Semiclassical theory for the orbital magnetic moment of superconducting quasiparticles

TL;DR

This paper develops a semiclassical theory for the orbital magnetic moment of superconducting quasiparticles, verifying it with quantum methods, and explores its effects on energy spectra, local density of states, and the orbital Nernst effect.

Contribution

It introduces a new semiclassical formula for the quasiparticle orbital magnetic moment in superconductors and demonstrates its implications through a chiral d-wave model.

Findings

Orbital magnetic moment is not generated solely by pairing gap structure.

The semiclassical approach matches quantum linear response calculations.

Orbital magnetic moment influences the energy spectrum and induces an orbital Nernst effect.

Abstract

We study the orbital magnetic moment of Bogoliubov quasiparticles in superconductors with the semiclassical approach. We derive the orbital magnetic moment of a quasiparticle wavepacket by considering the energy correction of the wavepacket to the linear order of the magnetic field. The semiclassical result is further verified by a linear response calculation with a full quantum mechanical method. From the analytical expression we find that nontrivial structure in the superconducting pairing gap alone is unable to produce quasiparticle orbital magnetic moment, which is in sharp contrast to the behavior of quasiparticle Berry curvatures. We apply the formula to study a tight-binding model with chiral $d$-wave superconducting gap, and show the influence of orbital magnetic moment on the energy spectrum and local density of states. We also calculate the orbital Nernst effect driven by the interplay between the orbital magnetic moment and the Berry curvature of Bogoliubov quasiparticles.