12,000

We have over 12,000 students, from over 100 countries, within one of the safest campuses in the UK

93%

93% of Lancaster students go into work or further study within six months of graduating

Home > Research > Publications & Outputs > Boundary conditions for quasiclassical equation...
View graph of relations

« Back

Boundary conditions for quasiclassical equations in the theory of superconductivity

Research output: Contribution to journalJournal article

Published

Journal publication date1/03/1997
JournalPhysical Review B
Journal number9
Volume55
Number of pages7
Pages6015-6021
Original languageEnglish

Abstract

In this paper we derive effective boundary conditions connecting the quasiclassical Green's function through tunnel barriers in superconducting-normal hybrid (S-N or S-S') structures in the dirty limit. Our work extends previous treatments confined to the small transparency limit. This is achieved by an expansion in the small parameter r(-1) = T/2(1 - T) where T is the transparency of the barrier. We calculate the next term in the r(-1) expansion for both the;normal and, the superconducting case. In both cases this involves the solution of an integral equation, which we obtain numerically. While in the normal case our treatment only leads to a quantitative change in the barrier resistance Rb, in the superconductor case, qualitative different boundary conditions are derived. To illustrate the physical consequences of the modified boundary conditions, we calculate the Josephson current and show that the next term in the r(-1) expansion gives rise to the second harmonic in the current-phase relation.