Majorana fermions on a disordered triangular lattice

TL;DR

This paper studies how disorder affects Majorana fermions on a triangular lattice, revealing localized modes at weak disorder and a transition to extended states with a gap closure at strong disorder.

Contribution

It introduces analysis of Majorana fermions on a disordered triangular lattice, highlighting the effects of disorder-induced localization and a percolation transition.

Findings

Localized sub-gap modes appear with weak disorder.

A percolation phase transition occurs with strong disorder.

The density of states diverges at zero energy in the disordered system.

Abstract

Vortices of several condensed matter systems are predicted to have zero-energy core excitations which are Majorana fermions. These exotic quasi-particles are neutral, massless, and expected to have non-Abelian statistics. Furthermore, they make the ground state of the system highly degenerate. For a large density of vortices, an Abrikosov lattice is formed, and tunneling of Majorana fermions between vortices removes the energy degeneracy. In particular the spectrum of Majorana fermions in a triangular lattice is gapped, and the Hamiltonian which describes such a system is antisymmetric under time-reversal. We consider Majorana fermions on a disordered triangular lattice. We find that even for very weak disorder in the location of the vortices localized sub-gap modes appear. As the disorder becomes strong, a percolation phase transition takes place, and the gap is fully closed by extended states. The mechanism that underlies these phenomena is domain walls between two time-reversed phases, which are created by flipping the sign of the tunneling matrix elements. The density of states in the disordered lattice seems to diverge at zero energy.