Modulation effects on Landau levels in a monolayer graphene

TL;DR

This paper investigates how spatially modulated magnetic fields influence Landau levels in monolayer graphene, revealing effects like dimensionality change, energy dispersion modification, and state degeneracy destruction.

Contribution

It introduces a detailed analysis of modulation effects on Landau levels in graphene using the Peierl's tight-binding model, highlighting the roles of field strength, period, and direction.

Findings

Presence of a robust Landau level at the Fermi level

Emergence of 1D parabolic subbands around original Landau levels

Density of states exhibits delta-function-like and asymmetric peak structures

Abstract

A monolayer graphene exists in an environment where a uniform magnetic field interacts a spatially modulated magnetic field. The spatially modulated magnetic field could affect Landau levels due to a uniform magnetic field. The modulation effects on Landau levels are investigated through the Peierl's tight-binding model. The magneto-electronic properties are dominated by the period, the strength, and the direction of a spatially modulated magnetic field. Such a field could induce the growth in dimensionality, the change of energy dispersions, the destroy of state degeneracy, and the creation of band-edge states. There are a robust Landau level at Fermi level and 1D parabolic subbands located around the original Landau levels, which make density of states exhibit a delta-function-like structure and many pairs of asymmetric peak structure, respectively. The density of states and the energies of band-edge states strongly depend on the strength, but not on the period and the direction.