Fig. 3: Symmetry breaking at ν = 2.
a, \({B}_{z}^{\rm{ac}}\left(x,\nu \right)\) QOs as in Fig. 2 but for electron doping and at a lower \({B}_\mathrm{a}=131\) mT, which provides higher resolution for analysing the symmetry breaking at \(\nu =2\). b, Cross section of \({B}_{z}^{\rm{ac}}\left(\nu \right)\) along the white dashed line in a with red (blue) triangles marking local maxima (minima). A Gaussian filter was used to smooth the data and locate the extrema. c, Fraction of electrons populating the Dirac sector as electrons are added to the system, \(\mathrm{d}{n}_\mathrm{D}/\mathrm{d}n\), extracted from the maxima (red) and minima (blue) points in b. d, \(\mathrm{d}{n}_\mathrm{D}/\mathrm{d}n\) derived from the Hartree calculation, assuming an ansatz of a \(\pm 20\) meV flavour degeneracy lifting for \(2\le \nu \le 2.6\) (shaded region). e,f, BS at \(\nu =2\) with the proposed Stoner ansatz. Compared to the symmetric case (e), in the symmetry-broken state (f), the energy of one flavour (A) is decreased by 20 meV whereas the energy of the other flavour (B) is increased by 20 meV. In the symmetry-broken state, \({\varepsilon }_\mathrm{F}\) increases, and hence, further carriers are transferred into the Dirac cone (shaded green). g, Schematic of the occupation \({\nu }_{i}\), where i corresponds to the different flavours, with the ansatz of symmetry breaking for \(2\le \nu \le 2.6\) (Supplementary Information Section III).
