Gap opening in two-dimensional periodic systems

2018/10/20 by D. I. Borisov, Borisov, D. I., Pavel Exner +1
Computer Science · Physics and Astronomy · #35J10 #35P15 #81Q10 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Photonic Crystals and Applications #Quantum Physics (quant-ph) #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.1810.08824

openalex publication_date 2018/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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