Physics – Condensed Matter – Superconductivity
Scientific paper
2001-04-26
PRB 64, 224508 (2001)
Physics
Condensed Matter
Superconductivity
18 pages REVTex, 3 figures, references added
Scientific paper
10.1103/PhysRevB.64.224508
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 $d_{x^2-y^2}$ 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 $\frac{\hbar}{8\pi}$. 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 $H_{c1} \ll B \ll H_{c2}$. We then derive the Wiedemann-Franz law for the spin and thermal Hall conductivity in the vortex state. In the limit of $T \to 0$, the thermal Hall conductivity satisfies $\kappa_{x y}=\frac{4\pi^2}{3}(\frac{k_B}{\hbar})^2 T \sigma^s_{xy}$. The transitions between different quantized values of $\sigma^s_{xy}$ as well as relation to conventional superconductors are discussed.
Melikyan Armen
Tesanovic Zlatko
Vafek Oskar
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