Bifurcating standing waves for effective equations in gapped honeycomb structures

Abstract

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.

Submitted to the proceedings of the conference "Mathematical Challenge of Quantum Transport in Nanosystems. Pierre Duclos Workshop" - Saint Petersburg, September 14-16, 2020