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

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