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

Abstract

It has long been believed that skin modes are equivalent to the nontrivial point gap. However, we find that this concomitance can be broken, in that skin modes can be absent or present when the point gap is nontrivial or trivial, respectively, named anomalous non-Hermitian skin effect. This anomalous phenomenon arises whenever unidirectional hopping amplitudes emerge among subsystems, where sub-chains have decoupling-like behaviors and contribute only to the energy levels without particle occupation. The occurrence of anomalous non-Hermitian skin effect is accompanied by changes in open boundary eigenvalues, whose structure exhibits multifold exceptional points and can not be recovered by continuum bands. Moreover, an experimental setup is proposed to simulate this effect. Our results reveal the topologically inequivalence of skin modes and point gap. This effect not only provides a deeper understanding of non-Bloch theory and critical phenomena, but may inspire applications, such as in sensor field.