Is the diagonal part of the self-energy negligible within an isolated vortex in weak-coupling superconductors?

TL;DR

This paper investigates whether the diagonal self-energy term, often neglected in weak-coupling superconductivity, is significant within vortices, especially in odd-parity superconductors, revealing it can induce symmetry breaking.

Contribution

The study demonstrates that the diagonal self-energy is non-negligible within vortices in odd-parity superconductors, challenging traditional assumptions in weak-coupling theory.

Findings

Diagonal self-energy can be finite within vortices in odd-parity superconductors.

It can induce breaking of axisymmetry in chiral p-wave vortices.

Neglecting the self-energy may overlook important vortex properties.

Abstract

In the weak-coupling theory of superconductivity, the diagonal self-energy term is usually disregarded so that this term is already included in the renormalized chemical potential. Using the bulk solution, we can easily see that the term vanishes in the quasiclassical level. However, the validity of this treatment is obscured in non-uniform systems, such as quantized vortices. In this paper, we study an isolated vortex both analytically and numerically by the quasiclassical theory and demonstrate that the finite magnitude of the self-energy can emerge within a vortex in some odd-parity superconductors. We also find that the existence of diagonal self-energy can induce the breaking of axisymmetry of vortices in chiral p-wave superconductors. This implies that the diagonal self-energy is not negligible within a vortex in odd-parity superconductors in general, even in the weak-coupling limit.