Dirac points merging and wandering in a model Chern insulator

TL;DR

This paper introduces a square lattice Chern insulator model with complex hoppings, revealing rich physics including Dirac point dynamics and a novel phase transition line, distinct from the Haldane model.

Contribution

The model demonstrates Dirac points that can move, merge, and split in momentum space, and features a phase transition line between topological phases, unlike previous models.

Findings

Dirac points can move, merge, and split in the Brillouin zone.

The phase diagram includes a phase transition line between topological phases.

The model can be simulated in optical lattices for experimental studies.

Abstract

We present a model for a Chern insulator on the square lattice with complex first and second neighbor hoppings and a sublattice potential which displays an unexpectedly rich physics. Similarly to the celebrated Haldane model, the proposed Chern insulator has two topologically non-trivial phases with Chern numbers $\pm1$. As a distinctive feature of the present model, phase transitions are associated to Dirac points that can move, merge and split in momentum space, at odds with Haldane's Chern insulator where Dirac points are bound to the corners of the hexagonal Brillouin zone. Additionally, the obtained phase diagram reveals a peculiar phase transition line between two distinct topological phases, in contrast to the Haldane model where such transition is reduced to a point with zero sublattice potential. The model is amenable to be simulated in optical lattices, facilitating the study of phase transitions between two distinct topological phases and the experimental analysis of Dirac points merging and wandering.