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

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.

11 pages, 8 figures

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Cited by in corpus (12)

• Theory of 2D crystals: graphene and beyond
• Electronic Structure Theory of Strained Two-Dimensional Materials with Hexagonal Symmetry
• Unconventional phases in a Haldane model of dice lattice
• Distinctive signatures of the spin- and momentum-forbidden dark exciton states in the photo-luminescences of strained WSe${}_2$ monolayers under thermalization
• Optical orientation with linearly polarized light in transition metal dichalcogenides
• Electronic properties of single-layer antimony: Tight-binding model, spin-orbit coupling and the strength of effective Coulomb interactions
• Field-created diverse quantizations in phosphorenes
• High-energy Landau levels in graphene beyond nearest-neighbor hopping processes: Corrections to the effective Dirac Hamiltonian
• Magnetic Bulk Photovoltaic Effect: Strong and Weak Field
• Magnetizations and de Haas-van Alphen oscillations in massive Dirac fermions
• Effective lattice Hamiltonian for monolayer tin disulphide: tailoring electronic structure with electric and magnetic fields
• Engineering stacking-induced topological phase transitions in bilayer heterostructures