Effective Mass of a Vortex in a Clean Superconductor

TL;DR

This paper calculates the effective mass of a vortex in a clean superconductor at finite temperature, revealing how different electronic transitions contribute and diverge, and linking mass and friction through fermionic interactions.

Contribution

It introduces a spectral function-based method to compute vortex mass, highlighting the roles of various electronic transitions and their divergences near zero temperature.

Findings

Vortex mass is of order of displaced electron mass near T=0.

Extended states contribute a linearly divergent term to the mass.

Mass and friction originate from the same fermionic interaction mechanism.

Abstract

We calculate the effective mass of a single quantized vortex in the BCS superconductor at finite temperature. Using the effective action for a vortex, we arrive at the mass formula as the integral of the spectral function $J(\omega)/\omega^3$ over frequency. The spectral function is given in terms of the transition elements of the gradient of the Hamiltonian between Bogoliubov-deGennes eigenstates. We show that core-core, and core-extended transitions yield the vortex mass, near T=0, of order of electron mass displaced by the normal core. The extended-extended states contributions are linearly divergent with the low frequency cutoff $\omega_c$, in accordance with the Ohmic character of the spectral function at low energies. We argue that the mass and friction are closely related in this system and arise from the same mechanism - interaction with the surrounding fermionic degrees of freedom.