Andreev reflection from a topological superconductor with chiral symmetry

Abstract

It was pointed out by Tewari and Sau that chiral symmetry (H -> -H if e <-> h) of the Hamiltonian of electron-hole (e-h) excitations in an N-mode superconducting wire is associated with a topological quantum number Q\in\mathbb{Z} (symmetry class BDI). Here we show that Q=Tr(r_{he}) equals the trace of the matrix of Andreev reflection amplitudes, providing a link with the electrical conductance G. We derive G=(2e^2/h)|Q| for |Q|=N,N-1, and more generally provide a Q-dependent upper and lower bound on G. We calculate the probability distribution P(G) for chaotic scattering, in the circular ensemble of random-matrix theory, to obtain the Q-dependence of weak localization and mesoscopic conductance fluctuations. We investigate the effects of chiral symmetry breaking by spin-orbit coupling of the transverse momentum (causing a class BDI-to-D crossover), in a model of a disordered semiconductor nanowire with induced superconductivity. For wire widths less than the spin-orbit coupling length, the conductance as a function of chemical potential can show a sequence of 2e^2/h steps - insensitive to disorder.

10 pages, 5 figures. Corrected typo (missing square root) in equations A13 and A14

References in corpus (6)

• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Tunneling of anyonic Majorana excitations in topological superconductors
• Topological minigap in quasi-one-dimensional spin-orbit-coupled semiconductor Majorana wires
• Dephasing-enabled triplet Andreev conductance
• Anisotropic universal conductance fluctuations in disordered quantum wires with Rashba and Dresselhaus spin-orbit interaction and applied in-plane magnetic field

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