Anomalous non-Hermitian skin effect: the topological inequivalence of skin modes versus point gap

Non-Hermitian skin effect, the localization of an extensive number of eigenstates at the ends of the system, has greatly expanded the frontier of physical laws. It has long been believed that the present of skin modes is equivalent to the topologically nontrivial point gap of complex eigenvalues under periodic boundary conditions, and vice versa. However, we find that this concomitance can be broken, i.e., the skin modes can be present or absent whereas the point gap is topologically trivial or nontrivial, respectively, named anomalous non-Hermitian skin effect. This anomalous phenomenon arises when the unidirectional hopping amplitudes leading to the decoupling-like behaviors among subsystems are emergence. The emergence of the anomalous non-Hermitian skin effect is accompanied by the mutations of the open boundary energy spectrum, whose structure exhibits the multifold exceptional point and can not be recovered by continuum bands. Moreover, an experimental setup using circuits is proposed to simulate this novel quantum effect. Our results reveal the topologically inequivalent between skin modes and point gap. This new effect not only can give a deeper understanding of non-Bloch theory and the critical phenomenon in non-Hermitian systems, but may also inspire new applications such as in the sensors field.