Dirac-point engineering and topological phase transitions in honeycomb optical lattices

TL;DR

This paper investigates the electronic structure and topological phase transitions of Dirac points in honeycomb optical lattices, revealing how asymmetry in hoppings induces merging and gap opening, with observable effects on thermodynamic properties.

Contribution

It provides a detailed analysis of Dirac point evolution and topological phase transitions in honeycomb optical lattices using analytical and numerical methods.

Findings

Dirac points approach and merge at a critical hopping asymmetry.

Merging of Dirac points opens an energy gap, changing the spectrum topology.

Phase transition affects specific heat and structure factor signatures.

Abstract

We study the electronic structure and the phase diagram of non-interacting fermions confined to hexagonal optical lattices. In the first part, we compare the properties of Dirac points arising in the eigenspectrum of either honeycomb or triangular lattices. Numerical results are complemented by analytical equations for weak and strong confinements. In the second part we discuss the phase diagram and the evolution of Dirac points in honeycomb lattices applying a tight-binding description with arbitrary nearest-neighbor hoppings. With increasing asymmetry between the hoppings the Dirac points approach each other. At a critical asymmetry the Dirac points merge to open an energy gap, thus changing the topology of the eigenspectrum. We analyze the trajectory of the Dirac points and study the density of states in the different phases. Manifestations of the phase transition in the temperature dependence of the specific heat and in the structure factor are discussed.