Quasiparticle Hall transport of d-wave superconductors in the vortex state -: art. no. 224508

We present a theory of quasiparticle Hall transport in strongly type-II superconductors within their vortex state. We establish the existence of integer quantum spin Hall effect in clean unconventional d(x2-y2) superconductors in the vortex state from a general analysis of the Bogoliubov-de Gennes equation. The spin Hall conductivity sigma (s)(xy) is shown to be quantized in units of (h) over bar /8 pi. This result does not rest on linearization of the BdG equations around Dirac nodes and therefore includes inter-nodal physics in its entirety. In addition, this result holds for a generic inversion-symmetric lattice of vortices as long as the magnetic field B satisfies H-c1<<B <<H-c2. We then derive the Wiedemann-Franz law for the spin and thermal Hall conductivity in the vortex state. In the limit of T-->0, the thermal Hall conductivity satisfies kappa (xy) = (4 pi (2)/3)(k(B)/(h) over bar)T-2 sigma (s)(xy). The transitions between different quantized values of sigma (s)(xy) as well as relation to conventional superconductors are discussed.