Lifshitz transitions in magic-angle twisted bilayer graphene

In magic-angle twisted bilayer graphene, the flat band fosters the emergence of rich physics associated with strong correlations. Here we report on magneto-transport measurements of a twisted bilayer graphene device(1.17°±0.02°). From Hall measurements, we extract the Hall number n_H, which provides information about the Fermi surface topology as a function of doping within the flat band. At low filling, │n/n₀│< 2, we find n_H = n as expected for a system with closed Fermi pockets. Here n₀ is the carrier density corresponding to one electron per moire cell. Upon approaching fillings of 2 carriers per moire cell, n_H follows the logarithmic dependence predicted for a Lifshitz transition at a van-Hove singularity. Interestingly on the high doping side of the transition the linear dependence is restored but with an offset, indicating that the Fermi surface shrinks by 2 carriers per moire cell and a correlation gap opens. Moreover,a singular dependence around ±3n₀ is observed suggesting a Lifshitz transition but without a gap. As the field is increased above 4T a gap opens at n/n₀ = 3 signaled by the appearance of a Landau fan and quantized R_xy plateaus. At the same time n_H suggests yet another change in the Fermi surface topology.