Extended Data Fig. 2: Electric field dependence of v = −1 QAHE in device D(3.52°).
From: Observation of fractionally quantized anomalous Hall effect
All data in the main panel are taken at 500 mK. a, Antisymmetrized |Rxy| (blue) and symmetrized Rxx (red) at |µoH| = 100 mT as a function of electric field (D/ε0) at v = −1. As D/ε0 is decreased below Dc/ε0 ≈ −50 mV/nm, Rxy quickly drops from the quantized value while Rxx increases rapidly to above 100 kΩ. This demonstrates an electric field induced transition from a QAH insulator to topologically trivial correlated insulator. Inset, symmetrized Rxx at |µoH| = 100 mT versus electric field D swept down and up near the phase transition. The absence of hysteresis implies a continuous topological phase transition. The data in the inset are taken at 1.6 K to minimize electrical noise from the contacts. b, Illustration of fitting used to extract the energy gap \(\Delta \) at selected electric field values. The Arrhenius equation and extracted \(\Delta \) are shown for D/ε0 = −70 and 0 mV/nm. At the critical field Dc/ε0 ≈ −50 mV/nm, the longitudinal resistance is nearly constant versus temperature. c, Energy gap as a function of electric field. Error bars are obtained from fitting variance. Grey dashed lines are guides to the eye. The closing and reopening of the gap versus D/ε0 are evidence for a continuous topological quantum phase transition between the QAH state and a topologically trivial correlated insulator. d, Antisymmetrized Rxy at magnetic field |µoH| = 100 mT as a function D/ε0 and carrier density (n) at 1.6 K. The filling factor (v) is shown on the top axis. Black regions denote areas with resistance too large to be reliably measured. The yellow dashed line bounds the region where Rxy is > 95 % of h/e2. e, Reflective magnetic circular dichroism (RMCD) signal versus D/ε0 and v at µoH = 100 mT and 1.6 K. The comparison with panel d shows that the critical electric field DFM/ε0 for suppressing the ferromagnetic state is larger than Dc/ε0 for the QAH insulator (the yellow dashed line is as in panel d). Therefore, the topologically trivial state is a ferromagnetic insulator. f, Hartree-Fock calculations of the out-of-plane spin (Sz) and energy gap normalized to the hopping t1 as a function of electric field. The system is in a topologically trivial ferromagnetic insulating state between Dc and DFM, and becomes non-valley polarized and hence non-ferromagnetic above DFM. The calculated Chern number is C = −1 (blue region) and 0 (grey region) for below and above Dc, respectively.
