Electronic structure of correlated electron systems : theory and...
93
Electronic structure of correlated electron systems : theory and experiment Lecture 4 G.A.Sawatzky
Transcript of Electronic structure of correlated electron systems : theory and...
Electronicstructureofcorrelatedelectronsystems:theoryand
experimentLecture4G.A.Sawatzky
Surfacesandinterfacesofionicsolidsandpnic?des
ImportantforTMOxideinterfaces
• Charge,spin,orbital,laHcedegreesoffreedom
• ChargetransfervsMoJHubbardgaps
• Stronglyionic(Madelungpoten?aleffects)
• Polarsurfaces/interfaces• Stronglynonuniformpolarizabili?es
• Electronicpolaronsandbandgapclosingatinterfaces
CorrelatedElectronsinaSolid
• J.Hubbard, Proc. Roy. Soc. London A 276, 238 (1963) • ZSA, PRL 55, 418 (1985)
If Δ < (W+w)/2 Self doped metal
dn dn dn-1 dn+1 U :
p6 dn p5 dn+1 Δ :
U = EITM – EA
TM - Epol
Δ = EIO – EA
TM - Epol + δEM
EI ionization energy EA electron affinity energy EM Madelung energy
Cu (d9)
O (p6)
Epol depends on surroundings!!!
Atasurfacethechargetransferenergydecreases,Uincreases
NovelNanoscalePhenomenainTransi1on‐MetalOxides
IonicOxidePolarSurfacesStabiliza?onofpolarsurfacesbyepitaxy
Transparentinsulator½metallicFM
Applica1ons:Spintronics;CMR
SrO O
‐1+2‐2
Sr SrO
+1 +2‐2
<10ML
Ar1ficialMoleculesEmbeddedintoaMaterialCa,Mg,Sr,NivacanciesorO‐Nsubs?tu?oninoxides
Newclassofmagne?cmaterialsby‘‘low‐T’’MBEgrowthApplica1ons:Spintronics;NovelMagnets
JO N
LaMnO3eg
t2g
Mn3+3d4
Strained2DLayers Posi?veandnega?vepressure
Applica1ons:CMR;M‐ITransi?on;OrbitalOrdering
CorrelatedElectronSystemSurfaces
Kinksandstepsstabilizedbyepitaxy
NiO(100)1DMetallicstepsSuperconduc?ngCopperoxides
Applica1ons:NovelSC;QuBits
ElectronicStructureofInterfacesMetal‐Insulatorinterface:gapsuppression
Applica1ons:MolecularElectronics;FuelCells;ThermalBarrierCoa?ngs
Defectsstudy:Supercellapproxima?on
To study defects we want to “break” periodicity in one (surface), two (wires) or three (single impurity) dimensions.
Slab geometry:
Impurity in the bulk:
Sr
Ti O
Unit cell of perfect inf. crystal
Supercell with an impurity
Perfectly imperfect inf. crystal
NiObulk• Rock salt structure • AFM insulator (Exp. Gap ~4eV)
O2-: 2s2 2p6
Ni2+: 3d8
LSDA LSDA+U
U=8eV J=0.9eV
Neutral(110)surfacesofNiOLSDA+U: U=8eV J=0.9eV Slab of 7 NiO layers
Bandgapatthesurfacedecreasesfrom3eVto1.2eVCanwegetdeltatogonega1ve?Stepedgescouldbe1Dstronglycorrelatedmetals
CorrelatedElectronSystemSurfaces
Kinksandstepsstabilizedbyepitaxy
NiO(100)1DMetallicstepsSuperconduc?ngCopperoxides
Applica1ons:NovelSC;QuBits
Nega?veCTgapatsteppedsurfaces?
Ni2+goestoNi1+(d9)andholesinO2pfornega?vechargetransfergapi.e.selfdoping‐‐‐‐‐‐‐lookslikeholedopedcuprates!!!
NewHighTc??
IonicMaterialscanexhibitPolarsurfacesandinterfacesandcan
electronicallyreconstruct
Typesofreconstruc?on
Electronic Ionic Chemical
K3C60:R.Hesperetal.,Phys.Rev.B62,16046(2000).
