Landau Levels in graphene in the presence of emergent gravity

TL;DR

This paper studies how elastic deformations and emergent gravity in graphene influence Landau levels, showing that emergent gravity causes a renormalization of Fermi velocity and modifies degeneracies depending on sample geometry.

Contribution

It introduces a model of emergent gravity in graphene with elastic deformation, analyzing its effect on Landau levels and degeneracy corrections.

Findings

Emergent gravity causes a constant renormalization of Fermi velocity.

Degeneracy corrections depend on the sample's geometry.

Uniform stretching preserves Landau level degeneracies.

Abstract

We consider graphene in the presence of external magnetic field and elastic deformations that cause emergent magnetic field. The total magnetic field results in the appearance of Landau levels in the spectrum of quasiparticles. In addition, the quasiparticles in graphene experience the emergent gravity. We consider the particular choice of elastic deformation, which gives constant emergent magnetic field and vanishing torsion. Emergent gravity may be considered as perturbation. We demonstrate that the corresponding first order approximation affects the energies of the Landau levels only through the constant renormalization of Fermi velocity. The degeneracy of each Landau level receives correction, which depends essentially on the geometry of the sample. There is the limiting case of the considered elastic deformation, that corresponds to the uniformly stretched graphene. In this case in the presence of the external magnetic field the degeneracies of the Landau levels remain unchanged.