Fig. 3: Dielectric catastrophe near the Mott and Wigner–Mott transitions.

a, b Reflectance contrast spectrum of the sensor 2s exciton under varying electric fields at fixed electron filling factor of \(\nu\) = 3 (a) and 7/3 (b). The spectra are vertically displaced by a constant 0.03. The dashed lines represent the reflectance contrast spectra at high electric fields (0.28 V/nm and 0.24 V/nm for \(\nu\) = 3 and 7/3, respectively), in which the broad humps correspond to the band-to-band transitions. The vertical dotted lines denote the 2s exciton peak. c, Reflectance contrast spectrum at \(\nu\) = 3, normalized by that at 0.28 V/nm (in the metallic phase), at representative electric fields. The spectral weight S is extracted by integrating the shaded area. d The extracted 2s spectral weight S (symbols) as a function of electric field (bottom axis) and \({\triangle }_{c}\) (top axis) for \(\nu\) = 3 (upper panel) and \(\nu\) = 7/3 (lower panel). The band offset \({\triangle }_{c}\) is calculated using the applied electric field as described in Methods. The dashed lines are the smoothed data using the Savitzky-Golay algorithm with a window of 80 mV/nm. The solid lines are the dielectric constant \(\bar{\varepsilon }\) of the moiré heterobilayer (right axis) that is normalized to unity at 0.02 V/nm and −0.08 V/nm (upper and lower panel, deep in the insulating phase). It is obtained from the dashed lines using the empirical relation, \(S\propto {\varepsilon }^{-0.7}\) (Methods).