Impurity bands, line nodes, and anomalous thermal Hall effect in Weyl superconductors

We investigate the anomalous thermal Hall effect (ATHE) in Weyl superconductors realized by the ${E}_{1u}$ ($p$ wave and $f$ wave) chiral superconducting order for the point group ${D}_{6h}$. Using the quasiclassical transport theory, we analyze the influence of the impurity scatterings and the line-nodal excitations on the ATHE. We compare the extrinsic (impurity-induced) ATHE with the intrinsic (topological) ATHE to identify the dominant contribution. Because the transverse response is sensitive to the slope in the density of states (DOS) at the Fermi energy, the extrinsic ATHE vanishes in both the Born (weak impurity potential) and unitarity (strong impurity potential) limits. The amplitude of the impurity contribution to the thermal Hall conductivity (THC) reaches maximum between these limits when the slope of the DOS becomes large due to impurity bands near the Fermi energy. In such situations, the extrinsic ATHE dominates the intrinsic ATHE even at low temperatures. The extrinsic ATHE is sensitive to line-nodal excitations, whereas the intrinsic ATHE is insensitive to bulk excitations. When line nodes involve the sign change of the order parameter, the impurity contribution to the THC is suppressed even though the phase space for low-energy excitation is large. In contrast, if line nodes are not accompanied by such sign changes, the extrinsic ATHE is significantly enhanced. Our results form a basis for the comprehensive analysis of anomalous thermal transport in Weyl superconductors.