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00925njm 22002777a 4500 dc Gadella, Manuel author Mateos Guilarte, Juan María author Muñoz Castañeda, José María author Nieto Calzada, Luis Miguel author Santamaría Sanz, Lucía author 2020-10 We present a detailed study of a generalised one-dimensional Kronig–Penney model using δ- δ′ 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 δ- δ′ 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 δ′ interaction to the Dirac comb by comparing the band spectra and the density of states of pure Dirac-δ 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 δ′ couplings are above a critical value. http://hdl.handle.net/10259/10004 10.1140/EPJP/S13360-020-00818-6 2190-5444 Band spectra of periodic hybrid δ- δ′ structures