Emergent topological properties in spatially modulated sub-wavelength barrier lattices

TL;DR

This paper explores topological phenomena in a spatially modulated Dirac-delta lattice, revealing controllable quantum transport and connections to Hofstadter's model, with potential experimental realization using optically controlled atoms.

Contribution

It introduces a spatially modulated Kronig-Penney system that exhibits topological transport and links to Hofstadter physics, with a feasible experimental setup.

Findings

Energy spectrum shows Hofstadter butterfly pattern.

Topological transport characterized by non-trivial Chern numbers.

Experimental realization proposed using optically controlled atoms.

Abstract

We investigate topological phenomena in a spatially modulated Dirac-$\delta$ lattice, where the scattering potential varies periodically in space. Changing the potential modulation frequency leads to Hofstadter's butterfly-like energy spectrum and enables the emergence of topological transport regimes characterized by non-trivial Chern numbers. We show how the considered modulated system is connected to the Hofstadter model via the Harper equation. By adiabatically varying spatial modulation parameters, we demonstrate controllable quantum transport and verify the topological nature of these effects through Wannier center displacement and bulk invariant calculations. We also propose an experimentally feasible realization of such a system using optically controlled three-level atoms. Our findings showcase spatially engineered Kronig-Penney-type systems as versatile platforms for investigating and exploiting different topological quantum transport regimes.