Exceptional deficiency of non-Hermitian systems: high-dimensional coalescence and dynamics

Exceptional points (EPs) are non-Hermitian singularities associated with the coalescence of individual eigenvectors accompanied by the degeneracy of their complex energies. Here, we report the discovery of a generalization to the concept of EP called exceptional deficiency (ED), which features the complete coalescence of two eigenspaces with identical but arbitrarily large dimensions and the coincidence of entire spectral continua. The characteristics of the ED are studied using one-way coupled Hermitian and non-Hermitian lattices. The ED can induce an anomalous absence and presence of non-Hermitian skin effect (NHSE) that transcends the topological bulk-edge correspondence of NHSE, resulting in unexpected synergistic skin-propagative dynamics. The conditions of the ED are also explored for unprecedented control of localization and propagation in non-Hermitian systems. These effects are experimentally observed using active mechanical lattices. The discovery of ED opens multiple new frontiers in non-Hermitian physics and can potentially resolve long-standing challenges in related applications.