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Hall Effect in the Abrikosov Lattice of Type-II Superconductors

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 $0.5ξ_0$ is estimated to be about $ηΔ_{0}/(k_{\rm F}ξ_0)\times|e|$ C per $Δz=1$ nm along the flux line at low temperatures, where $η\equivπε_0Δz/|e|^2=1.09\times10^{18}$ ${\rm{J^{-1}}}$ with $e<0$ the charge of an electron, $Δ_0$ the energy gap at $T=0$, $k_{\rm F}$ the Fermi wave number, and $ξ_0$ the coherence length at $T=0$.