Observing Majorana bound states of Josephson vortices in topological superconductors

TL;DR

This paper demonstrates that fluxons in topological superconductor Josephson junctions can host Majorana modes, exhibiting non-Abelian statistics, and proposes experiments to observe these phenomena.

Contribution

It introduces the theoretical framework showing fluxons bind Majorana modes and suggests experimental setups for detecting non-Abelian statistics in topological superconductors.

Findings

Fluxons bind localized zero-energy Majorana modes.

Fluxons behave as non-Abelian anyons.

Proposed experiments to detect Majorana modes in fluxons.

Abstract

In recent years there has been an intensive search for Majorana fermion states in condensed matter systems. Predicted to be localized on cores of vortices in certain non-conventional superconductors, their presence is known to render the exchange statistics of bulk vortices non-Abelian. Here we study the equations governing the dynamics of phase solitons (fluxons) in a long Josephson junction in a topological superconductor. We show that the fluxon will bind a localized zero energy Majorana mode and will consequently behave as a non-Abelian anyon. The low mass of the fluxon, as well as its experimentally observed quantum mechanical wave-like nature, will make it a suitable candidate for vortex interferometry experiments demonstrating non-Abelian statistics. We suggest two experiments that may reveal the presence of the zero mode carried by the fluxon. Specific experimental realizations will be discussed as well.