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

Abstract

We calculate the joint distribution $P(S,Q)$ of the scattering matrix $S$ and time-delay matrix $Q=-i\hslash S^{†}dS/dE$ 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.

Contribution for the special issue of Physica E in memory of Markus Büttiker. 13 pages, 7 figures

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Cited by in corpus (3)

• Wigner time delay and related concepts -- Application to transport in coherent conductors
• Wigner-Smith time-delay matrix in chaotic cavities with non-ideal contacts
• Wigner-Smith matrix, exponential functional of the matrix Brownian motion and matrix Dufresne identity