Temperature-driven transition between momentum-resolved and disordered averaged Coulomb drag in 1D systems

Advancing the understanding of electron-electron interactions in one-dimensional systems remains one of the central challenges in low-dimensional physics, especially for Coulomb-coupled Tomonaga-Luttinger liquids. Notably, the difficulty of reliably extracting one-dimensional system parameters, combined with the presence of disorder, has hindered the interpretation of 1D Coulomb drag experiments. Here, we present a self-consistent experimental determination of the relative Luttinger liquid interaction parameters through 1D Coulomb drag measurements, and achieve quantitative agreement with theoretical predictions. Utilizing vertically coupled GaAs-AlGaAs quantum wires, we fully characterize the one-dimensional parameters through magnetic depopulation. Coulomb drag exhibits a systematic evolution with magnetic field, reflecting the successive depopulation of 1D subbands and the suppression of disorder effects. Two distinct temperature regimes are identified, marking the boundary between momentum-resolved and disordered-averaged Coulomb drag. The observed scaling, peak broadening, and nonlinear current-voltage characteristics establish a unified and quantitative framework for probing electron-electron interactions in 1D systems.