Exceptionally deficient topological square-root insulators

Bid, Subhajyoti and Schomerus, Henning (2026) Exceptionally deficient topological square-root insulators. Physical Review Research. ISSN 2643-1564 (In Press)

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Abstract

One of the most surprising features of effectively non-Hermitian physical systems is their potential to exhibit a striking nonlinear response and fragility to small perturbations. This feature arises from spectral singularities known as exceptional points, whose realization in the spectrum typically requires fine-tuning of parameters. The design of such systems receives significant impetus from the recent conception of \emph{exceptional deficiency}, in which the entire energy spectrum is composed of exceptional points. Here, we present a concrete and transparent mechanism that enforces exceptional deficiency through lattice sum rules in non-Hermitian topological square-root insulators. We identify the resulting dynamical signatures in static broadband amplification and non-Abelian adiabatic state amplification, differentiate between bulk and boundary effects, and outline routes to implementation in physical platforms.