Majorana bound states in vortex lattices on iron-based superconductors

TL;DR

This paper explores the emergence and behavior of Majorana bound states in vortex lattices on iron-based superconductor FeTe$_{0.55}$Se$_{0.45}$, using a 2D lattice model and advanced techniques to simulate disorder and compare with experiments.

Contribution

It introduces a modified singular gauge transformation method to simulate disordered vortex lattices and connects the findings to potential applications in topological quantum computation.

Findings

Successful replication of experimental Majorana vortex states

Development of a larger vortex lattice simulation technique

Proposal of a disordered Majorana lattice model

Abstract

Majorana quasi-particles may arise as zero-energy bound states in vortices on the surface of a topological insulator that is proximitized by a conventional superconductor. Such a system finds its natural realization in the iron-based superconductor FeTe$_{0.55}$Se$_{0.45}$ that combines bulk $s$-wave pairing with spin helical Dirac surface states, and which thus comprises the ingredients for Majorana modes in absence of an additional proximitizing superconductor. In this work, we investigate the emergence of Majorana vortex modes and lattices in such materials depending on parameters like the magnetic field strength and vortex lattice disorder. A simple 2D square lattice model here allows us to capture the basic physics of the underlying materials system. To address the problem of disordered vortex lattice, which occurs in real systems, we adopt the technique of the singular gauge transformation which we modify such that it can be used in a system with periodic boundary conditions. This approach allows us to go to larger vortex lattices than otherwise accessible, and is successful in replicating several experimental observations of Majorana vortex bound states in the FeTe$_{0.55}$Se$_{0.45}$ platform. Finally it can be related to a simple disordered Majorana lattice model that should be useful for further investigations on the role of interactions, and towards topological quantum computation.