Evolution of the transmission phase through a Coulomb-blockaded Majorana wire

TL;DR

This paper investigates how the transmission phase through a Coulomb-blockaded Majorana wire changes, revealing the disappearance of phase lapses in the topological superconducting phase, with a focus on electron interactions and fermion parity.

Contribution

It introduces a modified scattering matrix formalism to analyze electron transmission and phase behavior in Coulomb-blockaded Majorana wires, incorporating electron-electron interactions and fermion parity effects.

Findings

Phase lapses disappear in the topological phase.

Transmission phase depends on fermion parity.

Electron-electron interactions significantly influence phase behavior.

Abstract

We present a study of the transmission of electrons through a semiconductor quantum wire with strong spin-orbit coupling in proximity to an s-wave superconductor, which is Coulomb-blockaded. Such a system supports Majorana zero modes in the presence of an external magnetic field. Without superconductivity, phase lapses are expected to occur in the transmission phase, and we find that they disappear when a topological superconducting phase is stabilized. We express tunneling through the nanowire with the help of effective matrix elements, which depend on both the fermion parity of the wire and the overlap with Bogoliubov-de-Gennes wave functions. Using a modified scattering matrix formalism, that allows for including electron-electron interactions, we study the transmission phase in different regimes.