Fluxoid Pinning in Nonideal Type II Superconductors. II. Time-Dependent Ginzburg-Landau Equations

Abstract

A set of usual Ginzburg-Landau Equations is extended to discuss a slowly time-dependent phenomenon such as a flux flow in nonideal type II superconductors. A Hamiltonian is composed of interaction terms between electrons and elastic strain fields, together with a usual Hamiltonian including the BCS potential for superconductors. A derivation of the Ginzburg-Landau equations started from the above Hamiltonian is carried out by the scheme of the GLAG theory, except that the strain field is dealt with semi-classically.
The extensions of the Ginzburg-Landau equations to the case of nonideal samples so far have been carried out in phenomenological ways, besides the existing ones are only applicable to static phenomena and cannot be used to discuss dynamic phenomena such as a flux flow.