Effect of a tunnel barrier on the scattering from a Majorana bound state in an Andreev billiard

TL;DR

This paper investigates how a tunnel barrier influences the scattering properties and detection of Majorana bound states in a topological superconductor, revealing that conductance measurements can still indicate Majorana states despite hidden signatures in density of states.

Contribution

It introduces a detailed analysis of the joint distribution of scattering and time-delay matrices in chaotic quantum dots with tunnel barriers, linking these to Majorana state detection.

Findings

Majorana states can be hidden in density of states and thermal conductance.

Electrical conductance remains sensitive to Majorana states.

Presence of a tunnel barrier affects the correlation between scattering matrices.

Abstract

We calculate the joint distribution $P(S,Q)$ of the scattering matrix $S$ and time-delay matrix $Q=-i\hbar S^\dagger dS/dE$ of a chaotic quantum dot coupled by point contacts to metal electrodes. While $S$ and $Q$ are statistically independent for ballistic coupling, they become correlated for tunnel coupling. We relate the ensemble averages of $Q$ and $S$ and thereby obtain the average density of states at the Fermi level. We apply this to a calculation of the effect of a tunnel barrier on the Majorana resonance in a topological superconductor. We find that the presence of a Majorana bound state is hidden in the density of states and in the thermal conductance if even a single scattering channel has unit tunnel probability. The electrical conductance remains sensitive to the appearance of a Majorana bound state, and we calculate the variation of the average conductance through a topological phase transition.