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

摘要

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