Extended Data Fig. 7: Fractional quantum Hall and Chern insulator states at high magnetic field. | Nature

Extended Data Fig. 7: Fractional quantum Hall and Chern insulator states at high magnetic field.

From: Spin–orbit-driven band inversion in bilayer graphene by the van der Waals proximity effect

Extended Data Fig. 7

a, Fractional quantum Hall states (black labels) observed at 18 T in device S1. CP/Cref taken at D = 1.5 V nm−1 in Extended Data Fig. 6c (red dashed line), corresponding to a range of −4 < ν < −2. In the N = 0 orbital, fractional quantum Hall states up to sevenths are clearly observed. In the N = 1 orbital, an incompressible state is observed at half-filling. b, Fractional Chern insulator states in asymmetric device A3 at high magnetic fields with the BLG and hBN perfectly aligned. CP (normalized by Cref) is shown as a function of nominal electron density n0/c (where c is the geometric capacitance) and applied perpendicular magnetic field B, at a fixed polarizing electric field p0 \(\left(\frac{{p}_{0}}{c}=\frac{2{\epsilon }_{0}}{c}D=-6{\rm{V}}\right)\). c, Schematic of the observed insulating states in units normalized to the moiré unit cell area (Amoiré): these are the number of flux quanta per moiré unit cell nΦ (= B/AmoiréΦ0) and the number of electrons per moiré unit cell ne = n/Amoiré, where Φ0 = h/e is a flux quantum and n is the electron density. The insulating states are characterized by their inverse slope and intercept in these units, t and s, respectively. We observe a topological Chern band with δt = C = 1 and δs = 1, which originates at nΦ = 1 between insulating states (t, s) = (1, 1) and (2, 0) (black lines). We observe fractional Chern insulating states at 1/3, 2/5, 3/5, 2/3 filling of the band (blue lines) with quantum numbers t, s = (4/3, 2/3), (7/5, 3/5), (8/5, 2/5), (5/3, 1/3), labelled respectively.

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