Inserted: 13 jan 2021
Last Updated: 11 mar 2021
Journal: Nanosystems: Physics, Chemistry, Mathematics
Doi: DOI 10.17586/2220-8054-2021-12-1-5-14
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.