Title: Controllable suppression of Non-Hermitian skin effects

Abstract: The non-Hermitian skin effect (NHSE) is a phenomenon where the bulk states tend to the boundary within a non-Hermitian Hamiltonian system, with broad applications across various fields. A comprehensive understanding of anomalies in skin modes associated with NHSEs is essential for practical applications. Recently, some innovative works reported the suppression and enhancement of NHSEs through the application of magnetic fields, respectively. In our work, we engineered onsite potential energy distribution and found non-monotonic and monotonic suppression patterns on skin modes similar to magnetic fields. These suppression patterns represent characteristic transitions as the onsite potential distribution shifts from order to disorder. Relying only on onsite potential energy engineering, we have not only deepened our insight into the relationship and distinctions between order and disorder, but also developed a general strategy to demonstrate both robustness and controllable adjustability of the skin modes. By integrating with the scaling theory of disorder, we have extended the concept of controllable suppression of NHSEs to higher-dimensional systems.