Two-dimensional Chern semimetals on the Lieb lattice

TL;DR

This paper introduces a simple tight-binding model on the Lieb lattice that supports gapless Chern semimetals with topologically protected edge states, characterized by a well-defined Chern number and relativistic dispersion at contact points.

Contribution

It presents a novel, minimal model for Chern semimetals with a Dirac-like point and relativistic dispersion, supported by topological invariants and robustness analysis.

Findings

Supports a single Dirac-like point with relativistic dispersion

Topologically protected edge states confirmed via entanglement spectrum

Chern number remains stable under weak disorder

Abstract

In this work, we propose a new and simple model that supports Chern semimetals. These new gapless topological phases share several properties with the Chern insulators like a well-defined Chern number associated to each band, topologically protected edge states and topological phase transitions that occur when the bands touch each, with linear dispersion around the contact points. The tight-binding model, defined on the Lieb lattice with intra-unit-cell and suitable nearest-neighbor hopping terms between three different species of spinless fermions, supports a single Dirac-like point. The dispersion relation around this point is fully relativistic and the $3\times3$ matrices in the corresponding effective Hamiltonian satisfy the Duffin-Kemmer-Petiau algebra. We show the robustness of the topologically protected edge states by employing the entanglement spectrum. Moreover, we prove that the Chern number of the lowest band is robust with respect to weak disorder. For its simplicity, our model can be naturally implemented in real physical systems like cold atoms in optical lattices.