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 quasiedge
states is challenging both from practical and conceptual viewpoints. In fact, in any realistic
system with a finite lattice size most of quasiedge states collapse and become metastable states.
Here we suggest a route toward the selective and tunable excitation of topological quasi-edge states
which 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.