Fig. 2: Resolving the onset of Landau quantization in milli-Tesla magnetic field.

a Schematic illustration of LATBG band structure at low magnetic field B and high D when Fermi level is tuned close to the CNP of one of graphene layers. b Fan diagram measured at D = −0.75 V/nm and 2 K shown as a function of chemical potential in the bottom graphene layer \({\mu }_{{\mbox{b}}}\). Black parabolic dashed lines indicate the expected position for the first five Landau levels (LLs) plotted using a standard graphene sequence \({E}_{{\mbox{N}}}=\sqrt{2\hslash {eB}{v}_{{\mbox{F}}}^{2}N+{\varDelta }^{2}}\), where \(\hslash\) is the reduced Plank constant, \(e\) is the electron charge, \({E}_{{\mbox{N}}}\) is the energy of the \({N}^{{\mbox{th}}}\) LL, and \({v}_{{\mbox{F}}}\) is the Fermi velocity in graphene, \(2\varDelta\) is a band gap discussed further in the text. The horizontal dashed line and the error bar mark the onset of Landau quantisation. Square root dashed lines indicate the limit of quantization set by the probe width (see Supplementary Note 5). c Schematic illustrations of electron-hole puddles in LATBG at zero (top) and under applied (bottom) displacement fields. Red and blue shaded regions represent positive and negative doping correspondingly, coloured circles in the hBN illustrate charged defects. d Simulated charge density profiles in top graphene calculated for hBN with impurity density \({n}_{{\mbox{imp}}}={10}^{10}\, {{\mbox{cm}}}^{-2}\) at zero doping of the bottom layer n_b = 0, and for n_b = 0.5 × 10¹² cm⁻² (see Supplementary Note 6). Scale bars are 250 nm. e Modelling of LATBG resistance subjected to high D under the assumption of a gapped graphene spectra (see Supplementary Note 7).