Flux-flow Hall effect in clean type-II superconductors

We calculate the Ohmic and Hall components of the flux-flow conductivity for clean superconductors in a magnetic field H≪${\mathit{H}}_{\mathit{c}2}$ and investigate the sign of the Hall effect. Each component of the conductivity consists of two contributions: from electrons localized in the vortex cores, and from electrons above the gap. These contributions are determined by the parameters ${\mathrm{\omega }}_0$τ and ${\mathrm{\omega }}_{\mathit{c}}$τ, respectively, where ${\mathrm{\omega }}_0$∼${\mathrm{\Delta }}^2$/${\mathit{E}}_{\mathit{F}}$ is the distance between the energy levels in the vortex core, ${\mathrm{\omega }}_{\mathit{c}}$ is the cyclotron frequency (${\mathrm{\omega }}_{\mathit{c}}$≪${\mathrm{\omega }}_0$), and τ is the relaxation time. In the superclean limit, τ≫${\mathit{E}}_{\mathit{F}}$/${\mathrm{\Delta }}^2$, the Ohmic component is small and the Hall conductivity resembles that for the high-field regime in a normal metal. In a moderately clean case, ${\mathrm{\Delta }}^{\mathrm{-}1}$≪τ≪${\mathit{E}}_{\mathit{F}}$/${\mathrm{\Delta }}^2$, the Hall component is small. Its sign in the mixed state may differ from the sign in the normal state depending on the detailed structure of the Fermi surface. We conclude that the sign reversal can be intrinsic. We discuss implications of our results for mutual friction in superfluid ${}_{}{}^3{}_{}{}^{}\mathit{B}$.