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

TL;DR

This paper demonstrates that the finite Kronig-Penney model with arbitrary scattering potentials can exhibit topologically non-trivial states, including protected edge states and complex spectra, revealing new topological properties in a classic quantum model.

Contribution

The study introduces an exact solution for the finite Kronig-Penney model with arbitrary scatterers, uncovering topological phases and spectral features not previously identified in this model.

Findings

Presence of topologically protected edge states

Emergence of Hofstadter butterfly-like spectra

Distinct spectral behaviors in weak and strong scattering regimes

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.