Andreev reflection from a topological superconductor with chiral symmetry

TL;DR

This paper links the topological quantum number of a chiral symmetric superconductor to Andreev reflection and conductance, analyzing its behavior through random-matrix theory and effects of symmetry breaking.

Contribution

It establishes a direct relation between the topological quantum number and Andreev reflection, deriving conductance bounds, and explores symmetry breaking effects in disordered nanowires.

Findings

Q equals the trace of Andreev reflection amplitudes matrix

Conductance G is proportional to the topological quantum number Q

Disorder-insensitive 2e^2/h conductance steps observed in certain nanowires

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.