Fig. 4: Investigating the interaction-driven nature of the insulating state.

a, STM micrographs of arrays F, D and E (left to right), with inter-dot separation a ≈ 15 nm and distinct quantum dot areas A. The predicted interaction strength U is shown for each array. b, Bias spectroscopy for the three arrays, with bias voltage V_dc normalized by the Mott–Hubbard gap \({\Delta }_{{\rm{c}}}^{{\rm{th}}}\). A total depletion of charge transport occurs in the Coulomb gap \({\Delta }_{{\rm{eh}}}^{{\rm{th}}}\), indicated by the coloured arrows. The stronger-interacting devices D and E show a coherence peak at the Mott–Hubbard value \(e{V}_{{\rm{dc}}}\approx \pm 2{\Delta }_{{\rm{c}}}^{{\rm{th}}}\), indicated by the vertical dashed lines, whereas device F exhibits one just outside the Coulomb gap. c, Increase of the charge gap Δ_c in an applied magnetic field, normalized by the interaction U. The linear dependence suggests electron exchange as the underlying mechanism; an effective Landé factor g_eff is extracted from a linear fit for each device. The data are offset by 0.3 for better visibility. d, Thermal activation of the low-bias conductance σ_xx in the three arrays. Transport is driven by incoherent or coherent electron co-tunnelling, with a switch at the cross-over scale T_c indicated by the vertical dashed lines. In both regimes, the conductance follows an Efros–Shklovskii (ES) law and depends exponentially on the inverse square root of temperature, but with distinct activation temperatures \({T}_{0}^{{\rm{in}},{\rm{el}}}\) (slopes of fitted dashed grey lines). e, The quantum dot level spacing δ (in meV) and the spin susceptibility χ_s (dimensionless), extracted from analysis of the data in Figs. 3b and 4c, versus the quantum dot area A.