superconductivity

λp = λL ( j (r ) = −a js = −
ξ0 1/2 ) ξp ξp A (r ) ξ0
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m ∂ js ∂B )=− 2 ns e ∂t ∂t ∂ m [ ∇ × js + B ] = 0 ∂t ns e2 ∇×( Ï m ∇ × js + B = C ns e 2 ∇×( m js ) = −B ns e 2 4
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10
'9NaC 3÷X-‚Ha = Hij (T )þSi = Sj K dSi dSj = dT dT ‡©• dSi ∂Si ∂Si dHij )T =( )Ha + ( dT ∂T ∂Ha dT Ù'9N• ci = T ( '9NaC• cj − ci = T dHij (T ) ∂Sj ∂Si [( )T − ( )T ] dT ∂Ha ∂Ha ∂Si )H ∂T a
ξ0 • ƒZ• ݧ ξp •PippardƒZ• ݧŒ †,Ÿk'" Œ±wѧ,:r >6—Ý´Œ7T:ξ ålSA(r )È© Šû½ § Ø==2´::éA Û•'X" † ð Ž d ‰ • § éá § \ þ > . ^ ‡ §Pippard• § K þ Œ ± ¦ ч N ^|Ú>6©Ù" 'X 1 1 1 = + ξp ξ0 l Œ±• ξp ‘ X ² þ g d §l ~ Ý Œ¤§Bß Ýλ Œ" 94•½Ôí4• ξp ≈ l λ Pippard Bß Ý ~ " ² þ g d §l £ξp §,Ÿß
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∂E = µ0 js ∂t
m m js ) = ∇ × (∇ × B ) = −B 2 ns e ns µ0 e2
|^úªa@(b@c) =b(a#c) -c(a#b) ∇ × (∇ × B ) = ∇(∇ · B ) − ∇2 B ∇·B =0 B= λ2 = {z• 1 B=0 λ2 ù‡•§‡¦‡ NSÜB é¯P~•"" 3N «•≡ Be j ;3NS§÷v ∇2 B − 1 d2 By (x) − 2 by (x) = 0 2 dx λ >.^‡• By (x)|x=0 = Be = By (0) ) By (x) = By (0)e−x/λ x = λž § ^ | ® ² P ~ 5 λ½Â•Bß Ý" dL P~ ^| ) p >6 1/e§xŒ u A ‡λ §^|ž”§ m ∇2 B n s e 2 µ0 m ns e2 µ0
Superconductivity
Wang Jinlong June 13, 2014
1
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Ï~r>{â,C•" §Ý¡•‡ =C §Ý§½ .§Ý §PŠTC " ± Y > 6 { µò7႘u^|¥§ü$§Ý¦ ¬u)=C§Ý§, ’ ^|§ù´ )a)>6"XJ±LL«‚ ga§RL«>{§K L dI + IR = 0, I (t) = I (0)e−Rt/L dt
B Ï•E = 0,¤± ∂∂t = 0"ù`²B ≡ B0 §•dЩG û½" ‡ N%ØÓ§Šâ¢ •§B ≡ 0"òBd AL²ØC •U u"" ‡ NB ≡ 0 d>^Æúª
^Ï
B = µ0 (H + M ) Œ• M = −H qÏ• M = χH , B = µ H ^zÇχ = −1 ,^ ǵ = 0
cj − ci = T ( du
dHij 2 ∂Bj ∂Bi ) [( )T − ( )T ] dT ∂Ha ∂Ha ∂Bβ |H = ∞ ∂Ha c1
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11
5.2
GinzN" ‡ >f 1•dk żêψ (r)5£ " |ψ (r)|2 = ns (r), ψ (r) ns (r)eiϕ(r) ϕ(r)•ƒ §éu ~ƒψ (r) = 0 ùpM§ψ (r)†þfåÆ Å¼êkƒqƒ?"§£ã÷*‡ XÚ NG §=XÚ¥Œþ m∗ ,e∗ >fÑ/và03Ó˜þf þ§Ïd ‡ •^˜‡Ú˜ żê£ã" , §kïáG-L•§ 1 b µψ (r)´I“XÚkSz§Ý Së þ§ÙŠdU—Ýf 3²ïG 4 Šû½" ‡ Ú ~ gdUƒ Œ±Ðm•|ψ (r)|2 ˜?ê" "|e§3 .:Tc NC§ns → 0 Ðmª 3 1 ‘ 1 fs (0, T ) − fn (T ) = α(T )|ψ |2 + β (T )|ψ |4 + · · · 2 α,β ´=•6u§ÝT •ƒëþ§d²ï^‡ ∂f =0 ∂ns Ú α2 = µ0 Hc (T ) β Œ α=− ?Øk^| œ¹" g =f −B·H u´ 1 fs (0, T ) − fn (T ) = α(T )|ψ |2 + β (T )|ψ |4 + · · · 2
(
∂Si ∂Bi ∂ 2 Fi ∂Bi ∂Si )T = ( )T ( )T = −( )( )T ∂Ha ∂Bi ∂Ha ∂Bi ∂T ∂Ha
½Ha ÚT §Gi 7L´4 §Ïd ( = ( ∂Fi )H ,T = Ha ∂Bi a ∂Gi )H ,T = 0 ∂Bi a
( oĤ
∂Si ∂Ha ∂Bi )T = −( )Bi ( )T ∂Ha ∂T ∂Ha
Pippardu y , Ÿ ß Ý O Œ § = > f ² þ g d § á § ^ | 3 ‡ N ¥ Bß Ýλ •‘ƒOŒ"ù´dÔínØλL = m/ns e2 µ0 Ã{)º "• 7
Ÿoλ ¬‘X>f²þgd§l UCQº Pippard @•^|ÚåkSݽ‡ >f—Ý Cz§¿Ø•u^|B ß S§ ´u)3• ˜ ‰ŒS§ù«^|K• *Ð ‰š Û • A"ù‡*Ð ål^ξp 5L«§ ‰ƒZ •Ý" ξp “ L ‡ > f ' é å l § = u ) 3r : ? , « 6 Ä § Ø = K • r =f§ …ér :NCξp ‰ŒS >fѬkK•" r : ‡ > f — Ýns Ø = û u T : ^ | § •‡ dξp ‰ Œ S ˆ : ^ |5û½"éuXÀ ‡ N§ù‡ål‡ŒuλL . Pippard•§´Ô핧 šÛ•í2" Pippard•§ j (r , t) = Ù¥ a= 1 ns e2 = 2 m λ µ0 −3a 4πξ0 d3 r R[R · A(r )] −r/ξ0 e R4
µ0 js = ∇ × B òBy (x) = By (0)e−x/λ “\ òdB A Ÿ µŠâmÃÚ^{K§L ‡ >6 ^|3‡ N S† ^|‡•ƒž§ L 6Ä ‡ >6¶^|§¦ƒØ U?\§ù´/¤òdB A Ÿ" 5