Charge instabilities and topological phases in the extended Hubbard model on the honeycomb lattice with enlarged unit cell

TL;DR

This paper investigates how extended interactions and enlarged unit cells in a honeycomb lattice influence charge instabilities and topological phases, revealing that certain interactions can suppress or restore topological order.

Contribution

It extends previous models by including next-nearest neighbor interactions and larger unit cells, analyzing their effects on topological phases in a mean field framework.

Findings

Topological phases are suppressed by charge density fluctuations.

Adding next-nearest neighbor interaction V2 restores topological phases.

Enlarged unit cell impacts symmetry breaking and phase stability.

Abstract

We study spontaneous symmetry breaking in a system of spinless fermions in the Honeycomb lattice paying special emphasis to the role of an enlarged unit cell on time reversal symmetry broken phases. We use a tight binding model with nearest neighbor hopping t and Hubbard interaction V1 and V2 and extract the phase diagram as a function of electron density and interaction within a mean field variational approach. The analysis completes the previous work done in Phys. Rev. Lett. 107, 106402 (2011) where phases with non--trivial topological properties were found with only a nearest neighbor interaction V1 in the absence of charge decouplings. We see that the topological phases are suppressed by the presence of metallic charge density fluctuations. The addition of next to nearest neighbor interaction V2 restores the topological non-trivial phases.