for model Hamiltonians, like the one-band Hubbard model (for an

introdu tion into DMFT and its appli ations see [8℄). And, with the re ent merger [9, 10, 11℄

of LDA and DMFT, we are now able to handle this kind of orrelation physi s within realisti

al ulations for transition metal oxides.

A parti ularly simple transition metal oxide system is Ca

1�x

Sr

x

VO

3

with a 3d

1

ele troni

on�guration and a ubi perovskite latti e stru ture, whi h is ideal for SrVO

3

and or-

thorhombi ally distorted upon in reasing the Ca-doping x. Fujimori et al. [12℄ initiated the

present interest in this 3d

1

series, reporting a pronoun ed lower Hubbard band in the pho-

toemission spe tra (PES) whi h annot be explained by onventional LDA. Subsequently,

thermodynami properties were studied, and the Sommerfeld oeÆ ient, resistivity, and

paramagneti sus eptibility were found to be essentially independent of x [13℄.

On the other hand, PES [14℄, seemed to imply dramati di�eren es between CaVO

3

and

SrVO

3

, with CaVO

3

having (almost) no spe tral weight at the Fermi energy. Rozenberg et

al. [15℄ interpreted these results in terms of the (DMFT) Mott-Hubbard transition in the

half-�lled single-band Hubbard model. With the same theoreti al ansatz, albeit di�erent

parameters, the opti al ondu tivity [16℄ and the PES experiments [17℄ for di�erent dopings

x were reprodu ed.

The puzzling dis repan y between these spe tros opi and the thermodynami measure-

2

ments, suggesting a Mott-Hubbard metal-insulator transition or not, were resolved re ently

by bulk-sensitive PES obtained by Maiti et al. [17℄ and Sekiyama et al. [18, 19℄. In the lat-

ter work it was shown that (i) the te hnique of preparing the sample surfa e (whi h should

preferably be done by fra turing) is very important, and that (ii) the energy of the X-ray

beam should be large enough to in rease the photoele tron es ape depth to a hieve bulk-

sensitivity. Theoreti ally, pronoun ed di�eren es between SrVO

3

surfa e and bulk spe tra

were reported by Liebs h [20℄. Besides bulk-sensitivity, the beam should provide a high in-

strumental resolution (about 100 meV in [18, 19℄). With these experimental improvements,

the PES of SrVO

3

and CaVO

3

were found to be almost identi al [17, 18, 19℄, implying onsis-

ten y of spe tros opi and thermodynami results at last. This is also in a ord with earlier

1s x-ray absorption spe tra (XAS) by Inoue et al. [21℄ whi h di�er only slightly above the

Fermi energy, as well as with BIS data [14℄. Parameterfree LDA+DMFT results by us [22℄,

reported in the joint experimental and theoreti al Letter by Sekiyama et al. [19℄, showed

good agreement with the high-resolution bulk-sensitive PES. Independent LDA+DMFT al-

ulations for 3d

1

vanadates, in luding SrVO

3

and CaVO

3

have been reported by Pavarini et

al. [23℄. Most re ently Anisimov et al. employed a full-orbital omputational s heme based

on Wannier fun tions formalism for LDA+DMFT to al ulate total densities of states for

SrVO

3

whi h are in good agreement with new PES data. [24℄

In this paper we present details of our LDA+DMFT al ulation [22℄ whi h ould not be

in luded in the joint Letter [19℄. In parti ular, we dis uss the rystal stru ture of SrVO

3

and CaVO

3

, explain the origin of the surprisingly small hange in bandwidth of these two

systems, and ompare the al ulated spe trum for energies E > E

F

with XAS data [21℄. We

start with dis ussing the stru tural di�eren es between SrVO

3

and CaVO

3

in Se tion IIA,

based on the most re ent rystallographi data provided by Inoue [26℄. How these di�eren es

re e t in the LDA results is shown in Se tion IIB, before we turn to the LDA+DMFT

s heme in Se tions IIIA and the e�e ts of ele troni orrelations in Se tion IIIB. Se tion IV

on ludes our presentation.

