Andreev reflection from a topological superconductor with chiral symmetry

M. Diez; J. P. Dahlhaus; M. Wimmer; C. W. J. Beenakker

doi:10.1103/PhysRevB.86.094501

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Andreev reflection from a topological superconductor with chiral symmetry

M. Diez, J. P. Dahlhaus, M. Wimmer, C. W. J. Beenakker

DOI 10.1103/PhysRevB.86.094501 · Physical Review B

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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∈Z (symmetry class BDI). Here we show that Q=Trrhe equals the trace of the matrix of Andreev reflection amplitudes, providing a link with the electrical conductance G. We derive G=(2e2/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 2e2/h steps—insensitive to disorder.