Topological States with Broken Translational and Time-Reversal Symmetries in a Honeycomb-Triangular Lattice

TL;DR

This paper explores topological phases in fermionic lattice systems with attractive interactions, revealing complex symmetry-breaking phenomena and rich phase diagrams in honeycomb-triangular geometries.

Contribution

It introduces a study of topological states with broken symmetries in mixed honeycomb-triangular lattices, highlighting novel phases due to geometry and interaction effects.

Findings

Identification of topologically non-trivial phases in mixed lattice geometries

Prediction of order parameters breaking time-reversal and translational symmetries

Rich phase diagrams influenced by spin imbalance and pairing mechanisms

Abstract

We study fermions in a lattice, with on-site and nearest neighbor attractive interactions between two spin species. We consider two geometries: both spins in a triangular lattice, and a mixed geometry with up-spins in honeycomb and down-spins in triangular lattices. We focus on the interplay between spin-population imbalance, on-site and valence bond pairing, and order parameter symmetry. The mixed geometry leads to a rich phase diagram of topologically non-trivial phases. In both geometries, we predict order parameters with simultaneous time-reversal and translational symmetry breaking.