Effective Vortex Mass from Microscopic Theory

TL;DR

This paper calculates the effective mass of a vortex in a BCS superconductor using a microscopic approach, revealing temperature-dependent behavior and the significance of core state transitions.

Contribution

It introduces a self-consistent numerical method to determine vortex mass from spectral functions derived from BdG eigenstates, a novel microscopic calculation.

Findings

Vortex mass at zero temperature is about the electron mass times (k_f ξ_0)^2.

Transitions between core states dominate the vortex mass.

Vortex mass peaks at around 0.5 T_c and vanishes at T_c.

Abstract

We calculate the effective mass of a single quantized vortex in the BCS superconductor at finite temperature. Based on effective action approach, we arrive at the effective mass of a vortex as integral of the spectral function $J(\omega)$ divided by $\omega^3$ over frequency. The spectral function is given in terms of the quantum-mechanical transition elements of the gradient of the Hamiltonian between two Bogoliubov-deGennes (BdG) eigenstates. Based on self-consistent numerical diagonalization of the BdG equation we find that the effective mass per unit length of vortex at zero temperature is of order $m (k_f \xi_0)^2$ ($k_f$=Fermi momentum, $\xi_0$=coherence length), essentially equaling the electron mass displaced within the coherence length from the vortex core. Transitions between the core states are responsible for most of the mass. The mass reaches a maximum value at $T\approx 0.5 T_c$ and decreases continuously to zero at $T_c$.