Microscopic theory of phase transitions and nonlocal corrections for free energy of a superconductor

TL;DR

This paper develops a microscopic approach to phase transitions in superconductors, deriving a generalized free energy functional from first principles that accounts for arbitrary inhomogeneities and nonlocal magnetic effects.

Contribution

It introduces a novel microscopic method to derive the superconductor's free energy functional without artificial parameters, extending Ginzburg-Landau theory to broader conditions.

Findings

Derived a generalized free energy functional for superconductors.

Obtained explicit extremals in low and high-temperature limits.

Connected vacuum amplitude with thermodynamic potentials.

Abstract

The new approach to the microscopic description of the phase transitions starting from the only first principles was developed on an example of the transition normal metal-superconductor. This means mathematically, that the free energy is calculated in the range of temperatures, which includes a point of pase transition, without introducing any artificial parameters similar to an order parameter, but only starting from microscopic parameters of Hamiltonian. Moreover the theorems about connection of a vacuum amplitude with thermodynamics potentials are realized. The functional of a superconductor's free energy in a magnetic field was obtained with help the developed method. The obtained functional is generalization of Ginzburg-Landau functional for the case of arbitrary value of a gap, arbitrary spatial inhomogeneities and nonlocal magnetic response. The explicit expressions for the extremals of this functional were obtained in the low-temperature limit and the high-temperature limit at the condition of slowness of gap's changes.