1 PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 34: Special Topics in Electrodynamics: Electromagnetic aspects of superconductivity  London equations  Tunneling between two superconductors 04/20/2015PHY 712 Spring Lecture 34

204/20/2015PHY 712 Spring Lecture 34

04/20/2015PHY 712 Spring Lecture 343 London model of superconducting state

04/20/2015PHY 712 Spring Lecture 344 London model, continued

04/20/2015PHY 712 Spring Lecture 345 London model – continued

04/20/2015PHY 712 Spring Lecture 346 Behavior of superconducting material – exclusion of magnetic field according to the London model x L

04/20/2015PHY 712 Spring Lecture 347 Magnetization field (At T=0K)

04/20/2015PHY 712 Spring Lecture 348 Magnetization field (for “type I” superconductor at T=0K) H B HCHC -4  M HCHC G S -G N HCHC H H

04/20/2015PHY 712 Spring Lecture 349 Temperature dependence of critical field From PR 108, 1175 (1957) Bardeen, Cooper, and Schrieffer, “Theory of Superconductivity” characteristic phonon energy density of electron states at E F attraction potential between electron pairs

04/20/2015PHY 712 Spring Lecture 3410 Type I elemental superconductors

04/20/2015PHY 712 Spring Lecture 3411 Quantization of current flux associated with the superconducting state (Ref: Ashcroft and Mermin, Solid State Physics)

04/20/2015PHY 712 Spring Lecture 3412 Quantization of current flux associated with the superconducting state -- continued dl Suppose a superconducting material has a cylindrical void. Evaluate the integral of the current in a closed path within the superconductor containing the void. Such “vortex” fields can exist within type II superconductors.

04/20/2015PHY 712 Spring Lecture 3413 Josephson junction -- tunneling current between two superconductors (Ref. Teplitz, Electromagnetism (1982)) d BzBz x

04/20/2015PHY 712 Spring Lecture 3414 Josephson junction -- continued BzBz Supercon left Supercon right Junction d

04/20/2015PHY 712 Spring Lecture 3415 Josephson junction -- continued AyAy Supercon left Supercon right Junction d

04/20/2015PHY 712 Spring Lecture 3416 Josephson junction -- continued d x LR Coupling parameter

04/20/2015PHY 712 Spring Lecture 3417 Josephson junction -- continued

04/20/2015PHY 712 Spring Lecture 3418 Josephson junction -- continued x LR JLJL JRJR JTJT

04/20/2015PHY 712 Spring Lecture 3419 Josephson junction -- continued x LR JLJL JRJR JTJT

04/20/2015PHY 712 Spring Lecture 3420 Josephson junction -- continued x LR JLJL JRJR JTJT

04/20/2015PHY 712 Spring Lecture 3421 Josephson junction -- continued x LR JLJL JRJR JTJT

04/20/2015PHY 712 Spring Lecture 3422 Josephson junction -- continued ITIT   Note: This very sensitive “SQUID” technology has been used in scanning probe techniques. See for example, J. R. Kirtley, Rep. Prog. Physics 73, (2010). SQUID =superconducting quantum interference device

04/20/2015PHY 712 Spring Lecture 3423 Scanning SQIUD microscopy Ref. J. R. Kirtley, Rep. Prog. Phys (2010)

04/20/2015PHY 712 Spring Lecture 3424