Multilayer Haldane model

TL;DR

This paper introduces a layered material model based on stacked Haldane layers, analyzing its topological properties and showing how interlayer hopping influences the overall topological invariant and quantum Hall conductivity.

Contribution

It extends the Haldane model to multilayer systems with ABC stacking and calculates the topological invariant for the combined structure.

Findings

Topological invariant scales with the number of layers in certain parameter ranges.

The invariant can be computed using low energy effective theory.

Interlayer hopping significantly affects the topological properties.

Abstract

We propose the model of layered materials, in which each layer is described by the conventional Haldane model, while the inter - layer hopping parameter corresponds to the ABC stacking. We calculate the topological invariant $N_3$ for the resulting model, which is responsible for the conductivity of intrinsic quantum Hall effect. It has been shown that in a certain range of the values of interlayer hopping parameter, the value of $N_3$ is equal to the number of layers multiplied by the topological invariant of each layer. At the same time this value may be calculated using the low energy effective theory.