3

II. SRVO

3

VS. CAVO

3

: STRUCTURAL DIFFERENCES AND LDA RESULTS

A. Stru tural di�eren es

Both SrVO

3

and CaVO

3

are perovskites, with SrVO

3

in the ideal ubi stru ture

Pm

�

3m [27℄ (Fig. 1) and CaVO

3

in the orthorhombi aly distorted (GdFeO

3

) Pbnm stru -

ture [26, 28℄ (Fig. 2). The ideal ubi stru ture of SrVO

3

implies that the VO

6

o tahedra,

the main stru tural elements of the rystal, are not distorted: The V-O

basal

and V-O

apex

distan es are the same, the O

apex

-V-O

basal

and O

basal

-V-O

basal

angles are 90

Æ

, and the V-O-V

bond angles are exa tly 180

Æ

. The substitution of the large Sr

2+

ions by smaller Ca

2+

ions

leads to a tilting, rotation, and distortion of the VO

6

o tahedra. Nonetheless, in CaVO

3

,

both the V-O

basal

and the V-O

apex

distan es are pra ti ally the same. Therefore, the most

important feature of the distortion is the hange of the V-O

basal

-V and V-O

apex

-V angles,

whi h determines the strength of the e�e tive V3d-V3d hybridization and, hen e, the band-

width. Due to the rotation and tilting of the o tahedra both angles (one of them is marked

as \123 in Figs. 1 and 2) have the same value � = 180

Æ

for SrVO

3

and �

basal

� 161

Æ

,

�

plane

� 163

Æ

for CaVO

3

.

B. LDA results

The valen e states of SrVO

3

and CaVO

3

onsist of ompletely o upied oxygen 2p bands

and partially o upied V 3d bands. Sin e the V ion has a formal oxidation of 4+, there is

one ele tron per V ion o upying the d-states ( on�guration d

1

). In Figs. 3 and 4 the LDA

density of states (DOS) are presented for both ompounds, as al ulated by the linearized

muÆn-tin orbitals method (LMTO) [29℄ with an orthogonal basis set of Sr(5s; 5p; 4d; 4f),

Ca(4s; 4p; 3d), V(4s; 4p; 3d), and O(3s; 2p; 3d) orbitals [30℄. These results are in agreement

with previous LDA al ulations in the basis of augmented plane waves (APW) by Tagekahara

[31℄. For a ombination of the LDA band stru ture with many-body te hniques [9℄ however,

the atomi -like LMTO wave fun tions employed here are parti ularly onvenient. As is

apparent from Figs. 3 and 4, the O-2p states lie between -7.5eV and -2.0eV in SrVO

3

and

between -6.5eV and -1.5eV in CaVO

3

. The 3d states of V are lo ated between -1.1eV and

6.5eV in SrVO

3

and between -1.0eV and 6.5eV in CaVO

3

. These results are in agreement

with previous LDA al ulations in the basis of augmented plane waves (APW) by Tagekahara

4

[31℄, but for our purposes LMTO is more appropriate.

In both ompounds, the V ions are in a o tahedral oordination of oxygen ions. The

o tahedral rystal �eld splits the V-3d states into three t

2g

orbitals and two e

g

orbitals. In

the ubi symmetry of SrVO

3

, hybridization between t

2g

and e

g

states is forbidden, and

the orbitals within both subbands are degenerate. In ontrast, the distorted orthorhombi

stru ture of CaVO

3

allows them to mix and the degenera y is lifted. In the lower part of

Figs. 3 and 4, we present these t

2g

and e

g

subbands of the V-3d band. For both Sr and

Ca ompounds, the reader an see an admixture of these Vanadium t

2g

and e

g

states to

the oxygen 2p states in the energy region [-8 eV,-2 eV℄. This is due to hybridization and

amounts to 12% and 15% of the total t

2g

weight for SrVO

3

and CaVO

3

, respe tively. The

main t

2g

(e

g

) weight lies in the energy region [-1.1 eV,1.5 eV℄ ([0.0 eV,6.5 eV℄) in SrVO

3

and

[-1.0 eV,1.5 eV℄ ([0.2 eV,6.5 eV℄) in CaVO

3

. Sin e the energy di�eren e between the enters

of gravities of the t

2g

and e

g

subbands is omparable with the bandwidth, t

2g

and e

g

states

an be onsidered as suÆ iently separated in both ompounds.

