Effect of topology on the critical charge in graphene

TL;DR

This paper investigates how the topology of graphene samples, especially conical shapes, influences the critical charge for Dirac excitations, revealing that topology can significantly alter electronic properties.

Contribution

It demonstrates that the critical charge in graphene depends on sample topology, particularly showing that conical geometries can reduce the critical charge to zero.

Findings

Critical charge varies with sample topology.

Conical graphene shapes can eliminate the critical charge.

Topology affects scattering and local density of states.

Abstract

We show that the critical charge for the Dirac excitations in gapless graphene depends on the spatial topology of the sample. In particular, for graphene cones, the effective value of the critical charge can tend towards zero for a suitable angle of the conical sample. We discuss the nature of the scattering phase shifts, quasi-bound state energies and local density of states for a gapless graphene cone and determine the dependence of these physical quantities on the sample topology.