title: 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=-iℏS^{†}dS/dE, the Hermitian energy derivative of the scattering matrix, related to the density of states by ρ=(2πℏ)^{-1}TrQ. 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.
authors.affiliation: Department of Physics, Lancaster University, LA1 4YB Lancaster, United Kingdom.|Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, Netherlands.
authors.forename: H
authors.initials: H
authors.lastname: Schomerus
authors.affiliation: Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, Netherlands.
authors.forename: M
authors.initials: M
authors.lastname: Marciani
authors.affiliation: Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, Netherlands.
authors.forename: C W J
authors.initials: CW
authors.lastname: Beenakker