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 (κ_xy) and zero temperature spin (σ^sp_xy) Hall conductivities, and longitudinal thermal conductance (G^th_xx) 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 κ_xy [in units of κ₀=π² k²_B T/(3h)], respectively, while the latter one in addition accommodates a quantized σ^sp_xy [in units of σ^sp₀=ℏ/(8 π)]. By contrast, the time-reversal invariant p ± ip pairing only displays a quantized G^th_xx at low T up to a moderate strength of disorder. In the strong disorder regime, all these topological responses (κ_xy, σ^sp_xy, and G^th_xx) vanish. Possible material platforms hosting such paired states and manifesting these robust topological thermal and spin responses are discussed.