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

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, in higher dimensions, achieving deterministic control over where skin modes accumulate remains a major challenge. Here, we propose a versatile route to program the skin-mode localization site 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. Our results establish a robust and broadly applicable route to engineer boundary accumulation and directed transport along prescribed directions in two-dimensional non-Hermitian systems, enabling reconfigurable wave routing in classical platforms and programmable transport functionalities in quantum settings.