Bimodal conductance distribution of Kitaev edge modes in topological superconductors

Abstract

A two-dimensional superconductor with spin-triplet p-wave pairing supports chiral or helical Majorana edge modes with a quantized (length $L$-independent) thermal conductance. Sufficiently strong anisotropy removes both chirality and helicity, doubling the conductance in the clean system and imposing a super-Ohmic $1/\sqrt{L}$ decay in the presence of disorder. We explain the absence of localization in the framework of the Kitaev Hamiltonian, contrasting the edge modes of the two-dimensional system with the one-dimensional Kitaev chain. While the disordered Kitaev chain has a log-normal conductance distribution peaked at an exponentially small value, the Kitaev edge has a bimodal distribution with a second peak near the conductance quantum. Shot noise provides an alternative, purely electrical method of detection of these charge-neutral edge modes.