Vortex-Core Charging Due to the Lorentz Force in a $d$-Wave Superconductor

TL;DR

This paper develops a theoretical framework to calculate vortex-core charge in $d$-wave superconductors, revealing its dependence on Fermi surface properties and temperature, with implications for high-$T_c$ materials.

Contribution

The authors derive augmented quasiclassical equations incorporating the Lorentz force, enabling quantitative analysis of charge redistribution in vortex cores.

Findings

Vortex-core charge depends on Fermi surface curvature and gap anisotropy.

The charge can change sign with temperature.

Numerical results confirm the theoretical predictions for high-$T_c$ superconductors.

Abstract

We derive augmented quasiclassical equations of superconductivity with the Lorentz force in the Matsubara formalism so that the charge redistribution due to supercurrent can be calculated quantitatively. Using it, we obtain an analytic expression for the vortex-core charge of an isolated vortex in extreme type-II materials given in terms of the London penetration depth and the equilibrium Hall coefficient. It depends strongly on the Fermi surface curvature and gap anisotropy, and may change sign even as a function of temperature due to the variation in the excitation curvature under the growing energy gap. This is also confirmed in our numerical study of high-$T_{\rm c}$ superconductors.