Extended Data Fig. 9: Quantum oscillations in device D3 (θ = 1.44°).
From: Electrically tunable correlated and topological states in twisted monolayer–bilayer graphene
a, ρxx and b, Rxy as a function of n and B⊥ at D = 0. c, Comparable Rxy map at D = − 0.2 V/nm. d, Schematic illustration of the prominent quantum oscillations observed in a. Quantum oscillations exhibit four-fold degeneracy at each value of n. For n < 0, we observe a sequence of quantum oscillations with filling factors νLL = − 2, − 6, − 10. . . . For n > 0, the sequence shifts from + 2, + 6, + 10. . . to + 4, + 8, + 12, . . . and back again as n is raised. These sequences can be understood by considering the monolayer- and bilayer-like corners of the moiré Brillouin zone as approximately uncoupled owing to the larger twist angle, in which the dominant quantum oscillations are the sum of the contributions from each band. e, Dashed blue lines denote the Landau levels of the monolayer-like bands as a function of energy, following \({E}_{LL,m}=\sqrt{2e\hslash {v}_{F}^{2}NB}\), where N is the Landau level index and vF is the Fermi velocity. Dashed red lines denote the same for the bilayer-like bands, with \({E}_{LL,b}=\frac{e\hslash B}{{m}^{* }}\sqrt{N(N-1)}\), where m* is the effective mass. The total filling factor νLL within each gap is given by the sum of the Landau level indexes for each band (solid bars). The experimentally observed sequence of quantum oscillations is well reproduced taking vF = 1.44 × 105 m/s, m* = 0.14m0, and including a charge neutrality band gap in the monolayer spectrum of ΔM = 5 meV and an offset between the monolayer and bilayer charge neutrality points of δ = 14.5 meV (indicative of band overlap). f, Similar energy diagram for D = − 0.2 V/nm. To account for the observation of νLL = − 2 at high magnetic field, a band gap for the bilayer spectrum of ΔB = 8 meV is included, and we take δ = 19.5 meV.
