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.

• Received 2 December 2021
• Revised 26 February 2022
• Accepted 4 March 2022

DOI:https://doi.org/10.1103/PhysRevB.105.165404