Majorana fermions in vortex lattices

TL;DR

This paper investigates Majorana fermions in vortex lattices of 2D chiral p-wave superconductors, revealing phase-dependent tunneling, flat bands at zero energy, and implications for topological quantum computing.

Contribution

It introduces a phase-dependent tunneling model for Majorana fermions in vortex arrays and demonstrates the formation of flat bands, enhancing understanding of their stability for quantum computation.

Findings

Tunneling amplitude depends on the sine of half the phase difference between vortices.

Flat Majorana bands form at zero energy in vortex lattices.

Majorana fermions exhibit less decoherence, favorable for quantum computing.

Abstract

We consider Majorana fermions tunneling among an array of vortices in a 2D chiral p-wave superconductor or equivalent material. The amplitude for Majorana fermions to tunnel between a pair of vortices is found to necessarily depend on the background superconducting phase profile; it is found to be proportional to the sine of half the difference between the phases at the two vortices. Using this result we study tight-binding models of Majorana fermions in vortices arranged in triangular or square lattices. In both cases we find that the aforementioned phase-tunneling relationship leads to the creation of superlattices where the Majorana fermions form macroscopically degenerate localizable flat bands at zero energy, in addition to other dispersive bands. This finding suggests that tunneling processes in these vortex arrays do not change the energies of a finite fraction of Majorana fermions, contrary to previous expectation. The presence of flat Majorana bands, and hence less-than-expected decoherence in these vortex arrays, bodes well for the prospects of topological quantum computation with large numbers of Majorana states.