Three-level Haldane-like model on dice optical lattice

TL;DR

This paper proposes a three-level Haldane-like model on a dice optical lattice for ultracold atoms, enabling topologically nontrivial band structures with higher Chern numbers through laser-assisted tunneling and synthetic magnetic fluxes.

Contribution

It introduces a generalized Haldane model on a dice lattice that achieves topological phases without real-valued next-neighbour transitions, enhancing topological properties and access to semimetal phases.

Findings

Supports topologically nontrivial bands with higher Chern numbers.

Enables realization of topological semimetal phases using only nearest neighbour coupling.

Provides analytical insights via Berry connection singularities.

Abstract

We consider ultracold atoms in a two-dimensional optical lattice of the dice geometry in a tight-binding regime. The atoms experience a laser-assisted tunneling between the nearest neighbour sites of the dice lattice accompanied by the momentum recoil. This allows one to engineer staggered synthetic magnetic fluxes over plaquettes, and thus pave a way towards a realization of topologically nontrivial band structures. In such a lattice the real-valued next-neighbour transitions are not needed to reach a topological regime. Yet, such transitions can increase a variety of the obtained topological phases. The dice lattice represents a triangular Bravais lattice with a three-site basis consisting of a hub site connected to two rim sites. As a consequence, the dice lattice supports three dispersion bands. From this point of view, our model can be interpreted as a generalization of the paradigmatic Haldane model which is reproduced if one of the two rim sub-lattices is eliminated. We demonstrate that the proposed upgrade of the Haldane model creates a significant added value, including an easy access to topological semimetal phases relying only on the nearest neighbour coupling, as well as enhanced topological band structures featuring Chern numbers higher than one. The numerical investigation is supported and complemented by an analytical scheme based on the study of singularities in the Berry connection.