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The spin quantum Hall effect in unconventional superconductors

T. Senthil·J. B. Marston·Matthew P. A. Fisher
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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.

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T. Senthil, J. B. Marston, Matthew P. A. Fisher. 1999-02-03. The spin quantum Hall effect in unconventional superconductors. https://doi.org/10.1103/physrevb.60.4245

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