Arbitrary Control of Non-Hermitian Skin Modes via Disorder and An 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 a significant challenging. Here, we propose a versatile approach to manipulate the localization of skin modes in two-dimensional non-Hermitian lattices by combining disorder with 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. In nonreciprocal lattices, when the nonreciprocal hopping is misaligned with the electric field, the hopping component perpendicular to the field guides wave-packet propagation and produces boundary localization. By tuning the relative orientation between the electric field and the nonreciprocal hopping direction, the boundary localization position can be continuously and arbitrarily controlled. We further demonstrate distinct geometry-dependent manipulation of skin modes in reciprocal lattices, where controllable boundary localization emerges solely from the lattice geometry. These results establish 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.