Surface versus bulk Mott transition in Ca$_x$La$_{1-x}$VO$_3$

5 Pages·0.15 MB·English

by  A. Liebsch

Surface versus bulk Mott transition in Ca La VO
x 1−x 3
A. Liebsch
Institut fu¨r Festk¨orperforschung, Forschungszentrum Ju¨lich, 52425 Ju¨lich, Germany
(Dated: February 2, 2008)
TheMottinsulatorLaVO3 isknowntobecomemetallicifLaisreplacedbysmall concentrations
of Ca. Since surface quasi-particle spectra of various perovskites are more strongly correlated than
3 theirbulkspectra,thecoexistenceofametallicbulkandaninsulatingsurfacelayermightbefeasible.
0 Toinvestigatethispossibility thedynamicalmeanfieldtheoryisusedtoevaluatethequasi-particle
0 spectra in the bulk and at thesurface of CaxLa1−xVO3 for various Ca concentrations.
2

n
a Significantsurfacecontributionstoquasi-particlespec- CaVO3 should indeed be very similar was recently also
J traofstronglycorrelatedtransitionmetaloxideshavere- foundbyNekrasovet al. [10]inbulk electronicstructure
8 centlybeenidentifiedinphotoemissionmeasurementson calculations combining the the local density approxima-
2 severalperovskitematerials: SrRuO3 [1],Sr2RuO4 [2,3], tion (LDA) with the many-body dynamical mean field
CaxSr1−xVO3[4,5,6],andCaxLa1−xVO3[7]. Thelatter theory (DMFT) [11, 12, 13].
l] seriesisparticularlyinterestingsinceLaVO3isinsulating As shown by Liebsch [14] using surface DMFT cal-
e and becomes metallic upon doping with Ca. By varying
culations, the enhancement of surface correlations can
r- the photonenergyMaitiet al. [7]were able to showthat at least in part be understood in terms of the reduced
t surfacecorrelationfeaturesaremorepronouncedthanin
s atomiccoordinationatthe surfaceandthe concomittant
. the bulk, in accord with the observations on the other
t narrowing of the local density of states. Thus, the ratio
a perovskites cited above. Thus, the coherent peak at the
of local Coulomb energy and band width U/W is effec-
m
Fermilevelislessintenseandthesatellitepeakbelowthe
tivelyenhancedatthesurface. Accordingly,thecoherent
- V t2g band is stronger than observed in the correspond- peak in surface quasi-particle spectra is less intense and
d
ing bulk photoemission spectra. Even more remarkably,
n the lower Hubbard band is enhanced compared to the
Maiti et al. identified a Ca concentration range where
o bulk. Other mechanisms, such as additional band nar-
c the bulk has become metallic while the surface still ap- rowing due to reconstruction and distortion of oxygen
[ pearsinsulating,before,atevenhigherCadoping,italso
octahedra, or less efficient screening of electron-electron

1 becomes metallic. Although sample preparation and ex- interactions at surfaces, might further increase the im-
perimental resolution make the data analysis difficult,
v portanceofcorrelationsinsurfacephotoemissionspectra.
7 these results addressa very interestingissue, namely the The recent work on CaxSr1−xVO3 therefore established
3 possible coexistence of different bulk and surface phases thatphotoemissionisconsistentwithlow-frequencybulk
5 in semi-infinite systems. In the case of magnetism, for
probes as long as surface effects are properly taken into
1 example, itis wellknownthat atfinite temperatures the
account.
0
magneticmomentcanbe reducedinthe surfacelayersof
3 a ferromagnet, but that both have the same Curie tem- ThesameconclusionappliestoSr2RuO4forwhichpre-
0 vious photoemission spectra seemed to contradict bulk
perature unless the surface is artificially decoupled from
/
t the bulk [8]. de Haas-van Alphen measurements [2, 15]. Recent ex-
a
perimental and theoretical work [3, 16] proved,however,
m
that this discrepancy can be resolved by taking into ac-
The identification surface-induced enhanced correla-
d- tionsisclearlyimportantinordernottointerpretethem countthelatticereconstructionatthesurfaceofSr2RuO4
which leads to significant changes in the photoemission
n erroneously as bulk correlations. For instance, earlier
o photoemission data on CaxSr1−xVO3 [4] appeared to be spectra.
