The non-commutative topology of two-dimensional dirty superconductors

Abstract

Non-commutative analysis tools have successfully been applied to the integer quantum Hall effect, in particular for a proof of the stability of the Hall conductance in an Anderson localization regime and of the bulk-boundary correspondence. In this work, these techniques are implemented to study two-dimensional dirty superconductors described by Bogoliubov-de Gennes Hamiltonians. After a thorough presentation of the basic framework and the topological invariants, Kubo formulas for the thermal, thermoelectric and spin Hall conductance are analyzed together with the corresponding edge currents.

published version in J Geo Phys

References in corpus (4)

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• On ${\mathbb{Z}}_2$-indices for ground states of fermionic chains
• Crystallographic bulk-edge correspondence: glide reflections and twisted mod 2 indices
• Středa formula for charge and spin currents
• Locally equivalent quasifree states and index theory
• The cohomology invariant for class DIII topological insulators