+Q
‐Q
+Q
‐Q
+Q/2
+Q/2
‐Q/2
‐Q
+Q
‐Q
NiO(111):D.Cappusetal.,Surf.Sci.337,268(1995).
+Q
‐Q
+Q
‐Q
Rearrangementofelectrons
RearrangementofIonsface?ng
K-depositon: M.A. Hossain et al., Nat.
Phys. 4, 527 (2008). NiO(111): D. Cappus et al., Surf. Sci. 337, 268 (1995).
VacanciesoraddIons(K+)orOH‐
Polar(111)SurfacesofMgO
2-
2+
Finite slab of charged planes
ΔV=58 Volt per double layer!
2- 2+
Interes?ngmaterialsinwhichelectronicreconstruc?oncanstronglyalterproper?esandwhichcanbeusedforinterfaceengineeringtodevelopnewdeviceswithexo?cproper?es.
SuperConductors:YBa2Cu3O6+δ
(Cu)1+
(BaO)0
(CuO2)2‐
(Y)3+
(CuO2)2‐
(BaO)0
(Cu)1+
Perovskites:LaTMO3(Ti,V,Mn...)Spin,chargeandorbitalordering
LaOFeAs
1+
1‐
1+
Simpleoxides:SrO,NiO,MnO...
(111)surface
(001)surfaceintrivalentcompounds
(110)surface
TiOCl
(Cl)1‐
(TiO)22+
(Cl)1‐
TiS2
(Ti)4+
(S)2‐
(S)2‐
Examplesofnonpolarlayerstructures
adatomstabiliza?onofPolarsurfacesImportantalsoforgrowth
• NiOgrownbyMBEiscoveredbyamonolayerofOH‐=1/2thechargeoftheNi2+layerunderneathandthereforestable
• MnSsinglecrystalsgrownwithvaportransportmethodsyieldlargecrystalswith111facets????CoveredbyasinglelayerofI‐andthecrystalgrowsunderneath.Likeasurfactant
• ½BamissingonthesurfaceofBaFe2As2• K+adionsonYBCO• Useaddlargeionsassurfactantsduringgrowthofpolarsurfacesystems
Octopolarreconstruc?onofMgO(111)slab
Topview Sideview
Effec?vesurfacelayercharge=+2(3/4)‐2(1/4)=+1
MgO O
‐1+2‐2
Mg MgO
+1 +2‐2
TransferoneelectronfromOlayertoMglayer
ELECTRONICRECONSTRUCTION
LSDABandStructureofCaO(111)SlabterminatedwithCaandO
-10
-5
0
5
10
Γ K M Γ A L H A
Ener
gy (e
V)
-10
-5
0
5
10
Γ K M Γ A L H A
Spin Up Spin Down
12
-4
-2
0
2
4
6
8
10
L X W L K
Ener
gy (e
V) Note:
Bulk material (no surface) is an insulator
But surface is metallic! And ferromagnetic
Ca 4s
O 2p
111surfaceofK3C60anditspolarnature.
