Anomalous Hall Effects in Chiral Superconductors

Abstract

We report theoretical results for the electronic contribution to thermal and electrical transport for chiral superconductors belonging to even or odd-parity E${}_1$ and E${}_2$ representations of the tetragonal and hexagonal point groups. Chiral superconductors exhibit novel properties that depend on the topology of the order parameter and Fermi surface, and -- as we highlight -- the structure of the impurity potential. An anomalous thermal Hall effect is predicted and shown to be sensitive to the winding number, $\nu$, of the chiral order parameter via Andreev scattering that transfers angular momentum from the chiral condensate to excitations that scatter off the random potential. For heat transport in a chiral superconductor with isotropic impurity scattering, i.e., point-like impurities, a transverse heat current is obtained for $\nu =\pm 1$, but vanishes for $|\nu |>1$. This is not a universal result. For finite-size impurities with radii of order or greater than the Fermi wavelength, $R\ge \hslash /p_f$, the thermal Hall conductivity is finite for chiral order with $|\nu |\ge 2$, and determined by a specific Fermi-surface average of the differential cross-section for electron-impurity scattering. Our results also provide quantitative formulae for analyzing and interpreting thermal transport measurements for superconductors predicted to exhibit broken time-reversal and mirror symmetries.

29 pages, 11 figures

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Cited by in corpus (2)

• Observation of Anomalous Thermal Hall Effect in a Kagome Superconductor
• Impurity bands, line-nodes, and anomalous thermal Hall effect in Weyl superconductors