One-Parameter Scaling of Ground-State Stark Localization in a Five-Layer Semiconductor Superlattice

Controlling the spatial localization of electronic states is a fundamental strategy for manipulating charge and energy at the nanoscale. In coupled nanostructures, however, the localization field depends strongly on coupling between confinement regions, complicating comparisons across geometries. Here, we show that ground-state electric-field-induced localization follows a common master curve governed by a single dimensionless parameter comparing electrostatic detuning and quantum coupling. Using a one-dimensional effective-mass model for the stacking direction of a disorder-free five-layer GaAs/Al_0.3Ga_0.7As superlattice with L_y= 10 nm, we vary only the interlayer barrier thickness, changing the zero-field coupling scale by more than two orders of magnitude. Despite widely different localization fields, charge-transfer and normalized Stark-shift curves nearly collapse when expressed in terms of Λ = eE_extd/W₁(0). A five-site nearest-neighbor tight-binding model, with hopping fixed by the continuum zero-field manifold width, reproduces the master curve and predicts reduced thresholds within a few percent without additional fitted parameters. Small systematic departures occur in the strong-coupling regime at deep localization, where absolute fields produce intra-well deformation beyond a one-orbital description. These results establish, within this structural family, a simple connection between the zero-field electronic spectrum and the electric field required for nanoscale ground-state localization, providing a predictive framework for the design of field-tunable coupled quantum structures.