Midgap states and charge inhomogeneities in corrugated graphene

TL;DR

This paper investigates how ripples in graphene induce effective gauge fields, leading to zero energy Landau levels, charge inhomogeneities, and valley symmetry breaking, which influence electronic properties and potential instabilities.

Contribution

It demonstrates the formation of zero energy Landau levels due to ripples and explores their impact on electronic inhomogeneities and valley symmetry breaking in graphene.

Findings

Zero energy Landau levels form when $h^2 / (l a) \,\gtrsim\, 1$.

Localized levels cause large zero-energy compressibility.

Ripples and magnetic fields break valley symmetry, enabling valley selection.

Abstract

We study the changes induced by the effective gauge field due to ripples on the low energy electronic structure of graphene. We show that zero energy Landau levels will form, associated to the smooth deformation of the graphene layer, when the height corrugation, $h$, and the length of the ripple, $l$, are such that $h^2 / (l a) \gtrsim 1$, where $a$ is the lattice constant. The existence of localized levels gives rise to a large compressibility at zero energy, and to the enhancement of instabilities arising from electron-electron interactions including electronic phase separation. The combined effect of the ripples and an external magnetic field breaks the valley symmetry of graphene leading to the possibility of valley selection.