Majorana boundary modes in Josephson junctions arrays with gapless bulk excitations

TL;DR

This paper demonstrates the existence of Majorana boundary modes in Josephson junction arrays with gapless bulk excitations, revealing new conditions under which unpaired states can appear beyond gapped systems.

Contribution

It shows that Majorana bound states can exist in gapless Josephson junction arrays, mediated by bulk modes, expanding the understanding of topological states in such systems.

Findings

Majorana boundary modes appear in gapless Josephson junction arrays.

Bulk modes mediate coupling between Majorana states via RKKY mechanism.

Energy splitting remains small even for short chains of about 10 units.

Abstract

The search for Majorana bound states in solid-state physics has been limited to materials which display a gap in their bulk spectrum. We show that such unpaired states appear in certain quasi-one-dimensional Josephson junctions arrays with gapless bulk excitations. The bulk modes mediate a coupling between Majorana bound states via the Ruderman-Kittel-Yosida-Kasuya mechanism. As a consequence, the lowest energy doublet acquires a finite energy difference. For realistic set of parameters this energy splitting remains much smaller than the energy of the bulk eigenstates even for short chains of length $L \sim 10$.