Fig. 4: Displacement field dependence and HF calculations.
a, \({B}_{z}^{\rm{ac}}\) QOs due to LLs in the Dirac band measured at a fixed SOT position (red circle, Fig. 1b) as a function of \(\nu\) and \(D\) at \({B}_\mathrm{a}=251\) mT. Diagonal streaks are an artefact coming from the bottom gate. The 0th Dirac LL has no \(D\) dependence. The \({N}_\mathrm{D}=\pm 1\) LL curves towards the CNP, whereas higher LLs curve away from the CNP. b, Same as a but at \({B}_\mathrm{a}=56\) mT. The 0th LL has no \(D\) dependence, but all other LLs curve towards the CNP. c, Simulation of Dirac LLs as a function of the layer potential difference \(U\) at \({B}_\mathrm{a}=251\) mT, using the NSM state obtained from a full HF treatment (purple) and the Hartree interaction only (dashed grey). The evolution of \({N}_\mathrm{D}=0,\pm 1\) LLs in the experiment is consistent with the simulation for a NSM. d, BS of NSM state (Extended Data Fig. 5b) at \(U=0\) (blue) and \(U=40\) meV (red). FB Dirac cones migrate towards \(\Gamma\). The HF gap at K+ and K− is \({\sim}{2\varDelta}_{\rm{HF}}=40\) meV. \(U\)-induced hybridization between the Dirac cone and FBs (red) causes a reduced \({v}_\mathrm{F}\) in the Dirac cone below the hybridization energy (Extended Data Fig. 5a). e, Cross section of \({B}_{z}^{\rm{ac}}\) averaged over a range around \(D\approx 0\) in the dashed box in b. The red arrow marks the first electron-doped paramagnetic peak, and the blue arrow marks the diamagnetic peak at \({N}_\mathrm{D}=1\). f, \(\mathrm{d}{n}_\mathrm{D}/\mathrm{d}n\) extracted from e. The shaded region marks the low carrier density where the Hartree interaction is negligible and the Fock interaction dominates. g, Theoretical calculation of \(\mathrm{d}{n}_\mathrm{D}/\mathrm{d}n\) using the Hartree interaction BS (grey) and the Fock-induced NSM BS (purple).
