Dirac fermions in armchair graphene nanoribbons trapped by electric quantum dots

We study the confinement of Dirac fermions in armchair graphene nanoribbons by means of electrostatic quantum dots. We provide an analytically feasible model where some bound states can be found explicitly. We show that the energies of these bound states belong either to the gap of valence and conducting bands or they represent bound states in the continuum whose energies are embedded in the continuous spectrum. The solutions satisfying armchair boundary conditions are found in an elegant manner with the use of specific projection operators.

Automated summary

We studied the confinement of Dirac fermions in armchair graphene nanoribbons using electrostatic quantum dots. We provided an analytically feasible model where some bound states can be explicitly found. We showed that the energies of these bound states either belong to the gap between the valence and conducting bands, or represent bound states in the continuum with energies embedded in the continuous spectrum. Solutions satisfying armchair boundary conditions were elegantly found using specific projection operators.