Theory of the electronic and transport properties of graphene under a periodic electric or magnetic field

TL;DR

This paper explores how applying periodic electric or magnetic fields to graphene alters its electronic properties, revealing anisotropic velocity renormalization, new Dirac fermions, and zero-energy modes, with potential implications for electronic applications.

Contribution

It provides analytical and numerical insights into the effects of one-dimensional periodic potentials on graphene's electronic structure, highlighting novel phenomena such as anisotropic velocity changes and new zero-energy modes.

Findings

Velocity is highly anisotropically renormalized under scalar potential.

New massless Dirac fermions are generated at supercell Brillouin zone boundaries.

Strong scalar potentials can produce additional zero-energy modes.

Abstract

We discuss the novel electronic properties of graphene under an external periodic scalar or vector potential, and the analytical and numerical methods used to investigate them. When graphene is subjected to a one-dimensional periodic scalar potential, owing to the linear dispersion and the chiral (pseudospin) nature of the electronic states, the group velocity of its carriers is renormalized highly anisotropically in such a manner that the velocity is invariant along the periodic direction but is reduced the most along the perpendicular direction. Under a periodic scalar potential, new massless Dirac fermions are generated at the supercell Brillouin zone boundaries. Also, we show that if the strength of the applied scalar potential is sufficiently strong, new zero-energy modes may be generated. With the periodic scalar potential satisfying some special conditions, the energy dispersion near the Dirac point becomes quasi one-dimensional. On the other hand, for graphene under a one-dimensional periodic vector potential (resulting in a periodic magnetic field perpendicular to the graphene plane), the group velocity is reduced isotropically and monotonically with the strength of the potential.