Abstract
It was pointed out by Tewari and Sau that chiral symmetry ( if ) of the Hamiltonian of electron-hole (e-h) excitations in an -mode superconducting wire is associated with a topological quantum number (symmetry class BDI). Here we show that equals the trace of the matrix of Andreev reflection amplitudes, providing a link with the electrical conductance . We derive for , and more generally provide a -dependent upper and lower bound on . We calculate the probability distribution for chaotic scattering, in the circular ensemble of random-matrix theory, to obtain the 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 steps—insensitive to disorder.
- Received 14 June 2012
DOI:https://doi.org/10.1103/PhysRevB.86.094501
©2012 American Physical Society