The Chern states on the honeycomb and Lieb lattices

TL;DR

This paper analyzes the topological phases of the Haldane model on Lieb and honeycomb lattices, revealing non-zero Chern numbers in flat bands and characterizing phase transitions between topological states.

Contribution

It provides a detailed phase diagram and identifies a topological metal state with continuous Chern number change, extending understanding of topological transitions in lattice models.

Findings

Non-zero Chern number in flat bands on Lieb lattice

Identification of a topological metal state as an intermediate phase

Continuous Chern number change during phase transition

Abstract

The Haldane model of the Chern insulator is considered on the Lieb and honeycomb lattices. We provide a detailed analysis of the model's ground-state phase diagram and demonstrate a scenario of the topological phase transitions in the system with a single-particle spectrum that includes flat and dispersion bands, that is realized on the Lieb lattice. We find that the Chern number of the flat band is non-zero, depending on the parameters of the model. We define the topological metal state as an intermediate state between topological insulator and trivial metal. The phase transition between topological insulator and topological metal states is accompanied by continuous changing of the Chern number, a jump of the surface charge or spin current defines the point of the topological metal-trivial metal phase transition. The results have been illustrated with numerical calculations of the model.