Bifurcating standing waves for effective equations in gapped honeycomb structures

TL;DR

This paper derives and proves the existence of bifurcating standing waves in effective two-dimensional cubic Dirac equations modeling gapped honeycomb structures, starting from cubic Schrödinger equations.

Contribution

It provides a formal derivation and rigorous proof of bifurcating standing waves in cubic Dirac equations for honeycomb structures, a novel connection between models.

Findings

Existence of standing waves bifurcating from a band-edge

Formal derivation from cubic Schrödinger equations

Application to 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 Schr\"odinger equations and prove the existence of standing waves bifurcating from one band-edge of the linear spectrum.