Dirac fermions in armchair graphene nanoribbons trapped by electric quantum dots

TL;DR

This paper investigates how Dirac fermions in armchair graphene nanoribbons can be confined using electrostatic quantum dots, revealing bound states within the band gap and in the continuum spectrum.

Contribution

It provides exact solutions for bound states in graphene nanoribbons under electrostatic confinement, including states in the continuum spectrum.

Findings

Bound states exist within the band gap.

Bound states in the continuum are identified.

Exact solutions for certain bound states are derived.

Abstract

We study the confinement of Dirac fermions in armchair graphene nanoribbons by means of a quantum-dot-type electrostatic potential. With the use of specific projection operators, we find exact solutions for some bound states that satisfy appropriate boundary conditions. We show that the energies of these bound states belong either to the gap of valence and conducting bands or they represent BIC's (bound states in the continuum) whose energies are embedded in the continuous spectrum.