Title: Ring Structure in the Complex Plane: A Fingerprint of non-Hermitian Mobility Edge

Abstract: By Avila's global theory, we analytically reveal that the non-Hermitian mobility edge will take on a ring structure in the complex plane, which we name as "mobility ring". The universality of mobility ring has been checked and supported by the Hermitian limit, $PT$-symmetry protection and without $PT$-symmetry cases. Further, we study the evolution of mobility ring versus quasiperiodic strength, and find that in the non-Hermitian system, there will appear multiple mobility ring structures. With cross-reference to the multiple mobility edges in Hermitian case, we give the expression of the maximum number of mobility rings. Finally, by comparing the results of Avila's global theorem and self-duality method, we show that self-duality relation has its own limitations in calculating the critical point in non-Hermitian systems. As we know, the general non-Hermitian system has a complex spectrum, which determines that the non-Hermitian mobility edge can but exhibit a ring structure in the complex plane.