Quantized thermal and spin transports of dirty planar topological superconductors

Abstract

Nontrivial bulk topological invariants of quantum materials can leave their signatures on charge, thermal, and spin transports. In two dimensions, their imprints can be experimentally measured from well-developed multiterminal Hall bar arrangements. Here, we numerically compute the low temperature (T) thermal (κxy) and zero temperature spin (σxysp) Hall conductivities, and longitudinal thermal conductance (Gxxth) of various prominent two-dimensional fully gapped topological superconductors, belonging to distinct Altland-Zirnbauer symmetry classes, namely p+ip (class D), d+id (class C), and p±ip (class DIII) paired states, in mesoscopic six-terminal Hall bar setups from the scattering matrix formalism using kwant. In both clean and weak disorder limits, the time-reversal symmetry breaking p+ip and d+id pairings show half-quantized and quantized κxy [in units of κ0=π2kB2T/(3h)], respectively, while the latter one in addition accommodates a quantized σxysp [in units of σ0sp=ℏ/(8π)]. By contrast, the time-reversal invariant p±ip pairing only displays a quantized Gxxth at low T up to a moderate strength of disorder. In the strong disorder regime, all these topological responses (κxy, σxysp, and Gxxth) vanish. Possible material platforms hosting such paired states and manifesting these robust topological thermal and spin responses are discussed.

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