Let us now on entrate on the t

2g

orbitals rossing the Fermi energy and ompare the

LDA t

2g

DOS of SrVO

3

and CaVO

3

. Most importantly, the one-ele tron t

2g

LDA bandwidth

of CaVO

3

, de�ned as the energy interval where the t

2g

DOS in Figs. 3 and 4 is non-zero, is

found to be only 4% smaller than that of SrVO

3

(W

CaVO

3

= 2:5 eV, W

SrVO

3

= 2:6 eV); in

general agreement with other LDA al ulations [23℄. This is in ontrast to the expe tation

that the strong latti e distortion with a de rease of the V-O-V bond angle from 180

Æ

to 162

Æ

a�e ts the t

2g

bandwidth mu h more strongly. Su h a larger e�e t indeed o urs in the e

g

bands for whi h the bandwidth is redu ed by 10%. To physi ally understand the smallness

of the narrowing of the t

2g

bands we have investigated a larger Hamiltonian onsisting of e

g

,

t

2g

, and oxygen p orbitals. We al ulated the overall dire t d�d and the indire t d�p�d hopping

for this larger Hamiltonian. The predominant ontribution to the e

g

-e

g

hopping is through

a d�p�d hybridization, whi h is onsiderably de reasing with the latti e distortion. This is

also the ase for the t

2g

orbitals. However, for the t

2g

orbitals, the dire t d�d hybridization

is also important. This hybridization in reases with the distortion sin e the t

2g

orbital lobes

point more dire tly towards ea h other in the distorted stru ture. Hopping parameters for

individual orbitals hange rather substantially from SrVO

3

to CaVO

3

. But, altogether, a

de reasing d�p�d hybridization and an in reasing d�d hybridization results in a very small

hange of the t

2g

bandwidth.

5

III. CORRELATION EFFECTS IN SRVO

3

AND CAVO

3

A. Dynami al Mean-Field Theory

As is well-known, LDA does not treat the e�e ts of strong lo al Coulomb orrelations ad-

equately. To over ome this drawba k, we use LDA+DMFT as a non-perturbative approa h

to study strongly orrelated systems [9, 10, 11℄. It ombines the strength of the LDA in

des ribing weakly orrelated ele trons in the s- and p-orbitals, with the DMFT treatment

of the dynami s due to lo al Coulomb intera tions. In the present paper we will dis uss the

relevant parts of the LDA+DMFT approa h only brie y, refering the reader to Ref. [10, 11℄

for details.

The LDA+DMFT Hamiltonian an be written as

^

H =

^

H

0

LDA

+ U

X

m

X

i

n

im"

n

im#

+

X

i m6=m

0

��

0

(U

0

� Æ

��

0

J) n

im�

n

im

0

�

0

: (1)

Here, the index i enumerates the V sites, m the individual t

2g

orbitals and � the spin. H

0

LDA

is the one-parti le Hamiltonian generated from the LDA band stru ture with an averaged

Coulomb intera tion subtra ted to a ount for double ounting [9℄; U and U

0

denote the

lo al intra-orbital and inter-orbital Coulomb repulsions, and J is the ex hange intera tion.

We al ulated these intera tion strengths by means of the onstrained LDA method [32℄

for SrVO

3

, allowing the e

g

states to parti ipate in s reening [33℄. The resulting value of

the averaged Coulomb intera tion is

�

U = 3:55 eV (

�

U = U

0

for t

2g

orbitals [10, 34℄) and

J = 1:0 eV. The intra-orbital Coulomb repulsion U is then �xed by rotational invarian e to

U = U

0

+2J = 5:55 eV. We did not al ulate

�

U for CaVO

3

be ause the standard pro edure

to al ulate the Coulomb intera tion parameter between two t

2g

ele trons, s reened by e

g

states, is not appli able for the distorted rystal stru ture where the e

g

and t

2g

orbitals are

not separated by symmetry. On the other hand, it is well-known that the hange of the

lo al Coulomb intera tion is typi ally mu h smaller than the hange in the DOS, whi h was

found to depend only very weakly on the bond angle. That means that

�

U for CaVO

3

should

be nearly the same as for SrVO

3

. Therefore we used

�

U = 3:55 eV and J = 1:0 eV for

both SrVO

3

and CaVO

3

. This is also in agreement with previous al ulations of vanadium

systems [33℄ and experiments [16℄.

