Non-Abelian Evolution of a Majorana Train in a Single Josephson Junction

TL;DR

This paper proposes a simplified setup using a single Josephson junction to observe non-Abelian statistics of Majorana fermions, revealing a fractional AC Josephson effect tunable by voltage.

Contribution

It introduces a novel single-junction device that demonstrates non-Abelian Majorana fermion statistics through a controllable fractional Josephson effect.

Findings

Detection of non-Abelian statistics via a train of Majorana fermions.

Observation of a tunable $2n ext{ extdegree} ext{pi}$ fractional AC Josephson effect.

Potential for simplified experimental realization of Majorana-based quantum phenomena.

Abstract

Demonstration of non-Abelian anyon statistics often requires dynamical controls of a complicated device that are challenging in realistic situations. We propose a {\it single} Josephson junction to detect a non-Abelian statistics effect of Majorana fermions, formed by two finite-size $s$-wave superconductors on a topological insulator under a magnetic field. At certain field strengths, a train of three localized Majorana fermions appears along the junction, while an extended chiral Majorana fermion encircles the train and the superconductors. A DC voltage bias across the junction causes the train to move and collide with the extended Majorana fermion. This involves interchange of fusion partners among the four Majorana fermions, leading to non-Abelian state evolution. The evolution gives rise to a $2n\pi$ fractional AC Josephson effect with an arbitrary integer $n\ge2$ tunable by the voltage.