Hall Effect in the Abrikosov Lattice of Type-II Superconductors

TL;DR

This paper investigates vortex charging and Hall voltage in the Abrikosov lattice of type-II superconductors, revealing how magnetic field influences charge accumulation within vortex cores through numerical analysis.

Contribution

The study introduces a numerical analysis of vortex charging in type-II superconductors using augmented quasiclassical equations, highlighting the field dependence of vortex core charge.

Findings

Vortex cores accumulate charge due to circulating supercurrent.

Charge density peaks near half of the upper critical field.

Estimated charge per vortex core at low temperatures.

Abstract

We study vortex charging caused by the Lorentz force on supercurrent based on the augmented quasiclassical equa- tions of superconductivity. Our numerical study on an s-wave vortex lattice in the range $H_{{\rm{c}}1} < H < H_{{\rm{c}}2}$ reveals that each vortex core with a single flux quantum also accumulates charge due to the circulating supercurrent and has a Hall voltage across the core. The field dependence of the charge density at the core center is well described by $H(H_{{\rm{c}}2}-H)$ with a peak near $H_{{\rm{c}}2}/2$ originating from competition between the increasing magnetic field and the decreasing pair potential. The peak value of the accumulated charge in a core region of radius $0.5\xi_0$ is estimated to be about $\eta\Delta_{0}/(k_{\rm F}\xi_0)\times|e|$ C per $\Delta z=1$ nm along the flux line at low temperatures, where $\eta\equiv\pi\epsilon_0\Delta z/|e|^2=1.09\times10^{18}$ ${\rm{J^{-1}}}$ with $e<0$ the charge of an electron, $\Delta_0$ the energy gap at $T=0$, $k_{\rm F}$ the Fermi wave number, and $\xi_0$ the coherence length at $T=0$.