Topological aspects of surface states in semiconductors are studied by an adiabatic deformation which connects a realistic system and a decoupled covalent-bond model. Two topological invariants are focused. One is a quantized Berry phase, and the other is

Typesetwithjpsj2.cls<ver.1.2>FullPaper

TopologicalAspectsofSurfaceStatesinSemiconductors

YoshihiroKuge1 ,IsaoMaruyama1 andYasuhiroHatsugai1,2

1

DepartmentofAppliedPhysics,Univ.ofTokyo,7-3-1Hongo,Bunkyo-kuTokyo113-8656,JAPAN

2

InstituteofPhysics,Univ.ofTsukuba,1-1-1Tennodai,TukubaIbaraki305-8571,JAPANTopologicalaspectsofsurfacestatesinsemiconductorsarestudiedbyanadiabaticdeforma-tionwhichconnectsarealisticsystemandadecoupledcovalent-bondmodel.Twotopologicalinvariantsarefocused.OneisaquantizedBerryphase,andtheotherisanumberoftheedgestates.Awindingnumberasanothertopologicalinvariantisalsoconsidered.ThesurfacestatesofSiandGeat(111),(110),and(100)surfacesareclassi edbythetopologicalinvariants.Sur-facestatesoftheGaAsasheterosemiconductorsarealsodiscussed.

arXiv:0802.2425v2 [cond-mat.str-el] 19 Feb 2008

KEYWORDS:semiconductorsurface,Berryphase,edgestate,danglingbond,Ge,Si,GaAs

1.Introduction

Forafewdecadesthetopologicalfeaturewhichdoesnotdependonthedetailofsystemshasbeenattractingattentioninthecondensedmatterphysics.OneofmostremarkableexamplesisaquantumHalle ect(QHE),1whereatopologicalinvariantknownastheChernnum-ber2hasbeenobservedexperimentally.TheChernnum-bersarede nedforabulkstatewithoutboundaries.IntheQHE,theedgestateswhicharecharacteristicforasystemwithboundaryalsohaveasigni canttopologicalimportance.3

Edgestatesorsurfacestates,whichlocalizeataboundaryofasystem,havesigni cante ectsinphys-icalphenomena;e.g.,thezerobiasconductancepeakstructureinanisotropicsuperconductivity,4,5single-layergraphite,6andtheboundarylocalmomentatanedgeofhexagonallybondedhoneycombsheetsconsistingofB,N,andCatoms.7Especially,inagraphene,itisnowwidelyunderstoodthatthereexistimportantedgestateswhicharerelatedtothechiralsymmetryofthesystemandtheDiracconespectrum.Inmetal-semiconductorin-terfaces,aninterfacestate,knownasthemetalinducedgapstate,hasanimportantroleinunderstandingFermi-levelpinning.8

Moreover,inrealisticmaterials,thereexistsasurfacereconstructionorasurfacerelaxation,whichissensitivetothedetailofsystems.However,weshalldiscussthattopologicalinvariantswhichisindependentofthedetailofmodelsisusefulforunderstandingthesurfacestatesof3dimensionalsemiconductors.Acandidateoftopologi-calinvariantsforsemiconductorsisthequantizedBerryphasewhichhasbeenproposedasalocalorderparam-eterforclari cationofthephaseofthegappedquan-tumliquids.Ithasbeendemonstratedthatquantizationofthislocalorderparameterhasanadvantageovertheusualorderparameterinafrustratedspinsystem,9andastronglycorrelatedsystem.10

Inthispaper,thequantizedBerryphaseisevaluatedforsurfacestatesintypicalsemiconductorssuchasSi,Ge,andGaAs.WenotethattheBerry(orZak)phase