Ring structure in the complex plane: A fingerprint of a non-Hermitian mobility edge

Abstract

The mobility edge, as the critical energy separating the extended and localized states, is an important concept in Anderson localization theory. However, how the mobility edge works in non-Hermitian systems has not yet been revealed. Here, through Avila's global theory, the authors prove that the non-Hermitian mobility edge will develop into a ring structure in the complex plane. Combined with numerical calculations, it is convincing that the concept of mobility rings is universal in non-Hermitian quasiperiodic systems.