# Non-Hermitian Boundary State Engineering in Anomalous Floquet Topological Insulators

## TL;DR

This paper demonstrates how non-Hermiticity in Floquet topological insulators allows independent engineering of boundary states, enabling enhanced and directional boundary transport beyond Hermitian constraints.

## Contribution

It introduces non-Hermitian boundary state engineering in Floquet topological insulators, breaking Hermitian bulk-boundary constraints and enabling tailored boundary transport.

## Key findings

- Non-Hermitian systems can modify boundary states independently of the bulk.
- Boundary transport can be enhanced or made directional through non-Hermiticity.
- Experimental relevance shown for photonic waveguide lattices.

## Abstract

In Hermitian topological systems, the bulk-boundary correspondence strictly constraints boundary transport to values determined by the topological properties of the bulk. We demonstrate that this constraint can be lifted in non-Hermitian Floquet insulators. Provided that the insulator supports an anomalous topological phase, non-Hermiticity allows us to modify the boundary states independently of the bulk, without sacrificing their topological nature. We explore the ensuing possibilities for a Floquet topological insulator with non-Hermitian time-reversal symmetry, where the helical transport via counterpropagating boundary states can be tailored in ways that overcome the constraints imposed by Hermiticity. Non-Hermitian boundary state engineering specifically enables the enhancement of boundary transport relative to bulk motion, helical transport with a preferred direction, and chiral transport in the same direction on opposite boundaries. We explain the experimental relevance of our findings for the example of photonic waveguide lattices.