HesperetalPRB62,160462000coinedthephraseelectronicReconstruc?onforK3C60surfaces
severaltermina?onsarepossibleandatleast2differentPhotoemissionspectraatthesurfacehavebeenobservedcorrespondingtoC601.5‐,2.5‐
Hossainetal.,NaturePhysics4,527(2008)
Hossainetal.,NaturePhysics4,527(2008)
ElectronicReconstruc?on
• Energe?callyfavourableinionicsystemswithsmallbandgapsandinsystemswithmul?valentcomponents(Ti,V,C60,Ce,Eu‐‐‐‐)
MaanhartetalMRSbule?nreview
Ohtomo and Hwang Nature 427, 423, 2004
Metallic interface due to electronic reconstruction
Influence of the La AlO3 thickness on a SrTiO3 substrate on the conductivity
S.Thiel et al Science 313, 1942 (2006)
N.Reyren et al Science express 317, 1196 207
Superconducting interface SrTiO3/LaAlO3
Somekeypapersonpolarsurfacesandinterfaces
• R. Lacman, Colloq. Int. CNRS 152, 195 (1965) • The stability of ionic crystal surfaces P.W. Tasker, J. Phys. C 12, 4977 (1979) • Reconstruction of NaCl surfaces D. Wolf, PRL 68, 3315 (1992) • Adsorption on Ordered Surfaces of Ionic solids ed. H. J. Freund and E. Umbach, Springer Series in Surface Science, Springer, Berlin, 1993, vol. 33. • Electronic reconstruction of polar surfaces in K3C60: R. Hesper et al., PRB 62, 16046 (2000) • High mobility electron gas at LaAlO3 /SrTiO3 interface A. Ohtomo and H.Y. Hwang, Nature 427, 423 (2004)
InterfacesbetweennarrowbandsemiconductorsandmetalsmaybeverydifferentfrombroadbandsemiconductorslikeSiorGaAs
NarrowbandwidthultrathinlayersonPolarizablemedia
• correlatedelectronsystemsmostlyhavebandwidthsofonly1‐2eV
• Molecularsolidshaveverysmallbandwidthsof1eVorless
• Si,GaAshavebandwidthsof20‐30eVandbehaveverydifferentlyatinterfaces
Defini?onofConduc?vityGap
Egap=(EgrN‐1–EgrN)+(EgrN+1–EgrN)
=EgrN‐1+EgrN+1–2EgrN
Egr>Groundstate
+
eћ ћ
e
—
PES(EI) IPES(EA)
Fullpolariza?oncandevelopprovidedthatDynamicResponseTimeofthepolarizablemediumisfasterthan
hopping?meofthecharge
E(polarizability)>W;EMOenergyspliHnginmolecules,plasmafrequencyinmetals‐‐‐‐‐
APictureofSolva?onofionsinapolarizablemedium
Manipulating Material Properties
How about using Image Charge Screening ?
magnetic : (super) exchange, TC, TN
electrical : (super) conductivity, TC, M-I-T
optical : band gaps
Coulomb energy :
Charge transfer energy :
Band gap :
q’ q
2
1R1
R2n
a
0
Poten?alofapointchargeintheneighbourhoodofadielectric Macroscopiccon?nuum‐uniform
‐surfacecharge
Energytocreateachargeqata:
NotethatimagechargescreeninggoesasQsquared!!!
Cannotbetreatedasachangeinsinglepar?clepoten?alELECTRONICPOLARONS
Theenergiesofelectrons(cond.Band)andholes(valenceband)arebothlowered
Thereforeconduc?vitygapislowered
Bothelectronsandholeswillwanttomovetotheinterface
Frenkellikeexcitonstatesarenotaffectedtolowestorder
Si, Ge Molecular
Egap
Gap HOMO s
LUMO p W
Band width ~ 0.5 eV >10 eV
Exciton B.E. ~ 1 eV ~20 meV
Polarons ћ 0 ~ W ( ~ >1) —
Electr. – Electr. UW U<<W
Magnetism Yes (T-S~0.5eV) No
Cond. Gap Egap W Egap << W
Si, Ge, GaAs Molecules
EF
Egap~1eV
Egap=constant?
EF
Conven?onalwidebandsemiconductor–metalinterface
Narrowbandsemiconductor–metalinterfaceinwhichThepolariza?oncloudcanfollowtheelectronyielding“ELECTRONICPOLARON’’
Examplesaremolecularsolids,stronglycorrelatedsystems,TM,RE‐‐‐‐‐
Combinedphotoemission(solidlines)andinversephotoemission(dotswithsolidlinesasguidetotheeye)spectraoftheC60monolayeronAg(111)(upperpanel)andthesurfacelayerofsolidC60(lowerpanel).Alsoincludedarethephotoemissionspectra(dashedlines)ofthefullydopedC60(“K6C60”)monolayeronAg(111)andthesurfacelayerofsolidK6C60.
Bandgapisreduced!
MolecularOrbitalStructureisconserved!
R. Hesper, et al Strongly reduced band gap in a correlated insulator in close proximity to a metalEurophysics Letters 40, (1997) 177-182.
