4/16/2014. PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107

Transcription

1 PHY 71 Elctroynmics 1-1:5 AM MWF Olin 17 Pln for ctur 3: Spcil Topics in Elctroynmics: Elctromgntic spcts of suprconuctivity -- continu 4/14/14 PHY 71 Spring ctur 3 1 4/14/14 PHY 71 Spring ctur 3 4/14/14 PHY 71 Spring ctur 3 3 1

2 4/14/14 PHY 71 Spring ctur 3 4 Bhvior of suprconucting mtril clusion of mgntic fil ccoring to th onon mol mc Pntrtion lngth for suprconuctor: 4 n / B (, t) B (, t) z z Vctor potntil for A : A yˆ Ay ( ) Ay ( ) Bz ( ) n / Currnt nsity: J y ( ) B z () mc n n J A or mv A = mc m c / Typiclly, 1 7 m 4/14/14 PHY 71 Spring ctur 3 5 Mgntiztion fil Trting onon currnt in trms of corrsponing mgntiztion fil M: B= H 4 M For, H 4 M Gibbs fr nrgy ssocit with mgntiztion for suprconuctor: H 1 GS ( H ) GS ( H ) HM ( H ) G () S H 8 Gibbs fr nrgy ssocit with mgntiztion for norml conuctor: G ( H ) G ( H ) N N Conition t phs bounry btwn norml n suprconucting stts: 1 GN ( HC ) GN () GS ( HC ) GS () HC 8 1 GS () GN () HC 8 1 H H for H H GS ( H ) GN ( H ) 8 for H H C C C 4/14/14 PHY 71 Spring ctur 3 6

3 Mgntiztion fil (for typ I suprconuctor) B -4M H C H G S -G N H C H C H H 4/14/14 PHY 71 Spring ctur 3 7 Empls of typ I suprconuctors 4/14/14 PHY 71 Spring ctur 3 8 4/14/14 PHY 71 Spring ctur 3 9 3

4 Josphson junction -- tunnling currnt btwn two suprconuctors B z 4/14/14 PHY 71 Spring ctur 3 1 Josphson junction -- continu Suprcon lft Junction Suprcon right B z ( /)/ B / Bz ( ) B / / ( /)/ B / 4/14/14 PHY 71 Spring ctur 3 11 Josphson junction -- continu Suprcon lft Junction Suprcon right A y ( /)/ B / / Ay ( ) B / / ( /)/ B / / 4/14/14 PHY 71 Spring ctur 3 1 4

5 Josphson junction -- continu Quntum mchnicl mol of tunnlling currnt t i t E i i i t t not wvfunction for Coopr pir on lft not wvfunction for Coopr pir on right E 4/14/14 PHY 71 Spring ctur 3 13 Josphson junction -- continu Solving for wvfunctions 1 i i i E t t 1 i i i E t t n n n n ( nn) sin t t E n cos t n E n cos t n 4/14/14 PHY 71 Spring ctur 3 14 Josphson junction -- continu n 4 Tunnling currnt: JT ( nn ) sin t E E If n = n n in bsns of mgntic fil, ( t) () t J J J A m c J A m c ltionship btwn suprconuctor currnts J n J n tunnling currnt. Within th suprconuctor, not th gnrliz currnt oprtor cting on pir wvfunction 1 vˆ i A m c i * * with currnt J vˆ vˆ 4/14/14 PHY 71 Spring ctur

6 Josphson junction -- continu J J J A nv m A nv J m c mv mv A A c c n 4 Tunnling currnt: JT ( nn) sin t N to vlut in prsnc of mgntic fil 4/14/14 PHY 71 Spring ctur 3 16 c Josphson junction -- continu J J m v mv A A c c cll tht for v n A / B yˆ for v n A / B yˆ Intgrting th iffrnc of th phs ngls lon g y : B ( ) y 4 Tunnling currnt: JT ( nn ) sin 4/14/14 PHY 71 Spring ctur 3 17 Josphson junction -- continu J J Intgrting th iffrnc of th phs ngls long y : ( ) 4 Tunnling currnt B nsity: y JT n sin Intgrting currnt nsity throughout with w of suprconuctors w/ sin( T h T y T sin( ) / w/ I J hwj whr B w( ) n / ) c 4/14/14 PHY 71 Spring ctur