Extended Data Fig. 8: Gap size at v = 2.

a, Normalized penetration capacitance \({C}_{{\rm{p}}}/{C}_{{\rm{series}}}\) as a function of \(\nu\) and \(E\) at \(T=1.6\) K and \({B}_{\perp }=0\) T. The Kondo lattice regime is marked by the blue dashed line. An incompressible state is observed at \(\nu =2\). b, Electric-field dependence of the thermodynamic gap size \(\varDelta\) at \(\nu =2\), obtained by integrating the normalized penetration capacitance \({C}_{{\rm{p}}}/{C}_{{\rm{series}}}\) (see Methods). c, Electric-field dependence of the estimated thermal activation gap from the temperature dependence of \({R}_{{\rm{bulk}}}\). Error bars denote the standard deviation from data fitting. The dashed lines in b, c indicate the phase boundaries (\({E}_{1}\) and \({E}_{2}\), see main text) separating three regimes: a band insulator, mixed-valence insulator and TKI. d, Arrhenius fits (solid lines) for the temperature dependence of \({R}_{{\rm{bulk}}}\) at two representative electric fields (\(E=0.63\,{\rm{V}}/{\rm{nm}}\) and \(E=0.75\,{\rm{V}}/{\rm{nm}}\)). (The results in a, b, and c, d are from devices 1 and 2, respectively.).