S. Altieri, et al. Reduction of Coulomb and charge transfer energies in oxide films on metals Phys. Rev. B59 (1999) R2517-2520.
polarizabilityinTMcompoundsisverynonuniform
Thedielectricconstantisafunc1onofr,r’,wandnotonlyr‐r’,wandsoIsafunc1onofq,q’,w
Stronglocalfieldcorrec1onsforshortrangeinterac1onsMeindersetalPRB52,2484(1995)VandenBrinketalPRL75,4658(1995)
arXiv:0808.1390Heavyanionsolva?onofpolarityfluctua?onsinPnic?desG.A.Sawatzky,I.S.Elfimov,J.vandenBrink,J.Zaanen
arXiv:08110214vElectronicpolaronsandbipolaronsinFe‐basedsuperconductorsMonaBerciu,IlyaElfimovandGeorgeA.Sawatzky
HomogeneousMaxwellEqua?ons
(r,r’)—>(r–r’)—>(q)
Okifpolarizabilityisuniform
InmostcorrelatedelectronsystemsandmolecularsolidsthepolarizabilityisactuallyVeryNONUNIFORM
Effec?veHamiltonianscanbemisleading
• Hubbardlikemodelsarebasedontheassump?onthatlongerrangecoulombinterac?onsarescreenedandtheshortrangeonsiteinterac?onsremain
• HoweverUfortheatomisabout20eVbutUasmeasuredinthesolidisonlyoforder5eVandforthepnic?desevenlessthanthis
• HOWISTHISPOSSIBLE?
Reduc?onofonsiteinterac?onsandchangingthenearestneighborinterac?onswithpolarizableionsinalaHce
Weassumethattheholeandelectronmoveslowlycomparedtotheresponse?meofthepolarizabilityoftheatoms.Notetheoppositelypolarizedatomsnexttotheholeandextraelectron
Sothereduc?onoftheHubbardUinapolarizablemediumlikethisintroducesastrongNextnnrepulsiveinterac?on.Thischangesourmodel!!
Foradifferentgeometryactuallytheintersiteinterac?oncanalsobestronglyreducedperhapsevenAJrac?ve(FePnic?des)
Rest comes from bond Polarization involving O 2p and TM 4s states
Noteshortrangeinterac?onsarereduced“screened”andintermediaterangeinterac?onsareenhancedoran?screened‐quiteoppositeto
conven?onalwisdominsolidstatephysics
JeroenvandenBrinkThesisUofGroningen1997
Usingnonuniformpolarizabilityinar?ficiallyengineeredstructures?
UseanFeAslayerasinLaFeAsOasanexample
Nowtocompounds
• InTMcompoundstheTMisweaklypolarizablewhiletheanionsarestronglypolarizable
• Thechargemo?onisusuallyontheca?oni.eTMion.
• Sothepolarizableen??esarenottheonesonwhichthemobilechargeresides.
• Asforionsinpolarsolvents
Iwillshowthat
• Thepolarizabilityofanionsresultsinastrongreduc?onoftheHubbardonsiteU
• Thechargedcarrierslivingontransi?onmetalionsaredressedbyvirtualelectronholeexcita?onsontheanionsresul?nginelectronicpolarons
• Thenearestneighborcoulombinterac?onscanbeeitherscreenedoran?screeneddependingonthedetailsofthestructure
+
eћ ћ
e
—
PES(EI) IPES(EA)
Fullpolariza?oncandevelopprovidedthatDynamicResponseTimeofthepolarizablemediumisfasterthan
hopping?meofthecharge
E(polarizability)>W;EMOenergyspliHnginmolecules,plasmafrequencyinmetals‐‐‐‐‐
APictureofSolva?onofionsinapolarizablemedium
WearealivebecauseofSolva?on
Ionsbothposi?veandnega?veinourbodiesregulatemosteverything
Reduc?onofUduetopolarizabilityofO2‐(SOLVATION)
U = EITM – EA
TM -2Epol
EI ionization energy EA electron affinity energy
Epol = 2 For6nnofO2‐~13eVFor4nnAs3‐~17eV
ELECTONICPOLARON
Whataboutintersiteinterac?onV?
