Eur. Phys. J. Plus (2020) 135: 786
https://doi.org/10.1140/epjp/s13360-020-00818-6

Regular Article

Band spectra of periodic hybrid structures

¹ Departamento de Física Teórica, Atómica y Óptica, Universidad de Valladolid, 47011, Valladolid, Spain
² Departamento de Física Fundamental, IUFFyM, Universidad de Salamanca, Salamanca, Spain

^d luismiguel.nieto.calzada@uva.es

Received: 2 July 2020
Accepted: 28 September 2020
Published online: 6 October 2020

Abstract

We present a detailed study of a generalised one-dimensional Kronig–Penney model using potentials. We analyse the band structure and the density of states in two situations. In the first case, we consider an infinite array formed by identical potentials standing at the linear lattice nodes. This case will be known throughout the paper as the one-species hybrid Dirac comb. We investigate the consequences of adding the interaction to the Dirac comb by comparing the band spectra and the density of states of pure Dirac- combs and one-species hybrid Dirac combs. Secondly, we study the quantum system that arises when the periodic potential is the one obtained from the superposition of two one-species hybrid Dirac combs displaced one with respect to the other and with different couplings. The latter will be known as the two-species hybrid Dirac comb. One of the most remarkable results is the appearance of a curvature change in the band spectrum when the couplings are above a critical value.