Measuring topology in a laser-coupled honeycomb lattice: From Chern insulators to topological semi-metals

TL;DR

This paper investigates how laser-induced synthetic magnetic flux in ultracold fermions on a honeycomb lattice can realize and detect topological phases like Chern insulators and semi-metals, expanding the understanding of topological matter.

Contribution

It explores a broad parameter space to identify topologically non-trivial regimes and highlights the existence of topological semi-metals not present in the original Haldane model.

Findings

Identification of parameter regimes for Chern insulators

Detection methods for topological phases in cold-atom systems

Discovery of topological semi-metals with non-zero winding numbers

Abstract

Ultracold fermions trapped in a honeycomb optical lattice constitute a versatile setup to experimentally realize the Haldane model [Phys. Rev. Lett. 61, 2015 (1988)]. In this system, a non-uniform synthetic magnetic flux can be engineered through laser-induced methods, explicitly breaking time-reversal symmetry. This potentially opens a bulk gap in the energy spectrum, which is associated with a non-trivial topological order, i.e., a non-zero Chern number. In this work, we consider the possibility of producing and identifying such a robust Chern insulator in the laser-coupled honeycomb lattice. We explore a large parameter space spanned by experimentally controllable parameters and obtain a variety of phase diagrams, clearly identifying the accessible topologically non-trivial regimes. We discuss the signatures of Chern insulators in cold-atom systems, considering available detection methods. We also highlight the existence of topological semi-metals in this system, which are gapless phases characterized by non-zero winding numbers, not present in Haldane's original model.