Spontaneous time-reversal symmetry breaking for spinless fermions on a triangular lattice

TL;DR

This paper investigates how interactions and kinetic frustration in a triangular lattice of spinless fermions lead to spontaneous breaking of time-reversal and translational symmetries, revealing various ordered phases.

Contribution

It introduces a minimal model showing multiple symmetry-breaking phases due to kinetic frustration and interactions, analyzed via mean-field theory.

Findings

Identification of loop current patterns breaking time-reversal symmetry

Discovery of density wave and trimerization phases breaking translational symmetry

Mapping of the phase diagram with various ordered states

Abstract

As a minimal fermionic model with kinetic frustration, we study a system of spinless fermions in the lowest band of a triangular lattice with long-range repulsion. We find that the combination of interactions and kinetic frustration leads to spontaneous symmetry breaking in various ways. Time-reversal symmetry can be broken by two types of loop current patterns, a chiral one and one that breaks the translational lattice symmetry. Moreover, the translational symmetry can also be broken by a density wave forming a kagome pattern or by a Peierls-type trimerization characterized by enhanced correlations among the sites of certain triangular plaquettes (giving a plaquette-centered density wave). We map out the phase diagram as it results from leading order Ginzburg-Landau mean-field theory. Several experimental realizations of the type of system under study are possible with ultracold atoms in optical lattices.