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1、NSF-KITP-08-123PUPT-2278arXiv:0810.1563[hep-th]HolographicSuperconductorsSeanA.Hartnoll[,ChristopherP.Herzog]andGaryT.Horowitz[Je ersonPhysicalLaboratory,HarvardUniversityCambridge,MA02138,USA]DepartmentofPhysics,PrincetonUniversityPrinceton,NJ08544,USADepartmentofPhysics,UCSBSan
2、taBarbara,CA93106,USAhartnoll@physics.harvard.edu,cpherzog@princeton.edu,gary@physics.ucsb.eduAbstractIthasbeenshownthatagravitationaldualtoasuperconductorcanbeobtainedbyarXiv:0810.1563v1[hep-th]9Oct2008couplinganti-deSittergravitytoaMaxwell eldandchargedscalar.Wereviewourearlieran
3、alysisofthistheoryandextenditintwodirections.First,weconsiderallvaluesforthechargeofthescalar eld.Awayfromthelargechargelimit,backreactiononthespacetimemetricisimportant.Whilethequalitativebehaviourofthedualsuperconductorisfoundtobesimilarforallcharges,inthelimitofarbitrarilysmallc
4、hargeanewtypeofblackholeinstabilityisfound.Wegoontoaddaperpendicularmagnetic eldBandobtaintheLondonequationandmagneticpenetrationdepth.WeshowthattheseholographicsuperconductorsareTypeII,i.e.,startinginanormalphaseatlargeBandlowtemperatures,theydevelopsuperconductingdropletsasBisred
5、uced.Contents1Introduction22Thebulkequationsforaholographicsuperconductor43Normalandsuperconductingphases53.1Thehairyblackholeansatz...........................53.2Phasediagram..................................93.3Anewtypeofinstability.............................123.4Thehairyblackh
6、oleaction...........................134Conductivities144.1Formulaefortheconductivities.........................154.2Numericalresultsfortheconductivity.....................184.3Commentsongapsandpairing.........................225Criticalmagnetic elds235.1Superconductingdroplets.....
7、.......................245.2Thermodynamics.................................276Magneticallyinducedcurrentsinthesuperconductingphase306.1TheLondonequationatlowtemperatures...................316.2Thesuperconductorina nitemagnetic eld.................346.2.1Smallmagnetic elds..........
8、.................356.2.2Sm