DMFT maps the latti e problem Eq. (1) onto a self- onsistent auxiliary impurity prob-

lem, whi h is here solved numeri ally by the quantum Monte-Carlo (QMC) te hnique [35℄.

6

Combined with the maximum entropy method [36℄, this te hnique allows us to al ulate

spe tral fun tions [37, 38, 39, 40℄.

A omputationally important simpli� ation is due to the fa t that, in ideal ubi per-

ovskites, the (degenerate) t

2g

states do not mix with the (degenerate) e

g

states. In this

parti ular ase, the self-energy matrix �(z) is diagonal with respe t to the orbital indi es.

Under this ondition, the Green fun tions G

m

(z) of the latti e problem an be expressed in

the DMFT self- onsisten y equation by the Hilbert transform of the non-intera ting DOS

N

(0)

m

(!):

G

m

(z) =

Z

d�

N

0

m

(�)

z ��

m

(z)� �

: (2)

This pro edure avoids the rather umbersome and problemati k-integration over the Bril-

louin zone by the analyti al tetrahedron method [41℄. We obtain N

(0)

m

(�) for SrVO

3

and

CaVO

3

from the t

2g

-proje ted DOS of Figs. 3 and 4 by trun ating the ontribution in the

oxygen range below -1.5 eV and multiplying by a renormalization fa tor (to have maximally

one ele tron per site and orbital). This pro edure is employed as it resembles the three

e�e tive bands of t

2g

hara ter whi h ross the Fermi energy and are, hen e, responsible for

the low-energy physi s.

B. LDA+DMFT(QMC) results and dis ussion

The al ulated LDA+DMFT(QMC) spe tra for SrVO

3

(right panel) and CaVO

3

(left

panel) are presented in Fig. 5 for di�erent temperatures. Due to genuine orrelation e�e ts,

a lower Hubbard band at about �1:5 eV and an upper Hubbard band at about 2:5 eV is

formed, with a well pronoun ed quasiparti le peak at the Fermi energy. The 4% di�eren e

in the LDA bandwidth between SrVO

3

and CaVO

3

is only re e ted in some additional

transfer of spe tral weight from the quasiparti le peak to the Hubbard bands, and minor

di�eren es in the positions of the Hubbard bands. Clearly, the two systems are not on the

verge of a Mott-Hubbard metal-insulator transition. Both, SrVO

3

and CaVO

3

, are strongly

orrelated metals, though SrVO

3

is slightly less orrelated than CaVO

3

with somewhat more

quasiparti le weight, in a ord with their di�erent LDA bandwidth. As one an see from

Fig. 5, the e�e t of temperature on the spe trum is small for T . 700 K.

In the left panel of Fig. 6, we ompare our LDA+DMFT spe tra (300K), whi h were mul-

tiplied with the Fermi fun tion at the experimental temperature (20K) and Gauss broadened

7

with the experimental resolution of 0:1 eV [18℄ with the experimental PES data obtained by

subtra ting the experimentally estimated surfa e and oxygen ontributions. Due to the high

photon energy (several hundred eV) [18℄, the PES transition matrix elements will have no

strong energy dependen e in the energy interval of a few eV studied here, whi h justifyies

that we do not take su h matrix elements into a ount.

The quasiparti le peaks in theory and experiment are seen to be in very good agreement.

In parti ular, their heights and widths are almost identi al for both SrVO

3

and CaVO

3

.

The di�eren e in the positions of the lower Hubbard bands may be partly due to (i) the

subtra tion of the (estimated) oxygen ontribution whi h might also remove some 3d spe tral

weight below �2 eV, and (ii) un ertainties in the ab-initio al ulation of

�

U .

