Effect of chiral symmetry on chaotic scattering from Majorana zero modes

TL;DR

This paper investigates how chiral symmetry influences the spectral and dynamical properties of chaotic scatterers hosting Majorana zero modes, using random-matrix theory to analyze the distribution of time delays and density of states.

Contribution

It demonstrates that chiral symmetry significantly affects the properties of chaotic systems with Majorana zero modes, providing new insights into their spectral statistics.

Findings

Chiral symmetry alters the distribution of the Wigner-Smith time-delay matrix.

The number of Majorana zero modes influences spectral properties significantly.

Chiral ensembles of random-matrix theory capture the impact of symmetry on these systems.

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 $\rho=(2\pi\hbar)^{-1}\,{\rm Tr}\,Q$. 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.