Hall Effect in the Abrikosov Lattice of Type-II Superconductors

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 $T=0$.