Variational Approach for the Effects of Periodic Modulations on the Spectrum of Massless Dirac Fermion

TL;DR

This paper introduces a variational method to analyze how one-dimensional periodic modulations in magnetic and electrostatic fields affect the energy spectrum of massless Dirac fermions in graphene, providing more stable solutions than perturbation theory.

Contribution

The study presents a novel variational approach to evaluate the electronic spectrum of Dirac fermions under periodic modulations, improving upon traditional perturbation methods.

Findings

Variational energies are lower than perturbation energies.

The method yields more stable and accurate spectral solutions.

Periodic modulations significantly influence Landau levels.

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.