Hall Coefficient of Equilibrium Supercurrents Flowing inside Superconductors

TL;DR

This paper derives an analytic expression for the Hall coefficient in equilibrium supercurrents within superconductors, revealing how magnetic Lorentz forces induce charge distributions and electric fields, with implications for high-$T_c$ materials.

Contribution

It introduces an augmented quasiclassical framework including the Lorentz force, providing new insights into charge distribution and Hall effects in superconductors with anisotropic gaps.

Findings

Hall coefficient has the same sign and magnitude at zero temperature as the normal state for s-wave pairing.

Gap anisotropy can cause temperature-dependent sign changes in the Hall coefficient.

Sign change of the Hall coefficient may be observable in some high-$T_c$ superconductors.

Abstract

We study augmented quasiclassical equations of superconductivity with the Lorentz force, which is missing from the standard Ginzburg-Landau and Eilenberger equations. It is shown that the magnetic Lorentz force on equilibrium supercurrents induces finite charge distribution and the resulting electric field to balance the Lorentz force. An analytic expression is obtained for the corresponding Hall coefficient of clean type-II superconductors with simultaneously incorporating the Fermi-surface and gap anisotropies. It has the same sign and magnitude at zero temperature as the normal state for an arbitrary pairing, having no temperature dependence specifically for the s-wave pairing. The gap anisotropy may bring a considerable temperature dependence in the Hall coefficient and can lead to its sign change as a function of temperature, as exemplified for a model d-wave pairing with a two-dimensional Fermi surface. The sign change may be observed in some high-$T_{c}$ superconductors.