The spin quantum Hall effect in unconventional superconductors

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 $d_{x^2-y^2}+i{d}_{xy}$ superconductor which we argue has a dimensionless spin Hall conductance equal to two. A theory of the edge states of the $d_{x^2-y^2}+i{d}_{xy}$ 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.

12 pages

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• Exact exponents for the spin quantum Hall transition
• Dual Order Parameter for the Nodal Liquid
• Quantum Hall plateau transitions in disordered superconductors
• Quasiparticle density of states in dirty high-T_c superconductors
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