Spectral flow in vortex dynamics of d-wave superconductors

We calculate Ohmic and Hall flux-flow conductivities in the mixed state of clean d-wave superconductors taking into account the spectral flow along the anomalous branch of the states bound to vortex cores. Two parameters governing the strength of the spectral flow at low temperatures are found. They are determined by the ratios of the width of the localized levels 1/τ and (1) the interlevel spacing in the core, and (2) Δ²₀/E_F. These parameters determine three regimes of vortex dynamics. In the moderately clean limit the contribution of the spectral flow to the conductivities coincides with that for s superconductors. In the superclean regime in low magnetic fields both Ohmic and Hall conductivities acquire τ-independent universal values. The contribution of the spectral flow in the superclean regime is suppressed in higher fields. Unusual temperature and magnetic-field dependence of the conductivity tensor is discussed.