# Edge states in dynamical superlattices

## TL;DR

This paper explores the unique edge states and localization phenomena in one-dimensional dynamically modulated superlattices, revealing their topological properties and potential for robust edge transport.

## Contribution

It introduces the concept of edge states in dynamically modulated superlattices and analyzes their topological origin and localization behavior.

## Key findings

- Edge states exist within specific coupling constant intervals.
- Dynamical localization occurs due to quasi-energy band collapse.
- Edge states show enhanced robustness and unique transport properties.

## Abstract

We address edge states and rich localization regimes available in the one-dimensional (1D) dynamically modulated superlattices, both theoretically and numerically. In contrast to conventional lattices with straight waveguides, the quasi-energy band of infinite modulated superlattice is periodic not only in the transverse Bloch momentum, but it also changes periodically with increase of the coupling strength between waveguides. Due to collapse of quasi-energy bands dynamical superlattices admit known dynamical localization effect. If, however, such a lattice is truncated, periodic longitudinal modulation leads to appearance of specific edge states that exist within certain periodically spaced intervals of coupling constants. We discuss unusual transport properties of such truncated superlattices and illustrate different excitation regimes and enhanced robustness of edge states in them, that is associated with topology of the quasi-energy band.