Topological states in the Kronig-Penney model with arbitrary scattering potentials

Abstract

We use an exact solution to the fundamental finite Kronig-Penney model with arbitrary positions and strengths of scattering sites to show that this iconic model can possess topologically non-trivial properties. By using free parameters of the system as extra dimensions we demonstrate the appearance of topologically protected edge states as well as the emergence of a Hofstadter butterfly-like quasimomentum spectrum, even in the case of small numbers of scattering sites. We investigate the behaviour of the system in the weak and strong scattering regimes and observe drastically different shapes of the quasimomentum spectrum.

arXiv comment10 pages, 7 figures

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• The Lieb excitations and topological flat mode of spectral function of Tonks-Girardeau gas in Kronig-Penney potential
• Characteristic determinant approach to the spectrum of one-dimensional $\mathcal{P}\mathcal{T}$-symmetric systems
• Topological control of the nonlinear-optical response of hybrid quantum systems
• Emergent topological properties in spatially modulated sub-wavelength barrier lattices