Abstract
The energy gap equation and the current density expression for a superconductor in a slowly varying static magnetic field are derived on the basis of a generalization of Nambu's Green's function formalism to finite temperatures. In the integral equation for the quasiparticle Green's function , expansions of , the self-energy part , and the vector potential A, about the center-of-mass coordinates R, are introduced. The integral equation is solved by iteration, and the contributions of all orders in the gap are summed up. With the help of , the generalized Ginzburg-Landau-Gor'kov (GLG) equations, valid at all temperatures for slowly varying A(R) and , are derived. For temperatures near , correction terms to the coefficients of the GLG equations occur which are proportional to powers of . For temperatures near 0°K, the function multiplying the term behaves like . The first-order correction to the term proportional to is found to be proportional to , for near and near 0°K (H=magnetic field strength, ). Our results are consistent with the formula of Nambu and Tuan for the reduction of the gap at 0°K in the London region.
- Received 10 June 1963
DOI:https://doi.org/10.1103/PhysRev.132.595
©1963 American Physical Society