A new magnetic field dependence of Landau levels on a graphene like structure

TL;DR

This paper investigates a honeycomb lattice model under magnetic fields, revealing a novel Landau level dependence on the field with a 2/3 power law, linked to Berry phase effects, expanding understanding of quantum behaviors in graphene-like structures.

Contribution

It introduces a new magnetic field dependence of Landau levels in a honeycomb lattice with special hopping parameters, connecting tight-binding and continuum models.

Findings

Landau levels follow a (n+γ)B^{2/3} dependence

Berry phase cancellation leads to γ=1/2

Spectrum linked to a modified quartic oscillator

Abstract

We consider a tight-binding model on the honeycomb lattice in a magnetic field. For special values of the hopping integrals, the dispersion relation is linear in one direction and quadratic in the other. We find that, in this case, the energy of the Landau levels varies with the field B as E_n(B) ~ [(n+\gamma)B]^{2/3}. This result is obtained from the low-field study of the tight-binding spectrum on the honeycomb lattice in a magnetic field (Hofstadter spectrum) as well as from a calculation in the continuum approximation at low field. The latter links the new spectrum to the one of a modified quartic oscillator. The obtained value $\gamma=1/2$ is found to result from the cancellation of a Berry phase.