Forpnic?destheFe‐As‐Fennbondangleis~70degreesThereforethecontribu?ontoVisaJrac?ve~4eV
CanberepulsiveoraJrac?vedependingonbondangle
Polariza?oncloudForTwochargesonNeighboringFe“ELECTRONIC
BIPOLARON
Roughes?mateAtomicorionicpolarizability~volume
• Consideratom=nucleusatthecenterofauniformlychargesphereofelectrons
• InafieldEadipolemomentisinducedP=αE
• ForZ=1and1electronrestoringforce=
WhatstheimportanceofAsorP?
• Verylargeanions• Electronicpolarizabili?esroughlyequaltovolume
• 4porbitalshave2radialnodes–verydiffuse• Weakhybridiza?onwithhighlydirectedlocalFe3dorbitals(frombandtheory)
• LargepolarizabilitystronglyreducesUonFeandthenearestneighborinterac?onVbetweenFe3d
SomeearlierpapersonpolarizabiiityMeindersetalPRB52,2484(1995)VandenBrinketalPRL75,4658(1995)J.vandenBrinketalEurophysicsLeJers50,447(2000)
ComparisonofCupratesandPnic?desTheroleofpolarizableheavyanions
GeorgeSawatzkyPhysicsandastronomydept.
UBCVancouverBCCanada
AreCupratesandPnic?desreallysimilar?
Cuprates• LocalmomentsS=1/2
• Largecrystalfield>dbanddispersion
• LargesuperexchangeAn1ferromagne1c
• ChargetransfergapsnotMoZHubbard
• Chargecarriersmostlyofanionpcharacter
• StrongCu3d‐O2phybridiza1on• 2Dimensional• Noorbitaldegreesoffreedom
FePnic1des
• SmallvariableamplitudeSDW
• Smallcrystalfields<Fedbanddispersion
• Someevidenceoflargespinwavedispersion
• ReportssupportsmallMoZHubbardgapifany
• ChargecarriersFedelectronsandholes
• Rela1velyweakFe3d‐As4phybrid.
• Weakanisotropy(pen.depth)
• Possibleorbitalordering
WhatwouldtheFe3dstateslooklikeifwestartedinthesamewayasinthe
Cuprates?
As
Fe
NotlayeredlikeTiS2!!thesurfaceasdrawnisPOLAR!!
~Tetrahedralcoordina?onCrystalfieldspliHngIsinvertedascomparedtoOctahedral
Ba122MarkGoldenB455,and218surfaceBaordering
Localcrystal/ligandfieldpictureasinCuprates?
Bandtheory‐Cystal/ligandfieldspliHngisnotverylargeAndlessimportantthanthe3dbandstructure.
Verydifferentfromthecuprates!!
ElectronicStructureofLaOFeAsbandtheory(Elfimov)
GGA;nonmagne?c
FatbandsshowAs4pcharacter
MTRadii(A):
La 1.22
Fe 1.01
As 1.38
O 1.11
CorrelatedElectronsinaSolid
• J.Hubbard, Proc. Roy. Soc. London A 276, 238 (1963) • ZSA, PRL 55, 418 (1985)
dn dn dn-1 dn+1 U :
p6 dn p5 dn+1 Δ :
U = EITM – EA
TM - Epol
Δ = EIO – EA
TM - Epol + δEM
EI ionization energy EA electron affinity energy EM Madelung energy
Cu (d9)
O (p6)
Epol depends on surroundings!!!
Sincethepurepnic?deslikeLaFeAsO,BaFe2As2,etcare(bad)metalswe
wouldhavetoconcludethatU<the3dbandwidth
HowevertheTdependentconduc?vityandmagne?csuscep?bili?esare
strange
arXiv:0808.0708 LaFeAsO$_{1-x}$F$_x$ R. Klingeler et al IFW Dresden)
Howcanweexplainthelowstronglyvaryingmagne?cmoment?
• LowHubbardUi.e.U<3dbandwidth‐strongpolarityfluctua?ons–reducetheeffectofJH
• Bandwidthisabout2‐3eVsoU~2‐3eV?• Howdowereduceanonsiteinterac?onfromabout20eVinthefreeiontolessthan2eV?
