2001/04/30 by Oskar Vafek, O. Vafek, A. Melikyan +3 · 1 citation
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat.supr-con
paper · pdf · doi:10.1103/physrevb.64.224508
published as PRB 64, 224508 (2001) · 18 pages REVTex, 3 figures, references added
arxiv created 2001/05/03 · openalex publication_date 2001/11/20 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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\ensuremath-y2 superconductors in the vortex state from a general analysis of the Bogoliubov--de Gennes equation. The spin Hall conductivity \ensuremathσxys is shown to be quantized in units of \ensuremath\Elzxh/8\ensuremathπ. 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 Hc1\ensuremath≪B\ensuremath≪Hc2. We then derive the Wiedemann--Franz law for the spin and thermal Hall conductivity in the vortex state. In the limit of \stackrel\ensuremath→T0, the thermal Hall conductivity satisfies \ensuremathκxy=(4\ensuremathπ2/3)(kB/\ensuremath\Elzxh)2T\ensuremathσxys. The transitions between different quantized values of \ensuremathσxys as well as relation to conventional superconductors are discussed.