Topological $\pi$-junctions from crossed Andreev reflection in the Quantum Hall regime

TL;DR

This paper demonstrates how crossed Andreev reflection in a quantum Hall 2DEG with spin-orbit coupling can create tunable topological $\pi$-junctions hosting Majorana modes, enabling protected quantum operations.

Contribution

It introduces a novel method to realize topological $\pi$-junctions and Majorana modes via CAR processes in a quantum Hall system with external tunability.

Findings

Topological superconducting gaps can be induced and controlled by CAR amplitude.

Opposite sign topological gaps form a robust $\pi$-junction hosting Majorana zero modes.

Protected non-Abelian operations can be performed without fine tuning.

Abstract

We consider a two-dimensional electron gas (2DEG) in the Quantum Hall regime in the presence of a Zeeman field, with the Fermi level tuned to filling factor $\nu=1$. We show that, in the presence of spin-orbit coupling, contacting the 2DEG to a narrow strip of an s-wave superconductor produces a topological superconducting gap along the contact as a result of crossed Andreev reflection (CAR) processes across the strip. The sign of the topological gap, controlled by the CAR amplitude, depends periodically on the Fermi wavelength and strip width and can be externally tuned. An interface between two halves of a long strip with topological gaps of opposite sign implements a robust $\pi$-junction, hosting a pair of Majorana zero modes that do not split despite their overlap. We show that such a situation can be exploited to perform protected non-Abelian tunnel-braid operations without any fine tuning.