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NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2021, 12 (1), P. 5–14

Bifurcating standing waves for effective equations in gapped honeycomb structures

W. Borrelli – Centro De Giorgi, Scuola Normale Superiore, Piazza dei Cavalieri 3, I-56100, Pisa, Italy; william.borrelli@sns.it
R. Carlone – 2Università “Federico II” di Napoli, Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, MSA, via Cinthia, I-80126, Napoli, Italy; raffaele.carlone@unina.it

In this paper, we deal with two-dimensional cubic Dirac equations, appearing as an 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.

Keywords: nonlinear Dirac equations, bifurcation methods, existence results, honeycomb structures.

PACS 03.65.-w, 02.30.Rz

DOI 10.17586/2220-8054-2021-12-1-5-14

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