Selective and tunable excitation of topological non-Hermitian quasi-edge modes

Non-Hermitian lattices under semi-infinite boundary conditions sustain an extensive number of exponentially localized states, dubbed non-Hermitian quasi-edge modes. Quasi-edge states arise rather generally in systems displaying the non-Hermitian skin effect and can be predicted from the non-trivial topology of the energy spectrum under periodic boundary conditions via a bulk-edge correspondence. However, the selective excitation of the system in one among the infinitely many topological quasi-edge states is challenging both from practical and conceptual viewpoints. In fact, in any realistic system with a finite lattice size most of the quasi-edge states collapse and become metastable states. Here we suggest a route toward the selective and tunable excitation of topological quasi-edge states that avoids the collapse problem by emulating semi-infinite lattice boundaries via tailored on-site potentials at the edges of a finite lattice. We illustrate such a strategy by considering a non-Hermitian topological interface obtained by connecting two Hatano-Nelson chains with opposite imaginary gauge fields, which is amenable for a full analytical treatment.