Eur. Phys. J. B 74, 391-396 (2010)
https://doi.org/10.1140/epjb/e2010-00051-4

Variational approach for the effects of periodic modulations on the spectrum of massless Dirac fermion

Department of Physics, Faculty of Sciences, Ankara University, 06100 Tandoğan, Ankara, Turkey

Corresponding author: kandemir@science.ankara.edu.tr

Received: 17 December 2009
Revised: 20 January 2010
Published online: 9 February 2010

Abstract

In the variational framework, we study the electronic energy spectrum of massless Dirac fermions of graphene subjected to one-dimensional oscillating magnetic and electrostatic fields centered around a constant uniform static magnetic field. We analyze the influence of the lateral periodic modulations in one direction, created by these oscillating electric and magnetic fields, on Dirac like Landau levels depending on amplitudes and periods of the field modulations. We compare our theoretical results with those found within the framework of non-degenerate perturbation theory. We found that the technique presented here yields energies lower than that obtained by the perturbation calculation, and thus gives more stable solutions for the electronic spectrum of massless Dirac fermion subjected to a magnetic field perpendicular to graphene layer under the influence of additional periodic potentials.