Majorana bound states from exceptional points in non-topological superconductors

TLDR

Efforts to detect Majorana bound states have concentrated on engineering topological superconductivity. The study demonstrates an alternative route to fully localized zero‑energy Majorana bound states by strongly coupling a topologically trivial superconductor to a helical normal region. The authors realize the junction by proximitizing a finite spin–orbit coupled nanowire segment and using electrostatic depletion plus a Zeeman field to induce a helical phase in the remaining normal region. Majorana zero modes appear without fine‑tuning due to charge‑conjugation symmetry, linked to exceptional points where two Andreev levels split into two quasibound Majorana modes; after the EP, one mode becomes non‑decaying as the junction approaches perfect Andreev reflection, forming a Majorana dark state that exhibits all conventional Majorana properties (zero energy, self‑conjugation, 4π Josephson effect, non‑Abelian statistics) without requiring topological superconductivity.

Abstract

Recent experimental efforts towards the detection of Majorana bound states have focused on creating the conditions for topological superconductivity. Here we demonstrate an alternative route, which achieves fully localised zero-energy Majorana bound states when a topologically trivial superconductor is strongly coupled to a helical normal region. Such a junction can be experimentally realised by e.g. proximitizing a finite section of a nanowire with spin-orbit coupling, and combining electrostatic depletion and a Zeeman field to drive the non-proximitized (normal) portion into a helical phase. Majorana zero modes emerge in such an open system without fine-tuning as a result of charge-conjugation symmetry, and can be ultimately linked to the existence of `exceptional points' (EPs) in parameter space, where two quasibound Andreev levels bifurcate into two quasibound Majorana zero modes. After the EP, one of the latter becomes non-decaying as the junction approaches perfect Andreev reflection, thus resulting in a Majorana dark state (MDS) localised at the NS junction. We show that MDSs exhibit the full range of properties associated to conventional closed-system Majorana bound states (zero-energy, self-conjugation, $4\pi$-Josephson effect and non-Abelian braiding statistics), while not requiring topological superconductivity.