Arbitrary Control of Non-Hermitian Skin Modes via Disorder and Electric Field

Abstract: The non-Hermitian skin effect (NHSE), characterized by the accumulation of a macroscopic number of bulk states at system boundaries, is a hallmark of non-Hermitian physics. However, effective control of skin-mode localization in higher-dimensional systems remains challenging. Here, we propose a versatile approach to manipulate the localization of skin modes in a two-dimensional nonreciprocal lattice by combining disorder and a static electric field. While the electric field alone suppresses the NHSE in a clean system, the introduction of disorder induces transverse wave-packet transport perpendicular to the field. When the nonreciprocal hopping direction is misaligned with the electric field, the hopping component perpendicular to the field guides the wave-packet propagation and leads to boundary localization. By tuning the relative orientations of the electric field and the nonreciprocal hopping, arbitrary control over the boundary localization position can be achieved. Our results demonstrate a robust and tunable mechanism for engineering boundary accumulation and directed transport in non-Hermitian systems, offering new opportunities for applications in classical platforms and quantum materials.