gradient expansion approach to multiple-band fermi liquidsnew

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1、Gradientexpansionapproachtomultiple-bandFermiliquidsRyuichiShindou1,∗andLeonBalents11DepartmentofPhysics,UniversityofCalifornia,SantaBarbara,California93106,USA(Dated:today)PromotedbytherecentprogressofBerryphasephysicsinspingalvanomagneticcommunities,wedevelopasystematicderivationofthe

2、reducedKeldyshequation(RKE)whichcapturesthelow-energydynamicsofquasi-particlesconstrainedwithindoublydegeneratebandsformingasingleFermisurface.ThederivationbeginswiththeKeldyshequationforaquitegeneralmultiple-bandinteractingFermisystems,whichisoriginallyanNbbyNbmatrix-formedintegral(ori

3、nfinite-orderdifferential)equation,withNbbeingthetotalnumberofbands.ToderivetheRKEforquasi-particleonaFermisurfaceinquestion,weprojectoutthefullyoccupied/emptybanddegreesoffreedomperturbativelyinthegradientexpansion,whosecouplingconstantmeasureshowasystemisdisequi-librated.Asfortheelectro

4、n-electroninteractions,however,weonlyemploytheso-calledadiabaticassumptionoftheFermiliquidtheory,sothattheelectroncorrelationseffectontotheadiabatictransportofquasi-particles,i.e.thehermitian(real)partoftheself-energy,istakenintoaccountinanunbiasedmanner.TheRKEthusderivedbecomesanSU(2)co

5、variantdifferentialequationandtreatsthespinandchargedegreesoffreedomonanequalfooting.Namely,thequasi-particlespinprecessionsduetothenon-abeliangaugefieldsareautomaticallyencodedintoitscovariantderivatives.Whenfurthersolvedinfavorofspectralfunctions,thiscovariantdifferentialequationalsosugg

6、eststhatquasi-particlesonadoublydegenerateFermisurfaceacquirespin-selectiveBerrycurvaturecorrectionsundertheappliedelectromagneticfields.ThistheoreticalobservationgivesussomehintsofpossibleexperimentalmethodologyformeasuringtheSU(2)Berry’scurvaturesbyspin-resolvedphotoemissionexperiments

7、.Duetothenon-trivialfrequencydependenceof(thehermitianpartof)selfenergy,ourRKEiscomposedofBerry’scurvaturesinthed+1dualspace,i.e.k-ωspace,sothatthedualelectricfieldisalreadyintroduced.Toprovideasimplewaytounderstandthis“temporal”componentoftheU(1)Berry’scurvature,wealsoprovideth