c
in conflict with various low-frequency measurements [9]. Inthe presentworkwe investigatesurfacecorrelations
:
v While the latter data showed that this perovskite series in the perovskite series CaxSr1−xVO3 at Ca doping lev-
i is metallic for all Ca concentrations, the photoemission els where metallic bulk and insulating surface behavior
X
spectra seemed to suggest that SrVO3 is strongly corre- mightcoexist. Since doping with Ca leads only to minor
r
a latedandthatCaVO3isonthevergetoametal-insulator structural changes and nearly constant Hubbard U [17],
transition. Recent photoemission measurements [5, 6] the modifications of the electronic properties are almost
covering a wide range of photon energies demonstrated entirely caused by the degree of band filling. According
insteadthatthebulkspectraofbothmaterialsareconsis- to theoretical predictions by Potthoff and Nolting [18],
tentwithmetallicbehavior,butthatcorrelationfeatures a phase with metallic bulk and insulating surface prop-
are much more pronouncedat the surface. While SrVO3 erties cannot occur unless electronic coupling between
isacubicperovskite,theoxygenoctahedrainCaVO3are surface and bulk is assumed to be weak. These results
orthorhombicallydistorted. This leads to a slight reduc- were derived for the semi-infinite half-filled simple cu-
tionint2g bandwidthanda broadeningofthe vanHove bic s band, and by adopting a linearlized version of the
singularity. ThedensityofstatesatE ,however,isonly DMFT in which low- and high-frequency excitations are
F
weakly affected. That the bulk properties of SrVO3 and essentiallydecoupled. Itisthereforenotcleartowhatex-
2
systems [21]. Details concerning the application of this
V) 1.2 method to t2g bands are given Ref. [22]. As shown in
1/e (a) LaVO3 Fig. 1, the spectral weight is shifted from the low- and
s ( high-energyregionstointermediateenergiesclosetoEF.
ate 0.8 Thus, although the full band width coincides with the
ensity of St 0.4 surface dxz,yz bulk t2g osbunuretfiaoincnestlhsaheyoebwrunilski,nefftFheiecgt.liov1ce(alayl)dnaeannrdrsoi(twbye)odaf.rdeTxqhzu,eyazsliusttraaftativceeeslydinissittmhrie--
D
ilar. The small difference arises from slightly different
0 surface potentials which are employed in the electronic
-1.5 -1 -0.5 0 0.5 1
Energy (eV) structure calculation for semi-infinite CaxLa1−xVO3 in
order to ensure charge neutrality. In the deeper layers,
the local density of dxz,yz states approaches the bulk t2g
s (1/eV) 1.2 (b) Ca0.5La0.5VO3 dinenasnitoyscrailtlahteorrqyudicekvliya,titohnewmhaicinhmdeocdriefiacsaetsiownitchoinnscisrteiansg-
ate 0.8 ing distance from the surface. In contrast to the dxz,yz
St densities, the local density of d states in the surface
ensity of 0.4 surface dxz,yz bulk t2g lTahyeisrisisaaclomnosesqtuiednecnetiocfatlhteoptrhonexoyiusnotcreodppiclabnuarlkchdaernascitteyr.
D of the t2g states.
0
Thenarrowingofthelocaldensitystatesinthesurface
-1 -0.5 0 0.5 1 1.5
Energy (eV) layer has an important influence on the quasi-particle
distributions which we evaluate by using the multiband
QMC-DMFT. Essentially we are dealing with coupled
FIG.1: Solidcurves: isotropicbulkdensityofstatesofcubic
impurity problems where layer-dependent self-energies
(a)LaVO3(d2)and(b)Ca0.5La0.5VO3(d1.5). Dashedcurves: must be calculated and iterated until self-consistency is
local density of dxz,yz states in thefirst layer (EF =0).
achieved. Sincethefullsolutionofthisproblemformulti-
band systems is computationally not yet feasible, we ne-
glect the coupling between layer baths and treat bulk
tent they are applicable to realistic multi-band systems andsurfacelayersindependently. Inprevioussingle-band
atarbitrarybandfilling. Herewecalculatesurfacequasi- DMFT calculations for surfaces this coupling was found
particle spectra by using a realistic layer-dependent lo- to be small [18]. Enforcing charge neutrality at the sur-
caldensity ofstates appropriatefor CaxSr1−xVO3, com- face presumably alsodiminishes the importanceof inter-
bined with multi-band DMFT Quantum Monte Carlo layer coupling between the impurity baths. The key in-
(QMC) calculations. putintheDMFTcalculationisthereforetheorbital-and
Fig. 1 shows the bulk and surface density of states for layer-dependent local density of states. As a result of
LaVO3 and Ca0.5La0.5VO3. The main difference is the the one-electronbandnarrowingwe canexpect a similar
band filling. While the d2 occupancy of the V t2g bands enhancement of surface correlation effects as discussed
makesLaVO3insulating[19],Ca0.5La0.5VO3withitsd1.5 previously for SrVO3 and SrRuO3 [22].
