Energy spectrum of graphene multilayers in a parallel magnetic field

Abstract

We study the orbital effect of a strong magnetic field parallel to the layers on the energy spectrum of the Bernal-stacked graphene bilayer and multilayers, including graphite. We consider the minimal model with the electron tunneling between the nearest sites in the plane and out of the plane. Using the semiclassical analytical approximation and exact numerical diagonalization, we find that the energy spectrum consists of two domains. In the low- and high-energy domains, the semiclassical electron orbits are closed and open, so the spectra are discrete and continuous, correspondingly. The discrete energy levels are the analogs of the Landau levels for the parallel magnetic field. They can be detected experimentally using electron tunneling and optical spectroscopy. In both domains, the electron wave functions are localized on a finite number of graphene layers, so the results can be applied to graphene multilayers of a finite thickness.

11 pages, 13 figures. Added to v.2: Appendix A, Fig. 13, Refs. [18-23]. V.3: minor stylistic corrections from the published version

References in corpus (10)

• Electric Field Effect in Atomically Thin Carbon Films
• Unconventional Integer Quantum Hall effect in graphene
• Electronic states and Landau levels in graphene stacks
• Landau level spectroscopy of ultrathin graphite layers
• Infrared spectroscopy of Landau levels in graphene
• Tight--binding description of the quasiparticle dispersion of graphite and few--layer graphene
• Magneto-optical properties of multilayer graphenes
• High-Energy Limit of Massless Dirac Fermions in Multilayer Graphene using Magneto-Optical Transmission Spectroscopy
• Graphite from the viewpoint of Landau level spectroscopy: An effective graphene bilayer and monolayer
• Graphene magnetoresistance in a parallel magnetic field: Spin polarization effect

Cited by in corpus (6)

• Spin-polarized tunneling current through a thin film of topological insulator in a parallel magnetic field
• Magnetic ratchet effect in bilayer graphene
• Inter-subband Landau level couplings induced by in-plane magnetic fields in trilayer graphene
• Effects of a tilted magnetic field in a Dirac double layer
• Infrared magneto-spectroscopy of graphite in tilted fields
• Broken symmetry states in bilayer graphene in electric and in-plane magnetic fields