paper

Quantized thermal and spin transports of dirty planar topological superconductors

arXiv:2308.16908 · doi:10.1103/PhysRevB.109.195403

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 ( $I^º_{x y}$ ) and zero temperature spin ( $I ¨ _{x y}^{s p}$ ) Hall conductivities, and longitudinal thermal conductance ( $G_{xx}^{t h}$ ) of various prominent two-dimensional fully gapped topological superconductors, belonging to distinct Altland-Zirnbauer symmetry classes, namely $p + i p$ (class D), $d + i d$ (class C) and $p \pm i p$ (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 $p + i p$ and $d + i d$ pairings show half-quantized and quantized $I^º_{x y}$ [in units of $I^º_{0} = I ¨ ^{2} k_{B}^{2} T / (3 h)$ ], respectively, while the latter one in addition accommodates a quantized $I ¨ _{x y}^{s p}$ [in units of $I ¨ _{0}^{s p} = ℏ/ (8 I ¨ )$ ]. By contrast, the time-reversal invariant $p \pm i p$ pairing only displays a quantized $G_{xx}^{t h}$ at low $T$ up to a moderate strength of disorder. In the strong disorder regime, all these topological responses ( $I^º_{x y}$ , $I ¨ _{x y}^{s p}$ , and $G_{xx}^{t h}$ ) vanish. Possible material platforms hosting such paired states and manifesting these robust topological thermal and spin responses are discussed.

Published version in PRB: 13 pages, 4 figures, 1 Table