Robustness versus sensitivity in non-Hermitian topological lattices probed by pseudospectra

Abstract

Non-Hermitian topological systems simultaneously possess two antagonistic features: ultrasensitivity due to exceptional points and robustness of topological zero-energy modes, and it is unclear which one prevails under different perturbations. We study that question by applying the pseudospectrum theory on the prototypical non-Hermitian Su-Schrieffer-Heeger lattice. Topological modes around the underlying third-order exceptional point (EP3) are robust with respect to chiral perturbations but sensitive to diagonal perturbations. In fact, exactly at the EP3 the chiral symmetry leads to a suppressed sensitivity, that corresponds to an EP2. Finally, for nonlinearly induced perturbations we provide a connection between the pseudospectrum approach and a nonlinear phase shift, which is relevant for experiments.