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 equations of superconductivity. Our numerical study on an s-wave vortex lattice in the range Hc1 < H < Hc2 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 ρ(0) ∝ H(Hc2 − H) with a peak near Hc2/2 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 0.5ξ0 is estimated to be about ηΔ0/(kFξ0) × |e| C per Δz = 10 A along the flux line at low temperatures, where η ≡ πϵ0Δz/|e|2 = 1.09 × 1018 J−1 with e < 0 the charge of an electron, Δ0 the energy gap at T = 0, kF the Fermi wave number, and ξ0 the coherence length at T = 0.