Proximity-induced Josephson $\pi$-Junctions in Topological Insulators

TL;DR

This paper investigates how proximity effects in topological insulators coupled with superconductors can create $$-junctions that support topological superconductivity and Majorana fermions, using models with spin impurities and quantum dots.

Contribution

It introduces two microscopic models demonstrating the formation of $$-junctions with time-reversal symmetry, enabling topological superconductivity without magnetic fields.

Findings

The models show $$-junctions with sign-changing order parameters.

Time-reversal symmetry is preserved despite random spin orientations.

Proposed junctions can generate and manipulate Majorana fermions.

Abstract

We study two microscopic models of topological insulators in contact with an $s$-wave superconductor. In the first model the superconductor and the topological insulator are tunnel coupled via a layer of scalar and of randomly oriented spin impurities. Here, we require that spin-flip tunneling dominates over spin-conserving one. In the second model the tunnel coupling is realized by an array of single-level quantum dots with randomly oriented spins. It is shown that the tunnel region forms a $\pi$-junction where the effective order parameter changes sign. Interestingly, due to the random spin orientation the effective descriptions of both models exhibit time-reversal symmetry. We then discuss how the proposed $\pi$-junctions support topological superconductivity without magnetic fields and can be used to generate and manipulate Kramers pairs of Majorana fermions by gates.