Three-dimensional topological phase on the diamond lattice

TL;DR

This paper introduces a three-dimensional bosonic Kitaev model on the diamond lattice, revealing topological phases characterized by Majorana fermions and protected by symmetry, extending the understanding of topological matter into three dimensions.

Contribution

It proposes a novel 3D bosonic Kitaev model on the diamond lattice with topological phases, expanding the scope of Kitaev models beyond 2D.

Findings

Identification of weak and strong pairing phases

Topological superconducting phase with non-zero winding number

Protection of topological character by discrete symmetry

Abstract

An interacting bosonic model of Kitaev type is proposed on the three-dimensional diamond lattice. Similarly to the two-dimensional Kitaev model on the honeycomb lattice which exhibits both Abelian and non-Abelian phases, the model has two (``weak'' and ``strong'' pairing) phases. In the weak pairing phase, the auxiliary Majorana hopping problem is in a topological superconducting phase characterized by a non-zero winding number introduced in A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, arXiv:0803.2786. The topological character of the weak pairing phase is protected by a discrete symmetry.