Phase transitions in Hatano–Nelson lattice chains with periodically modulated disorder

Abstract We theoretically study a one-dimensional Hatano–Nelson lattice with mosaic-modulated on-site potentials to uncover the interplay between non-Hermiticity, disorder, and periodicity in shaping spectral and dynamical properties. Through analytical and numerical analyses, we demonstrate that the mosaic modulation generates closed-loop energy trajectories in the complex plane, which coalesce as the imaginary gauge field approaches a critical threshold. Remarkably, the periodic arrangement of disordered potentials enables tunable real–complex spectral transitions and localization–delocalization crossovers at well-defined spectral regions, marked by the emergence of mobility edges. Notably, delocalized states with complex eigenvalues exhibit characteristic nodal structures. To further elucidate the transport behavior, we investigate wave packet dynamics via the mean square displacement and center of mass. Our results reveal an abrupt transition from localization to ballistic spreading induced by the structured disorder—an effect absent in the standard Hatano–Nelson model with weak non-Hermiticity. Our work highlights the rich physics driven by structured disorder in non-Hermitian systems.