Spatially inhomogeneous states of charge carrier in graphene

TL;DR

This paper investigates how charge carriers in graphene interact with impurity potentials, revealing the existence of localized states in 1D wells but not in 2D wells, and analyzes scattering and geometric effects.

Contribution

It provides a detailed analysis of localized states and scattering in graphene with impurity potentials, including the derivation of an effective Hamiltonian for curved quantum wires.

Findings

Discrete localized states exist in 1D potential wells in graphene.

Scattering cross-section approaches a constant at high energies.

Curved quantum wires do not support 1D bound states due to geometric potential.

Abstract

We study an interaction of 2D quasiparticles with linear dispersion (graphene) with impurity potentials. It is shown that in 1D potential well (quantum wire) there are discrete levels, corresponding to localized states, whereas in 2D well (quantum dot) there are no such states. Scattering cross-section of electrons (holes) of graphene by an axially symmetric potential well is found and it is shown that for infinetily large energy of incoming particles the cross-section tends to a constant. The effective Hamiltonian for a curved quantum wire of graphene is derived and it is shown that the corresponding geometric potential cannot form 1D bound states.