Quantized thermal and spin transports of dirty planar topological superconductors

TL;DR

This paper numerically investigates thermal and spin transport properties of various two-dimensional topological superconductors, revealing quantized responses in clean and weak disorder regimes, with all responses vanishing under strong disorder.

Contribution

It provides a comprehensive numerical analysis of thermal and spin Hall conductivities in different classes of 2D topological superconductors using scattering matrix formalism.

Findings

Half-quantized thermal Hall conductivity in class D

Quantized thermal and spin responses in class C

Responses vanish under strong disorder

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 ($\kappa_{xy}$) and zero temperature spin ($\sigma^{sp}_{xy}$) 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 $p \pm ip$ (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 $\kappa_{xy}$ [in units of $\kappa_0=\pi^2 k^2_B T/(3h)$], respectively, while the latter one in addition accommodates a quantized $\sigma^{sp}_{xy}$ [in units of $\sigma^{sp}_0=\hbar/(8 \pi)$]. By contrast, the time-reversal invariant $p \pm ip$ 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 ($\kappa_{xy}$, $\sigma^{sp}_{xy}$, and $G^{th}_{xx}$) vanish. Possible material platforms hosting such paired states and manifesting these robust topological thermal and spin responses are discussed.