Influence of the van Hove singularity on the specific heat jump in BCS superconductors

TL;DR

This paper derives how a van Hove singularity near the Fermi level affects the specific heat jump in BCS superconductors using Ginzburg-Landau theory, highlighting the impact of band structure on thermodynamic properties.

Contribution

It provides a general form of the Ginzburg-Landau coefficients considering a van Hove singularity, offering a new analytical expression for the specific heat jump in such systems.

Findings

Derived a general Ginzburg-Landau coefficient form near VHS

Obtained a simple expression for the specific heat jump influenced by VHS

Showed how band-specific gaps affect thermodynamic properties

Abstract

Within the weak-coupling BCS scheme we derive a general form of the coefficients in the Ginzburg-Landau expansion of the free energy of a superconductor for the case of a Fermi level close to a van Hove singularity (VHS). A simple expression for the influence of the VHS on the specific heat jump is then obtained for the case where gaps for different bands are distinct but nearly constant at the corresponding sheets of the Fermi surface.