Energy spectrum of graphene multilayers in a parallel magnetic field

TL;DR

This paper investigates how a strong magnetic field parallel to graphene layers affects the energy spectrum of multilayer graphene, revealing discrete Landau-like levels and wave function localization, with implications for experimental detection.

Contribution

It provides a combined semiclassical and numerical analysis of the energy spectrum in multilayer graphene under parallel magnetic fields, highlighting the existence of discrete Landau-like levels.

Findings

Energy spectrum has discrete and continuous domains.

Discrete levels are analogous to Landau levels.

Wave functions are localized on finite layers.

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.