Extended Data Fig. 8: Estimated ratio between correlation and kinetic-energy scales, U/W, as a function of twist angle and magnetic field.
From: Correlation-driven topological phases in magic-angle twisted bilayer graphene
a, b, Estimates from the continuum model for the conduction (a) and valence (b) bands for w0/w1 = 0.4. c, d, The same calculation for w0/w1 = 0.7. e, Analytical estimate from equation (2). The bandwidth in a, b,c,d is evaluated as the total width of all levels that comprise the sub-band that includes the VHS (and carry C = −1 Chern number). Points very close to the magic angle are not shown owing to a lack of clear energy separation from adjacent levels. The plotted constant-U/W curves outline regions where U/W exceeds a threshold value, and qualitatively reproduce the structure of the experimental phase diagram in which Chern insulating phases are observed (Fig. 3f). In e, the large η values are necessary to compensate for the crude approximation of the bandwidth from equation (3), which underestimates the bandwidth compared to the numerical simulation in a, b,c,d.
