Extended Data Fig. 2: Calibration of the moiré density.
a,b, Longitudinal resistance R as a function of E and ν at 50 mK under B = 0 T (a) and 12 T (b). Large bias current is used in the measurement and superconductivity is not observed in a. Landau levels are clearly observed in b. Landau levels with index νLL = 2-8 (denoted by dotted lines) in the layer-polarized region are spin- and valley-polarized (i.e. nondegenerate). In addition, the Zeeman-split vHS features under B = 12 T are marked by dashed lines; these features interrupt the quantum oscillations (the vertical stripes in b). The midpoint of the Zeeman-split features is in good agreement with the location of the single vHS feature under B = 0 T (dashed line in a). c, Landau level index νLL as a function of moiré lattice filling ν follows a linear dependence (blue line). The moiré density is determined from the slope to be nM ≈ (4.25 ± 0.03) × 1012 cm−2. d, R as a function of B and ν at 50 mK and E = 100 mV/nm. Two sets of Landau fan emerging from the moiré band edges (i.e. ν = 0 and ν = 2) are marked by the dashed lines. The results give the same moiré density as above. e, The derivative of the sample conductance with respect to \(\nu ({dG}/d\nu )\) as a function of ν and 1/B at 50 mK and E = 100 mV/nm. Hofstadter’s oscillations are observed as periodic crossings of Landau levels in 1/B, as denoted by the horizontal dashed lines. f, 1/B at the dashed lines in e as a function of the periodic index q. A linear fit to the data gives a 1/B period (5.8 ± 0.1) × 10−3 T−1, which corresponds to nM ≈ (4.22 ± 0.06) × 1012 cm−2. The value is in good agreement with that obtained from a-c.
