Semiclassical theory for the orbital magnetic moment of superconducting quasiparticles

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.

12 pages, 3 figures

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