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

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+γ)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.

4 pages, 4 figures

References in corpus (5)

• Electric Field Effect in Atomically Thin Carbon Films
• Landau level spectroscopy of ultrathin graphite layers
• Zero modes of tight binding electrons on the honeycomb lattice
• BCS-BEC crossover on the two-dimensional honeycomb lattice
• Quantum Hall effect and the topological number in graphene

Cited by in corpus (14)

• A tight-binding approach to uniaxial strain in graphene
• Tilted anisotropic Dirac cones in quinoid-type graphene and alpha-(BEDT-TTF)_2I_3
• Merging of Dirac points in a two-dimensional crystal
• Gap opening in graphene by shear strain
• Comment on "Band structure engineering of graphene by strain: First-principles calculations"
• Dimensional crossover in topological matter: Evolution of the multiple Dirac point in the layered system to the flat band on the surface
• Ultracold Fermions in a Graphene-Type Optical Lattice
• Topologically Protected Zero Modes in Twisted Bilayer Graphene
• Strained bilayer graphene: Band structure topology and Landau level spectrum
• A semi-Dirac point in the Hofstadter spectrum
• Zero modes, energy gap, and edge states of anisotropic honeycomb lattice in a magnetic field
• The Hall conductance, topological quantum phase transition and the Diophantine equation on honeycomb lattice
• Quantum Phase Transition in Hall Conductivity on an Anisotropic Kagome Lattice
• Emergent Spin Liquids in the Hubbard Model on the Anisotropic Honeycomb Lattice