occupancy is metallic. In the bulk, the insulator-metal As mentioned above, LaVO3 is insulating, but hole
transition occurs at about x ≈ 0.2 [5]. Since our main dopingbyreplacementofLaviaCainducesaninsulator-
interest here is to study the effect of band filling on this metal transition at rather low Ca concentrations. This
transitioninthebulkandatthesurfaceweadoptforsim- can be seen clearly in the different shapes of the
plicity the ideal cubic symmetry and neglect the distor- imaginary-timeGreen’sfunctionforbulkCaxLa1−xVO3,
tionofoxygenoctahedra. Accordingto the LDA-DMFT as shown in Fig. 2 for several values of x. Note that the
calculationsforCaVO3[10]thesestructuralchangeshave value of G(τ) at τ ≈ β/2 is representative of the weight
littleinfluenceonthet2g quasi-particlespectra. Thebulk of the quasi-particle peak at EF, while G(β) gives the
density of states is therefore similar to that of SrVO3. occupancy per spin-band. In the case of LaVO3 (x=0)
It exhibits the characteristic asymmetric shape resulting already for U = 4.5...5.0 eV there is little weight near
fromthepronouncedplanarnatureofthet2gstateswhich τ ≈ β/2, indicating the reduction of intensity near EF
is found for various peroskite materials [20]. as U approaches the critical value for the Mott transi-
Inacubicstructure,thet2g bandsaredegenerate. The tion. Of course, since the DMFT-QMC calculations are
surface lifts this degeneracy since only the intra-planar carried out at finite temperatures, G(β/2) cannot ap-
d states exhibit strong dispersion within the surface proach zero, i.e., a finite spectral density at E remains
xy F
layerwhile d bands are modified due to the reduced even in the nominally insulating phase. According to
xz,yz
atomic coordination(the z-axisspecifies the surface nor- the results shown at finite Ca concentrations, however,
mal). The layer dependent local density of states is cal- G(β/2) diminishes much less rapidly, indicating the in-
culated using a tight-binding formalism for semi-infinite cipient metallicity for x > 0. Thus, in the range of
3
0
0.4 (a) U=4.0 eV
-0.2
V)
e
τ G() b -0.4 ωN () (1/b 0.2
-0.6 (a) LaVO3
-0.8 0
0 1 2 3 4 5 6 7 8 -4 -3 -2 -1 0 1 2 3 4
τ Energy (eV)
0
0.4 (b) U=4.5 eV
-0.2
V)
e
τ G() b -0.4 ωN () (1/b 0.2
-0.6 (b) Ca0.1La0.9VO3
-0.8 0
0 1 2 3 4 5 6 7 8 -4 -3 -2 -1 0 1 2 3 4
τ Energy (eV)
0
0.4 (c) U=5.0 eV
-0.2
V)
e
τ G() b -0.4 ωN () (1/b 0.2
-0.6 (c) Ca0.2La0.8VO3
-0.8 0
0 1 2 3 4 5 6 7 8 -4 -3 -2 -1 0 1 2 3 4
τ Energy (eV)
0
FIG. 3: Quasi-particle density of bulk t2g states of
-0.2 Ca0.1La0.9VO3 (d1.9) for (a) U = 4.0 eV, (b) 4.5 eV and
τG() b -0.4 (Dca)s5h.e0decVurvdeesr:ivbeadrefrdomensDitMy oFfTst(astoelsid. curves); J = 0.7 eV.