Sin e inverse photoemission spe tros opy (IPES) data for SrVO

3

and CaVO

3

are not yet

available we ompare [44℄ the al ulated spe trum for energies E > E

F

with XAS data by

Inoue et al. [21℄ (right panel of Fig. 6). We onsider ore-hole life time e�e ts by Lorentz

broadening the spe trum with 0.2 eV [42℄, multiply with the inverse Fermi fun tion (80K),

and apply Gauss broadening given by the experimental resolution of 0:36 eV [26℄. Again, the

overall agreement of the weights and positions of the quasiparti le and upper t

2g

Hubbard

band is good, in luding the tenden ies when going from SrVO

3

to CaVO

3

. For CaVO

3

(Ca

0:9

Sr

0:1

VO

3

in the experiment), the LDA+DMFT quasiparti le weight is somewhat lower

than in experiment.

In ontrast to one-band Hubbard model al ulations, our material spe i� results repro-

du e the strong asymmetry around the Fermi energy w.r.t. weights and bandwidths. Our

results also give a di�erent interpretation of the XAS than in [21℄ where the maximum at

about 2:5 eV was attributed solely to the e

g

band. We �nd that also the t

2g

upper Hubbard

band ontributes in this energy range.

The slight di�eren es in the quasiparti le peaks (see Fig. 5) lead to di�erent e�e tive

masses, namely m

�

=m

0

= 2:1 for SrVO

3

and m

�

=m

0

= 2:4 for CaVO

3

. These theoreti al

values agree with m

�

=m

0

= 2 � 3 for SrVO

3

and CaVO

3

as obtained from de Haas-van

Alphen experiments and thermodynami s [13, 43℄. We note that the e�e tive mass of CaVO

3

obtained from opti al experiments is somewhat larger, i.e., m

�

=m

0

=3:9 [16℄.

8

IV. CONCLUSION

In summary, we investigated the spe tral properties of the orrelated 3d

1

systems SrVO

3

and CaVO

3

within the LDA+DMFT(QMC) approa h. Constrained LDA was used to de-

termine the average Coulomb intera tion as

�

U = 3:55 eV and the ex hange oupling as

J=1:0 eV. With this input we al ulated the spe tra of the two systems in a parameter-free

way. Both systems are found to be strongly orrelated metals, with a transfer of the ma-

jority of the spe tral weight from the quasiparti le peak to the in oherent upper and lower

Hubbard bands. The al ulated DMFT spe tra of SrVO

3

and CaVO

3

, and in parti ular the

quasiparti le parts, are found to be very similar, di�eren es being slightly more pronoun ed

at energies above the Fermi energy. Our al ulated spe tra agree very well with re ent

bulk-sensitive high-resolution PES [18℄ and XAS [21℄ data, i.e., with the experimental spe -

trum below and above the Fermi energy. Both ompounds are similarly strongly orrelated

metals; CaVO

3

is not on the verge of a Mott-Hubbard transition.

Our results are in ontrast to previous theories and the expe tation that the strong

latti e distortion leads to a strong narrowing of the CaVO

3

bandwidth and, hen e, to mu h

stronger orrelation e�e ts in CaVO

3

. While the e

g

bands indeed narrow onsiderably, the

ompetition between de reasing d�p�d and in reasing d�d hybridization leads to a rather

insigni� ant narrowing of the t

2g

bands at the Fermi energy. This explains why the k-

integrated spe tral fun tions of CaVO

3

and SrVO

3

are so similar. With our theoreti al

results on�rming the new PES and XAS experiments, we on lude that the insulating-like

behavior observed in earlier PES and BIS experiments on CaVO

3

must be attributed to

surfa e e�e ts [20℄.

