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

Longhi, Stefano
Proceedings of the Royal Society A 478, 20210927 (1-15) (2022)

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.

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