Coulomb screening in graphene with topological defects

TL;DR

This paper investigates how topological defects in graphene, modeled as conical structures, influence Coulomb charge screening, revealing topology-dependent critical charges, altered transport properties, and unique resonance behaviors in both subcritical and supercritical regimes.

Contribution

It provides a detailed analysis of Coulomb screening in graphene with topological defects, highlighting the impact of sample topology on critical charge and transport phenomena, which was not previously characterized.

Findings

Critical charge depends on the conical defect topology.

Transport cross-section increases with the presence of a conical defect.

Fano resonances appear at lower Coulomb charges due to the defect.

Abstract

We analyze the screening of an external Coulomb charge in gapless graphene cone, which is taken as a prototype of a topological defect. In the subcritical regime, the induced charge is calculated using both the Green's function and the Friedel sum rule. The dependence of the polarization charge on the Coulomb strength obtained from the Green's function clearly shows the effect of the conical defect and indicates that the critical charge itself depends on the sample topology. Similar analysis using the Friedel sum rule indicates that the two results agree for low values of the Coulomb charge but differ for the higher strengths, especially in the presence of the conical defect. For a given subcritical charge, the transport cross-section has a higher value in the presence of the conical defect. In the supercritical regime we show that the coefficient of the power law tail of polarization charge density can be expressed as a summation of functions which vary log periodically with the distance from the Coulomb impurity. The period of variation depends on the conical defect. In the presence of the conical defect, the Fano resonances begin to appear in the transport cross-section for a lower value of the Coulomb charge. For both sub and supercritical regime we derive the dependence of LDOS on the conical defect. The effects of generalized boundary condition on the physical observables are also discussed.