Implementing Majorana fermions in a cold-atom honeycomb lattice with textured pairings

TL;DR

This paper proposes a theoretical model for creating Majorana fermions in a cold-atom honeycomb lattice by introducing textured pairings and analyzing topological phases, advancing the understanding of topological superconductivity in optical lattices.

Contribution

It introduces a novel effective model combining textured pairings and a generalized Haldane model to realize unpaired Majorana fermions at lattice edges.

Findings

The model exhibits both gapped and gapless phases with topological properties.

Majorana zero modes appear at edges in different topological phases.

The discriminant measures time-reversal symmetry breaking and phase distinctions.

Abstract

Recent studies in the realization of Majorana fermion (MF) quasiparticles have focused on engineering topological superconductivity by combining conventional superconductors and spin-textured electronic materials. We propose an effective model to create unpaired MFs at a honeycomb lattice edge by generalizing a 2-dimensional topologically nontrivial Haldane model and introducing textured pairings. The core idea is to add both the spin-singlet and textured spin-triplet pairings to a pseudospin-state dependent, time-reversal symmetry (TRS) noninvariant honeycomb lattice, and to satisfy generalized "sweet spot" conditions as in the Kitaev chain model. Our model has a gapped superconducting phase and a gapless phase; either phase may have zero or nonzero topological winding numbers. The discriminant that distinguishes those two phases gives a measure of TRS breaking and may have more general implications. Effective Majorana zero modes arise at edges in distinct phases with different degrees of degeneracy. Our theoretical model motivates concepts, such as "textured pairings" and the "strength" of TRS breaking, that may play important roles in future implementation of MFs with cold atoms in optical lattices.