• Alargecontribu?onisthePolarizabilityoftheanion!!!
2levelmodelforthedynamichighfrequencypolarizabilityandmo?onof
thepolaron/bipolaron
UseatwolevelmodelofAsi.e.4poccupiedand5sempty.InanelectricfieldduetothepointchargetheymixyieldingThepictureswedrawofthepolariza?oncloud.
MonaBerciuetalPRBinpress
=4p‐5sexcita?onenergy
BecauseOmegaisahighenergywecanuseperturba?ontheory
intasthesmallestWeassumeonlyonepar?clesothatU
isnotac?ve
TheelectronicPolaroneigenenergiesaregivenby
WeusetheknowelectronicpolarizabilityofAstodeterminegForsmallgi.e.inthelinearregime.g=2.5eVforα=10cubicA
TheMo?onofasinglequasipar?cleThesemovelikeelectronicpolarons
i.e.theoverlapintegralofthepolariza?onclouds
Theeffec?vepolaronmassissimplyt/teff=2.2thisislightcomparedtoconven?onallaHcepolaronmasses
AngularresolvedphtoemissioncomparisonwithLDALaFePOLuet.alNature455,812008
NOTEThebandtheoryresulthasbeenshi~edupby0.11eVandscaleddownbyafactorof2.2
Howaboutthereduc?onofthecoulombinterac?onsbetweentwo
electronsonFesites?
Canthisleadtobipolaronicboundstates?Andifsowhatistheirmass
Notethatthebipolaronmassisonly8?mesthefreepar?clemassthisIsagainmuchlighterthanforlaHcebipolaronsallowingforaneventualhighBoseEinsteincondensa?onT.
Systema?csofTc
• Tcvaria?onwithbondanglesbondlengthsandpolarizabili?es
• Notethato~entheAs‐Fe‐Asbondangleisusedortheorthorhombicdistor?onintheplaneortheFe‐As‐Fediagonalbondangleisusedforsystema?cs.
• OurmodelsuggestsratherusingbondlengthsandtheFe‐As‐Fenearestneighborbondangle
Effec?veinterac?onploJedvslogTc
Conclusions• TheFepnic?desandheavyanionchalcogenidesareverydifferent
fromthecuprateswithregardtolowenergyscaleproper?es:spin,charge,orbital,andlaHcedegreesoffreedom
• Hybridiza?oncovalencyinvolvingFe3disweakcrystalandligandfieldsaresmall,electronicstructuregivenbybandstructurewithweakcorrela?on
• WesuggestthattheAs4p–Fe4sand4phybridiza?onandespeciallytheArsenicELECTRONICpolarizabilitysetthesceneforabandstructureapproach.
• Thequasipar?clesareelectronicpolaronswithamodestmassofabout2‐3withpossiblyanaJrac?venninterac?onresul?nginbipolaronswiths,ordwavesuperconduc?vityandalsoamodestmass
• DESIGN(ARTIFICIAL)STRUCTURESUSINGHIGHLYPOLARIZABLEATOMSORSMALLMOLECULESALTERNATINGWITHNARROWBANDMETALFILMFORHIGHERTc’s?
Materialdesignandlimita?ons
WhatdoesCodo?Dope???
Someotherexperimentalresults
• NeutronscaJeringyieldsorderedmomentsrangingfromverysmallto0.9µB
• Magne?corderingisan?ferromagne?cSDWlike1Dferromagne?cchainscoupledan?ferromagne?cally
• Neutroninelas?cscaJeringyieldsalargespinwavevelocityi.e.largeJbutalsoalargespinwavegapof10meVandthespinwavesareheavilydampedaboveabout30meV.“StonerCon?nuum?”
SinghetalFermisurfaceLaFeAsOLDA
Pleaseciteas:
GeorgeSawatzky:LecturedeliveredattheXIVTrainingCourseinthePhysics ofStronglyCorrelatedSystems,VietrisulMare(Salerno) Italy,October5–16,2009.
