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.
- Pub Date:
- December 2020
- Mathematics - Analysis of PDEs;
- Mathematical Physics;
- Submitted to the proceedings of the conference "Mathematical Challenge of Quantum Transport in Nanosystems. Pierre Duclos Workshop" - Saint Petersburg, September 14-16, 2020