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In Hermitian topological systems, the bulk-boundary correspondence strictlyconstraints boundary transport to values determined by the topologicalproperties of the bulk. We demonstrate that this constraint can be lifted innon-Hermitian Floquet insulators. Provided that the insulator supports ananomalous topological phase, non-Hermiticity allows us to modify the boundarystates independently of the bulk, without sacrificing their topological nature.We explore the ensuing possibilities for a Floquet topological insulator withnon-Hermitian time-reversal symmetry, where the helical transport viacounterpropagating boundary states can be tailored in ways that overcome theconstraints imposed by Hermiticity. Non-Hermitian boundary state engineeringspecifically enables the enhancement of boundary transport relative to bulkmotion, helical transport with a preferred direction, and chiral transport inthe same direction on opposite boundaries. We explain the experimentalrelevance of our findings for the example of photonic waveguide lattices.

Non-Hermitian Boundary State Engineering in Anomalous Floquet Topological Insulators