Inserted: 13 jan 2021
Submitted to the proceedings of the conference "Mathematical Challenge of Quantum Transport in Nanosystems. Pierre Duclos Workshop" - Saint Petersburg, September 14-16, 2020
In this paper we deal with two dimensional cubic Dirac equations appearing as effective model in gapped honeycomb structures. We give a formal derivation starting from cubic Schrödinger equations and prove the existence of standing waves bifurcating from one band-edge of the linear spectrum.