Manipulating the non-Hermitian skin effect through nonreciprocal flux in topolectrical circuits

Abstract

Flux modulation refers to the phase accumulation of electrons along closed lattice loops, inducing the formation of colorful localized states. Traditional research focuses on the discrete π-flux, limiting the continuous control of skin mode transitions. Here, we discuss a non-Hermitian system that combines complex intracell hopping with nonreciprocal next-nearest-neighbor coupling, enabling continuous tuning of the flux phase over a full 2π period. Based on the phase diagrams of the Bloch winding number, we reveal multiple spectral transitions induced by nonreciprocal flux. Distinct spectral behaviors emerge, including directional windings, deformation, and eigenvalue overlaps in the complex plane. Theoretical predictions are experimentally validated using circuits, where the measured voltage responses show agreement with simulations. This method can be extended to two-dimensional mirror-stacked structures. This work provides a theoretical and experimental platform for programmable non-Hermitian devices and topological sensing applications.