Landau Levels in 2D materials using Wannier Hamiltonians obtained by first principles

TL;DR

This paper introduces a method combining DFT and Wannier functions to compute Landau levels and edge states in 2D materials, offering a versatile alternative to traditional effective mass models.

Contribution

The authors develop a first-principles based approach to calculate Landau levels in 2D materials using Wannier Hamiltonians derived from DFT, applicable to various crystals.

Findings

Successfully computed Landau levels for multiple 2D materials.

Reproduced edge state dispersions in ribbon geometries.

Provided a general method adaptable to different 2D crystals.

Abstract

We present a method to calculate the Landau levels and the corresponding edge states of two dimensional (2D) crystals using as a starting point their electronic structure as obtained from standard density functional theory (DFT). The DFT Hamiltonian is represented in the basis of maximally localized Wannier functions. This defines a tight-binding Hamiltonian for the bulk that can be used to describe other structures, such as ribbons, provided that atomic scale details of the edges are ignored. The effect of the orbital magnetic field is described using the Peierls substitution in the hopping matrix elements. Implementing this approach in a ribbon geometry, we obtain both the Landau levels and the dispersive edge states for a series of 2D crystals, including graphene, Boron Nitride, MoS$_2$ , Black Phosphorous, Indium Selenide and MoO$_3$ . Our procedure can readily be used in any other 2D crystal, and provides an alternative to effective mass descriptions.