Electronic states and Landau levels in graphene stacks

TL;DR

This paper provides an analytical study of the electronic structure and Landau levels in various graphene multilayer stacks, revealing how stacking order influences surface states and density of states, with implications for electronic properties.

Contribution

It introduces a minimal analytical model to explore how stacking order affects electronic states and Landau levels in graphene multilayers.

Findings

Electrostatic effects can cause divergent density of states in bi- and tri-layer graphene.

Surface density of states can vanish or form surface bands depending on stacking order.

Stacking order critically influences electronic surface states in graphene stacks.

Abstract

We analyze, within a minimal model that allows analytical calculations, the electronic structure and Landau levels of graphene multi-layers with different stacking orders. We find, among other results, that electrostatic effects can induce a strongly divergent density of states in bi- and tri-layers, reminiscent of one-dimensional systems. The density of states at the surface of semi-infinite stacks, on the other hand, may vanish at low energies, or show a band of surface states, depending on the stacking order.