Fig. 2: Numerical simulations of the localization length and comparison with experimental data.
From: Overactivated transport in the localized phase of the superconductor-insulator transition
a A sketch of the model used for numerical simulations. The electrode connected to the left edge is grounded, the electrode at the right edge has a potential V. The bottom panel shows a lateral view of the model where the capacitors C0 connecting the system to the gate can be seen. Grains are interconnected by random capacitors with average capacitance C. b Numerical results of the resistance as a function of inverse temperature. Each color corresponds to a different value of C0. The solid lines correspond to the clean case whereas the dashed lines correspond to the case where disorder is added (5% of the nodes have fixed charges ± 1 at random). c Characteristic temperature T0 as a function of the sample thickness (in Å) for different heat treatments (x = 13.5% sample). The solid line corresponds to Eqs. (4)-(6) with κ0 ≃ 250. For each thickness, the disorder level was averaged over the different heat treatments. Each dashed line corresponds to the exponential thickness dependence for a given heat treatment (as-deposited and θht = 160 ∘C). d Localization length on a logarithmic scale as a function of the disorder level W (relative to the kinetic energy t) for thicknesses ranging from 1 to 7 layers. e Exponential dependence of ξloc with d/W2, where d is the thickness.