-0.6 (d) Ca0.5La0.5VO3
-0.8 tra for Ca0.1La0.9VO3 for various Coulomb energies in
0 1 2 3 4 5 6 7 8
the critical region of the metal-insulator transition. The
τ
analogoussurfacespectraareshowninFig.4. Allspectra
exhibitthethree-peakstructurecharacteristicofstrongly
FIG.2: Quasi-particle Green’s function asfunction of imag- correlated systems: a coherent peak at E and upper
F
inary time for bulk t2g states of CaxLa1−xVO3 derived from and lower Hubbard bands which appear as satellites in
DMFT(β =8). G(β/2)isrepresentativeofthequasi-particle
photoemission or inverse photoemission data. As in the
weightatEF. (a)x=0;(b)x=0.1;(c)x=0.2;(d)x=0.5. systems studied previously [22], as a consequence of the
Plotted are G(τ) for U =3.0...5.0 eV [up to 6 eV in (d)]in
effective narrowing of the d subbands, correlations
steps of 0.5 eV (from below); J =0.7 eV. xz,yz
aremorepronouncedatthesurfacethaninthebulk: the
Hubbardpeaksaremoreintenseandthecoherentpeakis
a narrower. Since the QMC-DMFT calculations are per-
Coulomb energies where LaVO3 is insulating, i.e., for formed at about 1450 K (β = 8) the coherent peak per-
U ≈ 5.0 eV, CaxLa1−xVO3 for x > 0.2 is metallic. We sistsevenintheinsulatingphase. Nevertheless,inviewof
conclude from these calculations that within our model the temperature dependence of this feature known from
theborderlinedopinglevelbetweeninsulatingandmetal- one-bandsystems[11,23]thespectrainshowninFigs.3
lic behavior is about x≈0.1. and4 suggestthatatthe surfacethe likelihoodfor agap
According to these results we consider x = 0.1 as the toopenatE atlowtemperaturesisslightlygreaterthan
F
most promising Ca concentration at which the bulk is in the bulk. In the bulk there is clearly more spectral
already close to metallicity while the surface layermight weight near EF compared to pure LaVO3 (x = 0) [22],
still be insulating. Fig. 3 shows bulk quasi-particle spec- reflectingthebeginningmetallicbulkbehavioratx=0.1
4
behavior found in semi-infinite Heisenberg models: the
magnetization near the surface is smaller than in the
0.4 (a) U=4.0 eV
V) bulk, but the critical temperature for the transition to-
1/e wards paramagnetism is the same [8]. Only if surface
ω) ( and bulk are strongly decoupled their critical behavior
N (xy,xz 0.2 mwoiguhldtbaelsdoiffreerqeunitr.eAtocaarcecfouulnetxafomrinthateiocnouopfltihnigsqbueetwsteioenn
the layer dependent ‘impurity’ baths which we have ne-
0 glectedfor computationalreasons. Presumably this cou-
-4 -3 -2 -1 0 1 2 3 4
Energy (eV) pling whould diminish the differences between bulk and
surface spectra.
So far we have only considered the effect of band nar-
0.4 (b) U=4.5 eV
V) rowingonthedxz,yz stateswhichhybridizepreferentially
e
1/ inplanesnormaltothesurface. Surfacereconstructionor
ω) ( distortionofoxygenoctahedrapresumablywouldreduce
N (xy,xz 0.2 hleoapdpininggtaolsoadbdetitwioenenaldxeynhstaantceesminenttheofifrssturlafayceer,tchoerrreelbay-
tions. Moreover, less efficient electronic screening pro-
0 cesses near the surface could increase the local Coulomb
-4 -3 -2 -1 0 1 2 3 4
Energy (eV) energy. Both effects would make the surface electron-
ically different from the bulk. It is doubtful, however,
whether this decoupling would be strong enough to give
0.4 (c) U=5.0 eV
V) rise to separate bulk/surface Mott transitions.
e
1/
ω) ( In summary, we have calculated bulk and surface
N (xy,xz 0.2 dquynasaim-piacratlicmleeadnistfireiblduttihoenosryfo.rACtaixnLteag1−erxVocOc3upuasnincgy t(hd2e
for x = 0) this perovskite material is a Mott insulator.
At small Ca concentrations, however, the bulk material
0
-4 -3 -2 -1 0 1 2 3 4 becomes metallic. As a result of the reduced atomic co-
Energy (eV)
ordinationatthesurface,twoofthet2g subbandsexhibit
appreciablebandnarrowing,givingrisetostrongercorre-
FIG. 4: Quasi-particle density of surface dxy states (solid lationfeaturesinthe quasi-particlespectra. Inthe range
curves) and dxz,yz states (dashed curves) of Ca0.1La0.9VO3 of critical local Coulomb interactions for the Ca concen-
(d1.9) for U =4.0, 4.5 and 5.0 eV derived from DMFT; J = tration x=0.1 we have found at the surface a tendency
0.7 eV.Dotted curves: bare densities of states. forthe formationofanexcitationgapatalowervalue of
U than in the bulk. Whether this implies a coexistence
of metallic bulk and insulating surface behavior is, how-
Ca doping concentration. The surface spectra shown in
ever,difficult to estimate atpresent because of the finite
Fig. 4,on the other hand, indicate strongertendency to-
temperatureusedintheQMC-DMFTcalculations. Also,
wards gap formation, in particular for U =5 eV.
additionalsurfaceeffectsontheelectronicstructuresuch
In spite of the more pronounced surface correlations
as reconstruction, the charge state of the surface layer,
discussed above, it is not clear whether extrapolation
andweakerscreeningofthelocalCoulombenergyshould
to low temperatures would yield different Mott transi-
be considered.
tions for the bulk and the surface layer. Even though
the spectral weight at E is consistently smaller at the Acknowledgement: I like to thank A. Bringer, E.
F
surface, both N (E ) and N (E ) could still vanish at Eisenriegler,andD.D.Sarmafordiscussions. Ialsothank
s F b F
the same critical U. This would be analogous to the A.I. Lichtenstein for the QMC-DMFT code.
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