Extended Data Fig. 6: Details of the magnetic field evolution of R_xx (a) and R_yx (b,c) near ν = 7/2 in D2.

a,b,c, R_yx and R_xx measured at D = 0.466 V/nm. The corresponding contact configurations are shown in the diagrams above the plots. R_xx in (b) and (c) were measured on the opposite sides of the device. The tilted lines are guides for the eye and have the slope expected for C= ± 1 states. A number of fine features in (a-c), some of which persist down to zero field, align perfectly with these lines, providing further evidence for QAHE state at ν=7/2 which is deteriorated by the disorder. We speculate that the finite values of R_xx originate from the twist angle disorder which results in the presence of metallic regions in the device and hence interferes with the edge state transport. It is worth pointing out an interesting feature of R_xx: R_xx is low for B < 0, but becomes of the order of h/e² for B > 0, as shown in (b). This trend reverses on the opposite side of the device, as shown in (c). A plausible scenario that can produce this behavior is illustrated in d and e. Let us consider a situation when the device region between contacts ‘b’ and ‘e’ is insulating in the bulk (shown in white) and has fully-developed edge states, while the adjacent regions remain metallic (shown in red and blue) due to the local twist angle variation. The color marks local electrical potential, increasing from blue to red. As a result of the edge state transport, there is a significant voltage drop ΔV ≈ Ih/e² across the insulating region. In contrast to this, the electrical potential changes only gradually within the metallic regions since they have resistivity which is much smaller than h/e². Because of the chiral nature of the edge states, R_xx ~ h/e² when measured on the side of the device where the ‘cold’ edge state equilibrates with the metallic region, while R_xx ~ 0 on the other side of the device. We note that in this scenario, R_yx measured using contacts ‘b’ and ‘e’ is quantized.