Character of electronic states in graphene antidot lattices: Flat bands and spatial localization

TL;DR

This paper investigates the electronic properties of graphene antidot lattices, revealing flat and localized electron states, and discusses their implications for electron localization, spin qubits, and dephasing phenomena.

Contribution

It provides a detailed analysis of flat and quasi-flat bands in graphene antidot lattices and predicts real-space electron density profiles for localized states.

Findings

Existence of zero-energy flat bands related to bipartite lattice structure

Presence of low-energy quasi-flat bands and localized states

Potential link between localized states and electron dephasing saturation

Abstract

Graphene antidot lattices have recently been proposed as a new breed of graphene-based superlattice structures. We study electronic properties of triangular antidot lattices, with emphasis on the occurrence of dispersionless (flat) bands and the ensuing electron localization. Apart from strictly flat bands at zero-energy (Fermi level), whose existence is closely related to the bipartite lattice structure, we also find quasi-flat bands at low energies. We predict the real-space electron density profiles due to these localized states for a number of representative antidot lattices. We point out that the studied low-energy, localized states compete with states induced by defects on the superlattice scale in this system which have been proposed as hosts for electron spin qubits. We furthermore suggest that local moments formed in these midgap zero-energy states may be at the origin of a surprising saturation of the electron dephasing length observed in recent weak localization measurements in graphene antidot lattices.