Omar_Elementary Solid State Physics_Lecture12

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1、Chapter10:SuperconductivityFirstobservedin1911byH.K.Onnes:•resistivityofmercuryvanishedat4.2K(criticaltemperature,Tc)•newsuperconductingstatebelowTc•transitionsimilartophasetransitions,suchas:–vapor–liquidatthevaporizationpoint–ferromagnetictransitio

2、nattheCuriePoint•superconductingtransitionisreversible.Recallfrom§4.4:ρ=m/ne2τ=⇒resistivityofmetalτ=collisiontime:•ρ↓asT↓=⇒latticevibrationsbeginto“freeze”←−scatteringofelectronsdiminishes:τlonger=⇒ρsmaller.Ifτ−→∞,thenρ−→0.Thisiswhatisobservedinsuper

3、conductivity.BelowTc:•afractionoftheelectronsbecomesuperconducting(theyhaveinfinitecollisiontimes)=⇒theyundergonoscattering;•theseelectronsareresponsibleforsuperconductivity.OccurrenceofSuperconductivity(SC)•SCisnotrare(seeTable10.1):–exhibitedby27ele

4、mentsandmanyalloys•Tcvariesfrom0.01KforWto20.8KforNbAlGe.EmpiricalRules:•SCoccursonlyinsubstancesinwhich:valencenumberperatomisbetween2and8;•3,4.7,6.4(nearlyodd)areparticularlyfavorable=⇒higherTc;2,4,and5.6(nearlyeven)areparticularlyunfavorable•asmal

5、latomicnumber,plusasmallatomicmassfavorsSC.10.3PerfectDiamagnetism-MeissnerEffectIn1933MeissnerandOchsenfeldobserved:•aSCexpelsmagneticflux(seeFigure10.4)=⇒MeissnerEffect(ME)•MEisreversible.Magneticinductioninsidesubstance:B#=µ0(H#+M#)≡µ0(1+χ)H#H#=exter

6、nalmagneticfieldintensity,M#=magnetization,χ=magneticsusceptibility.2SinceB=0inSC:M=−H=⇒magnetizationisequaltoandopposedtoH=⇒χ≡χs=−1:Mediumisperfectlydiamagnetic.Innormalstate:−5

7、χn

8、∼

9、10

10、<<

11、χs

12、SomenewmechanismoperatesinSCstogive:suchanenormousdiamagne

13、tism.10.4TheCriticalFieldSuperconductivitycanbedestroyedbytheapplicationof:asufficientlystrongmagneticfield,calledthecriticalfield,Hc!Empiricalfinding(seeTable10.2):#$2THc(T)=Hc(0)1−=⇒CriticalfielddependsonT.Tc⇓Hc(T=0)=Hc(0)Hc(T=Tc)=0.Note:Criticalfield

14、neednotbeexternal.Acurrentflowinginasuperconductingringcreatesitsownmagneticfield:•ifcurrentlargeenoughsothatitsownfieldreachescriticalvalue,then:–SCisdestroyed=⇒•placeslimitonthestrengthofthecurrentwhichmayflowinaSC.310.5ThermodynamicsofSuperconductingT