Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures

TLDR

The authors propose a theoretical experimental scheme to detect Majorana fermions in semiconductor–superconductor heterostructures. The scheme uses a one‑dimensional semiconductor wire with strong Rashba spin‑orbit coupling embedded in a superconducting quantum interference device, where supercurrent measurements across the junction reveal topological phases by tuning magnetic field or gate voltage. They find that Andreev bound‑state spectra exhibit distinct even‑ or odd‑zero‑energy crossings in trivial versus nontrivial phases, and observing the resulting supercurrent‑driven phase transition directly confirms Majorana particles.

Abstract

We propose and analyze theoretically an experimental setup for detecting the elusive Majorana particle in semiconductor-superconductor heterostructures. The experimental system consists of one-dimensional semiconductor wire with strong spin-orbit Rashba interaction embedded into a superconducting quantum interference device. We show that the energy spectra of the Andreev bound states at the junction are qualitatively different in topologically trivial (i.e., not containing any Majorana) and nontrivial phases having an even and odd number of crossings at zero energy, respectively. The measurement of the supercurrent through the junction allows one to discern topologically distinct phases and observe a topological phase transition by simply changing the in-plane magnetic field or the gate voltage. The observation of this phase transition will be a direct demonstration of the existence of Majorana particles.