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This work investigates bistable current-voltage (I–V) characteristics in amorphous a-YxSi1−x thin films, where disorder is controlled by thermal annealing. When a disordered insulator is biased electrically, the electron system can heat up well above the phonon bath temperature due to weak electron-phonon coupling, giving rise to multiple non-equilibrium steady states and abrupt jumps of up to four orders of magnitude in current. Experiments were carried out in a dilution refrigerator down to 13 mK, allowing the identification of the critical disorder level at which bistability first emerges and the characterization of the associated hysteresis in the nonlinear I–V curves.
To interpret these results, the authors first provide a microscopic derivation of the phenomenological hot-electron model, grounding it in the physics of electron hops between metallic-like grains embedded in an insulating matrix. In this picture, Coulomb interactions enable fast phononless thermalization across the sample, justifying a single well-defined electronic temperature Teff, while energy relaxation is governed by intra-grain electron-phonon transitions scaling as P ∝ α(Teff^β − Tph^β) with β = 6.
For the more insulating samples (annealed at 95 °C), this standard hot-electron model provides excellent quantitative agreement with experiment. However, for samples with lower disorder (80 °C), significant discrepancies arise, motivating two extensions: (i) incorporation of electric field-assisted hopping, which lowers the effective activation energy in a field-dependent resistance, and (ii) phonon-mediated inter-grain charge transfer, which introduces an additional relaxation channel that becomes dominant at high voltages. The extended model reproduces the experimental I–V curves across all disorder regimes, with fitting parameters fully consistent with the linear-response data.