Effective Magnetic Fields in Graphene Superlattices

TL;DR

This paper shows that a slowly varying one-dimensional periodic potential in graphene creates an effective magnetic field, leading to Landau levels, which could impact electronic transport properties.

Contribution

The authors develop an effective theory linking superlattice potentials in graphene to emergent magnetic fields and confirm it with numerical analysis.

Findings

Landau level spectrum appears in graphene with slowly varying periodic potential

Effective magnetic field arises due to extra Dirac points in the spectrum

Numerical diagonalization confirms the theoretical predictions

Abstract

We demonstrate that the electronic spectrum of graphene in a one-dimensional periodic potential will develop a Landau level spectrum when the potential magnitude varies slowly in space. The effect is related to extra Dirac points generated by the potential whose positions are sensitive to its magnitude. We develop an effective theory that exploits a chiral symmetry in the Dirac Hamiltonian description with a superlattice potential, to show that the low energy theory contains an effective magnetic field. Numerical diagonalization of the Dirac equation confirms the presence of Landau levels. Possible consequences for transport are discussed.