Topological states with broken translational and time-reversal symmetries in a honeycomb-triangular lattice

Abstract

We study fermions in a lattice, with on-site and nearest neighbor attractive interactions between two spin species. We consider two geometries: (1) both spins in a triangular lattice and (2) 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 nontrivial phases. In both geometries, we predict order parameters with simultaneous time-reversal and translational symmetry breaking.

The Fulde–Ferrell–Larkin–Ovchinnikov state for ultracold fermions in lattice and harmonic potentials: a review

“…Observation and understanding of the classic FFLO state is a grand goal in itself, however, even more is expected when extending the basic ideas of the FFLO physics in simple square lattices to new contexts. In [327,328] the idea of mixed geometry pairing was introduced: the ↑ and ↓ fermionic species were residing in different lattice geometries, which resulted in stable Sarma/BP states, among other things. Rich new physics is expected from multiband systems, especially those that can host flat, that is, dispersionless bands.…”