Extended Data Fig. 7: Spectrum of a continuum model taking into account the effects of a displacement field.
From: Correlation-driven topological phases in magic-angle twisted bilayer graphene
a–c, The spectra correspond to twist angles of θ = 1.03° (a), θ = 1.06° (b) and θ = 1.09° (c). The displacement field, expressed as an energy difference between the two graphene monolayers, is 10 meV, and the ratio between AA and AB tunnelling amplitudes, w0/w1 = 0.4, is the same for all results. A similar spectrum is obtained for larger w0/w1 ratios. The simple continuum model, known to predict correct trends, can capture energetically offset Dirac cones by including a displacement field. However, it underestimates the bandwidth of the flat bands (or equivalently the separation between VHSs) and exhibits an unrealistically strong dependence on the twist angle; even at angles slightly far from the magic angle (θ = 1.06−1.09°), the model predicts a 2−4 times smaller bandwidth than that observed in the data. All spectra feature a well separated LL starting from each band edge that moves inwards with the field. This LL originates from the pocket near the centre of the moiré Brillouin zone and was not observed in the experiment. The bandwidth We (Wh) corresponding to the conductance (valence) flat VHS sub-band is used for estimating the U/W values in Extended Data Fig. 8.
