We present a new method for describing the electronic structure of graphene, by treating the honeycomb lattice as an arrangement of crisscrossing one-dimensional quantum wires. The electrons travel as free particles along the wires and interfere at the three-way junctions formed by the carbon atoms. The approach produces the linearly dispersive Dirac band structure as well as the chiral pseudo-spin-wave functions. When vacancies are incorporated, the model reproduces the well known zero mode states.

• Received 8 June 2016
• Revised 19 August 2016

DOI:https://doi.org/10.1103/PhysRevB.94.205126