Self-consistent superconducting proximity effect at the quantum spin Hall egde

TL;DR

This paper investigates the microscopic interface between a quantum spin Hall insulator and superconductors, revealing the nature of induced pairing and conditions for Majorana mode creation, with implications for topological quantum computing.

Contribution

It provides a self-consistent analysis of the superconducting proximity effect at QSHI edges, clarifying the pairing symmetry and Majorana mode conditions for different superconductor types.

Findings

Induced p-wave pairing exists at all doping levels with s-wave superconductors.

The superconducting gap in QSHI remains s-wave, supporting effective models.

Majorana modes form only at finite doping with d-wave superconductors, without excitation gap protection.

Abstract

We study self-consistently a microscopic interface between a quantum spin Hall insulator (QSHI) and a superconductor (SC), focusing on properties related to Majorana fermion creation. For an $s$-wave SC we show that odd-in-momentum, or $p$-wave, order parameters exist for all doping levels of the QSHI and that they can be related to different spinless Cooper pair amplitudes. Despite this, the induced superconducting gap in the QSHI always retains its $s$-wave character, validating the commonly used effective model for superconductivity in a topological insulator. For a $d_{xy}$-wave SC, we show that a Majorana mode is only created at finite doping and that there is no excitation gap protecting this mode.