The spin quantum Hall effect in unconventional superconductors

TL;DR

This paper explores a novel spin quantum Hall phase in unconventional superconductors, specifically a $d_{x^2-y^2} + id_{xy}$ superconductor, analyzing its edge states, phase transition, and potential experimental detection methods.

Contribution

It introduces the concept of a spin quantum Hall fluid in superconductors, develops a theory for its edge states, and models the disorder-induced transition using a supersymmetric spin chain.

Findings

Quantized spin Hall conductance of two in the $d_{x^2-y^2}+id_{xy}$ superconductor

Universal properties of the phase transition characterized numerically

Proposed experimental probes for detecting spin quantum Hall effects

Abstract

We study the properties of the "spin quantum Hall fluid" - a novel spin phase with quantized spin Hall conductance that is potentially realizable in superconducting systems with unconventional pairing symmetry. A simple realization is provided by a $d_{x^2-y^2} + id_{xy}$ superconductor which we argue has a dimensionless spin Hall conductance equal to two. A theory of the edge states of the $d_{x^2-y^2}+id_{xy}$ superconductor is developed. The properties of the transition to a phase with vanishing spin Hall conductance induced by disorder are considered. We construct a description of this transition in terms of a supersymmetric spin chain, and use it to numerically determine universal properties of the transition. We discuss various possible experimental probes of this quantum Hall physics.