Gap opening in two-dimensional periodic systems

DOI10.1142/S0219199719500809zbMATH Open1465.35146arXiv1810.08824OpenAlexW2979863441WikidataQ127104163 ScholiaQ127104163MaRDI QIDQ5129239

P. Exner, Denis Borisov

Publication date: 26 October 2020

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Abstract: We present a new method of gap control in two-dimensional periodic systems with the perturbation consisting of a second-order differential operator and a family of narrow potential `walls' separating the period cells in on direction. We show that under appropriate assumptions one can open gaps around points determined by dispersion curves of the associated `waveguide' system, in general any finite number of them, and to control their widths in terms of the perturbation parameter. Moreover, the distinctive feature of those gaps is that their edge values are attained by the corresponding band functions at internal points of the Brillouin zone.

Full work available at URL: https://arxiv.org/abs/1810.08824

zbMATH Keywords

periodic operatorsspectral gapsBrillouin zoneextrema at internal points

Mathematics Subject Classification ID

Spectral theory and eigenvalue problems for partial differential equations (35P99) Second-order elliptic equations (35J15) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

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