Spontaneous Time-Reversal Symmetry Breaking for Spinless Fermions on a Triangular Lattice

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 nearest-neighbor 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.

Extension of the Ginzburg–Landau approach for ultracold Fermi gases below a critical temperature

“…Recently, the GL method was re-derived in the context of superfluid ultracold Fermi gases [2,3,4,5]. The GL approach was also applied to explain the phenomenon of the "1.5-type" superconductivity.…”

Symmetry analysis of translational symmetry broken density waves: Application to hexagonal lattices in two dimensions

“…Interestingly, the M-point charge density waves (i.e., s waves) have been found as ground states or leading instabilities of interacting electron models, in the context of triangular lattice [53], honeycomb lattice [54], and kagome lattice [55] models with extended Hubbard interactions, using Hartree-Fock and renormalization group methods. Similarly, a mean-field study of spinless electrons on the triangular lattice has reported spontaneous time-reversal symmetry breaking with M-point modulations [56]. Clearly, a full study of leading instabilities requires including the spin channel [53,55,[57][58][59][60][61][62][63].…”

Temperature-Induced Spontaneous Time-Reversal Symmetry Breaking on the Honeycomb Lattice

“…Metallic systems with non-trivial topological properties, generically referred to as topological Fermi liquids (TFLs) [6], have come to play an important role in the study of marginal and other non-Fermi liquid phenomena [7]. Various instances [8][9][10][11][12][13][14][15][16] of TFLs and topological Mott insulators (TMIs) at commensurate fillings have been realized on the honeycomb lattice using a combination of mean-field theory and numerics.…”