V. ACKNOWLEDGMENTS

This work was supported by Russian Basi Resear h Foundation grant RFFI-GFEN-

03-02-39024 a (VA,IN,DK), RFFI-04-02-16096 (VA,IN,DK) and the Deuts he Fors hungs-

gemeins haft through Sonderfors hungsberei h 484 (DV,GK,IN) and in part by the joint

UrO-SO proje t N22 (VA,IN), the Emmy-Noether program (KH), by Grant of President

of Russian Federation for young s ientists MK-95.2003.02 (IN), Dynasty Foundation and

International Center for Fundamental Physi s in Mos ow program for young s ientists 2004

9

(IN), Russian S ien e Support Foundation program for young PhD of Russian A ademy of

S ien e 2004 (IN).

�

New permanent address: Institut f�ur Theoretis he Physik, Universit�at G�ottingen,

Friedri h-Hund-Platz 1, D-37077 G�ottingen, Germany.

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12

FIG. 1: SrVO

3

, an ideal ubi perovskite, with V-O-V angle �=\123=180

Æ

; V: large ions, O

basal

:

small bright ions, O

apex

: small dark ions.

FIG. 2: CaVO

3

, an orthorhombi aly distorted perovskite, with V-O-V angles �

basal

� 161

Æ

, �

plane

�

163

Æ

; V: large ions, O

basal

: small bright ions, O

apex

: small dark ions. The lo al -axis, later used

for the de�nition of the orbitals, is dire ted along the tilted V-O

apex

dire tion.

13

−8 −6 −4 −2 0 2 4 6 8

Energy (eV)

0

1

2

3

4

5

6D

OS

(st

ates

/ato

m/e

V)

V−3d(t2g

)

V−3d(eg)

0

1

2

3

4

5

6

7

V−3dO−2p

SrVO3

FIG. 3: DOS of SrVO

3

as al ulated by LDA(LMTO). Upper panel: V-3d (full line) and O-2p

(dashed line) DOS; lower panel: partial DOS of V-3d (t

2g

) (full line) and V-3d(e

g

) (dashed line)

orbitals. The Fermi level orresponds to 0 eV.

-8 -6 -4 -2 0 2 4 6 8

Energy (eV)

0

1

2

3

4

5

6

DO

S (s

tate

s/at

om/e

V)

V-3d(t2g

)

V-3d(eg)

0

1

2

3

4

5

6

7

V-3dO-2p

CaVO3

FIG. 4: DOS of CaVO

3

as al ulated by LDA(LMTO). Upper panel: V-3d (full line) and O-2p

(dashed line) DOS; lower panel: partial DOS of V-3d (t

2g

) (full line) and V-3d(e

g

) (dashed line)

orbitals. The Fermi level orresponds to 0 eV.

14

-2 0 2 4 6Energy (eV)

0

0.5

1

1.5

DO

S (s

tate

s/eV

/orb

ital)

T~300 KT~700 KT~1100 K

-2 0 2 4 6Energy (eV)

U=3.55 eV, J=1.0 eV

V3d(t2g

) orbitalsLDA+DMFT(QMC) results

CaVO3

SrVO3

FIG. 5: LDA+DMFT(QMC) spe trum of SrVO

3

(right panel) and CaVO

3

(left panel) al ulated

at T�300 K (solid lines), T�700 K (dashed lines), and T�1100 K) (doted lines).

-3 -2 -1 0Energy (eV)

Inte

nsity

(ar

bitr

ary

units

) SrVO3, LDA+DMFT(QMC)

CaVO3, LDA+DMFT(QMC)

SrVO3 (Sekiyama et al.)

CaVO3 (Sekiyama et al.)

0 1 2 3 4Energy (eV)

SrVO3, LDA+DMFT(QMC)

CaVO3, LDA+DMFT(QMC)

SrVO3 (Inoue et al.)

Ca0.9

Sr0.1

VO3 (Inoue et al.)

FIG. 6: Comparison of the parameter-free LDA+DMFT(QMC) spe tra of SrVO

3

(solid line)

and CaVO

3

(dashed line) with experiments below and above the Fermi energy. Left panel: high-

resolution PES for SrVO

3

( ir les) and CaVO

3

(re tangles) [18, 19℄. Right panel: 1s XAS for

SrVO

3

(diamonds) and Ca

0:9

Sr

0:1

VO

3

(triangles) [21℄. Horizontal line: experimental subtra tion

of the ba kground intensity.

15