Effect of Chiral Symmetry on Chaotic Scattering from Majorana Zero Modes

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 = -ihS(dagger)dS/dE, the Hermitian energy derivative of the scattering matrix, related to the density of states by rho = (2 pi h)(-1)TrQ. We compute the probability distribution of Q and rho, dependent on the number nu of Majorana zero modes, in the chiral ensembles of random-matrix theory. Chiral symmetry is essential for a significant nu dependence.