Arbitrary Chern number generation in the three-band model from momentum space

TL;DR

This paper presents a straightforward method to construct three-band lattice models with any desired Chern number by applying specific monopole charge-changing unitary operations, enabling precise topological property control.

Contribution

It introduces a general rule for generating three-band models with arbitrary Chern numbers using monopole charge-changing unitary operations.

Findings

A simple rule for Chern number generation in three-band models.

Implementation of unitary operations to control topological invariants.

Framework applicable to three-sublattice lattice models.

Abstract

A simple, general rule for generating a three-band model with arbitrary Chern numbers is given. The rule is based on the idea of monopole charge-changing unitary operations and can be realized by two types of simple unitary operations on the original Hamiltonian. A pair of monopole charges are required to produce desired topological numbers in the three-band model. The set of rules presented here offers a way to produce lattice models of any desired Chern numbers for three-sublattice situations.