Ginzburg-Landau surface energy of multiband superconductors: Derivation and application to selected systems

TL;DR

This paper derives the surface energy of multiband superconductors using Ginzburg-Landau theory, analyzing its dependence on material parameters and applying it to systems like MgB₂ and metallic hydrogen.

Contribution

It provides a comprehensive multiband Ginzburg-Landau framework for calculating interface energy and critical magnetic fields, including complex cases with phase frustration.

Findings

Surface energy depends on critical temperature, densities of states, and gap functions.

Numerical analysis reveals conditions for positive or negative surface energy.

Application to MgB₂ and metallic hydrogen demonstrates practical relevance.

Abstract

We determine the energy of an interface between a multiband superconducting and a normal half-space, in presence of an applied magnetic field, based on a multiband Ginzburg-Landau (GL) approach. We obtain that the multiband surface energy is fully determined by the critical temperature, electronic densities of states, and superconducting gap functions associated with the different band condensates. This furthermore yields an expression for the thermodynamic critical magnetic field, in presence of an arbitrary number of contributing bands. Subsequently, we investigate the sign of the surface energy as a function of material parameters, through numerical solution of the GL equations. Here, we consider two distinct cases: (i) standard multiband superconductors with attractive interactions, and (ii) a three-band superconductor with a chiral ground state with phase frustration, arising from repulsive interband interactions. Furthermore, we apply this approach to several prime examples of multiband superconductors, such as metallic hydrogen and MgB$_2$, based on microscopic parameters obtained from first-principles calculations.