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

Non-Hermitian topological systems simultaneously posses two antagonistic features: ultra sensitivity 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 pseudospectra theory on the prototypical non-Hermitian SSH (NHSSH) lattice. Topological modes are robust with respect to chiral perturbations and sensitive to parity-time (PT) symmetry preserving perturbations. In fact, the chiral symmetry exactly at the exceptional point leads to the suppression of its sensitivity, corresponding to a lower order exceptional point. However, counterintuitively, they are most sensitive with respect to unstructured perturbations, leaving the fingerprint of the pertinent higher order exceptional (HEP) point.