Effect of chiral symmetry on chaotic scattering from Majorana zero modes

Abstract

In many of the experimental systems that may host Majorana zero modes, a so-called chiral symmetry exists that protects overlapping zero modes from splitting up. This symmetry is operative in a superconducting nanowire that is narrower than the spin-orbit scattering length, and at the Dirac point of a superconductor/topological insulator heterostructure. Here we show that chiral symmetry strongly modifies the dynamical and spectral properties of a chaotic scatterer, even if it binds only a single zero mode. These properties are quantified by the Wigner-Smith time-delay matrix $Q=-i\hbar S^\dagger dS/dE$, the Hermitian energy derivative of the scattering matrix, related to the density of states by $ρ=(2π\hbar)^{-1}\,{\rm Tr}\,Q$. We compute the probability distribution of $Q$ and $ρ$, dependent on the number $ν$ of Majorana zero modes, in the chiral ensembles of random-matrix theory. Chiral symmetry is essential for a significant $ν$-dependence.