Exceptionally deficient topological square-root insulators

TL;DR

This paper introduces a mechanism for designing non-Hermitian topological insulators with a spectrum composed entirely of exceptional points, leading to unique dynamical behaviors like broadband amplification.

Contribution

It presents a lattice sum rule approach to achieve exceptional deficiency in non-Hermitian topological insulators, a novel spectral property.

Findings

Identification of dynamical signatures such as broadband amplification

Differentiation between bulk and boundary effects

Potential routes for physical implementation

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