a model of marginal fermi liquid superconductor at two dimensionsnew

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1、AmodelofmarginalFermiliquidsuperconductorattwodimensionsYu-LiangLiuandT.K.NgDepartmentofPhysics,HongKongUniversityofScienceandTechnology,ClearWaterBay,Kowloon,HongKong,People’sRepublicofChinaAbstractInthispaperwestudyamodelofs-wavemarginalFermiliquidsupercon-duct

2、orattwodimensions.BesidestheusualBardeen-Cooper-Schrieffer(BCS)pointattractiveinteraction,thefermionsinoursystemalsointeractviaalongrangerepulsiveinteractionv(q)=gD/q2.Wefindthatalthoughsu-perconductivityisnotdestroyedbythelong-rangedrepulsioninteraction(demonstrat

3、edbytheexistenceofMeissnereffect),neverthelesstheBCSpairingfunction∆BCSisstronglysuppressedresultinginpower-lawcorre-lation<∆BCS(~x)∆BCS(0)>∼

4、~x

5、−2γ.ThisobservationisexplainedwithinageneralpictureofmarginalFermiliquid.71.10.Hf,74.20.-z,74.25.-qarXiv:cond-mat/99081

6、62v1[cond-mat.supr-con]11Aug1999TypesetusingREVTEX1Sincethediscoveryofhigh-Tcsuperconductors,therehasbeenenormousinterestsinthestudyofnon-Fermiliquidtheoriesintwodimensions[1–3].Thenormalstateofhigh-Tcsuperconductorsshowsrichphysicalbehaviorswhichseemstodeviatefr

7、omusualLandauFermiliquidtheorypredictions.Forexample,intheoptimallydopedregime,resistivityshowsalineartemperaturedependence,whereasinunderdopedregime,theresistivityshowsapower-lawtemperaturedependence,andwithapseudo-gapinlowenergyexcitationspec-trum.Althoughthere

8、existsalotoftheoreticalstudiesonmicroscopictheoriesofnon-Fermiliquidnormalstates,atpresentthereexistsveryfewsystematicinvestigationintohowthesuperconductingstateisaffectedbynon-Fermiliquidbehaviours.Inthispaperwestudyamicroscopicmodelofs-wavemarginalFermiliquidsup

9、er-conductorattwodimensions.TheHamiltonianofourmodelconsistsoftwoparts,H=Hmfl+HBCS,whereX1X†Hmfl=ǫ(k)ψσ(~k)ψσ(~k)+2v(q)ρ(~q)ρ(−~q),(1a)2L~k,σ

10、~q

11、≤qcandZ2††∗12HBCS=−dx[∆(~x,t)ψ↓(~x,t)ψ↑(~x,t)+∆(~x,t)ψ↑(~x,t)ψ↓(~x,t)−

12、∆(~x,t)

13、](1b)Uk2P††whereǫ(k)=2m−µ,ρ(~x)=σψσ(~x)

14、ψσ(~x)istheelectrondensityoperator,ψσ(~x)(ψσ(~x))areelectronicannihilation(creation)operatorswithspinσ=↑,↓,L2isthevolumeofthesystem,q<