Bogomolnyi-type bounds in unconventional superconductors without external magnetic fields

TL;DR

This paper develops a method to establish rigorous lower bounds on the Landau-Ginzburg free energy in unconventional superconductors without external magnetic fields, enhancing understanding of their magnetic stability.

Contribution

It introduces a novel approach for deriving Bogomolnyi-type bounds in the absence of external fields, improving stability analysis of superconducting states.

Findings

Derived new stability conditions for homogeneous states

Established bounds for inhomogeneous equilibrium states

Enhanced understanding of magnetic instabilities in superconductors

Abstract

Following Bogomolnyi's classical treatment of vortices, we develop a method for finding rigorous lower bounds to the Landau-Ginzburg free energy describing unconventional superconductors in the absence of external magnetic fields. This allows a more precise description of the magnetic instabilities previously considered in these systems. In particular, we derive new sufficient conditions for the stability of both the homogeneous and inhomogeneous equilibrium states.