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 $Q=-i\hslash S^{†}dS/dE$, the Hermitian energy derivative of the scattering matrix, related to the density of states by $\rho =(2\pi \hslash {)}^{-1}\mathrm{Tr}Q$. 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.

5 pages, 3 figures + appendix (3 pages, 1 figure)

References in corpus (17)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Introduction to topological superconductivity and Majorana fermions
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Topological invariants and interacting one-dimensional fermionic systems
• Tunneling of anyonic Majorana excitations in topological superconductors
• Strongly interacting Majorana fermions
• Majorana fermions in ferromagnetic chains on the surface of bulk spin-orbit coupled $s$-wave superconductors
• Delay times and reflection in chaotic cavities with absorption
• Quantum to Classical Transition of the Charge Relaxation Resistance of a Mesoscopic Capacitor
• Spin connection and boundary states in a topological insulator
• Efficient semiclassical approach for time delays
• Capacitance and charge relaxation resistance of chaotic cavities - Joint distribution of two linear statistics in the Laguerre ensemble of random matrices
• Time-delay matrix, midgap spectral peak, and thermopower of an Andreev billiard
• Geodesic scattering by surface deformations of a topological insulator
• Charge fluctuations in open chaotic cavities
• Delay-Time and Thermopower Distributions at the Spectrum Edges of a Chaotic Scatterer

Cited by in corpus (1)

• Boltzmann electronic dc transport in multiorbital weakly-disordered crystals