Nonlocal free energy of a spatially inhomogeneous superconductor

TL;DR

This paper develops a microscopic approach to derive a nonlocal free energy functional for spatially inhomogeneous superconductors in magnetic fields, generalizing Ginzburg-Landau theory to all temperatures.

Contribution

It introduces a new microscopic method to obtain a nonlocal free energy functional applicable at any temperature and for arbitrary spatial variations of the order parameter.

Findings

Derived a general free energy functional for inhomogeneous superconductors

Explicitly analyzed extremals at low and high temperatures

Showed nonlocal magnetic response arises from order parameter nonlocality

Abstract

The microscopic approach was developed for obtaining of the free energy of a superconductor with help direct calculation of the vacuum amplitude. The functional of free energy of the spatially inhomogeneous superconductor in a magnetic field was obtained with help the developed approach. The obtained functional is generalization of Ginzburg-Landau functionals for any temperature, for arbitrary spatial variations of the order parameter and for the nonlocality of the order parameter and the magnetic response. Moreover the nonlocality of the magnetic response is the consequence of the order parameter's nonlocality. The extremals of this functional are considered in the explicit form in the low-temperature limit and in the high-temperature limit at the condition of slowness of spatial variations of the order parameter.