Fig. 2: Electrochemical potential balancing.
a, Circuit diagram for a reference measurement of the Hall resistance VB–D/IA–C without electrochemical potential balancing. The outer perimeter was electrically biased, which drove the d.c. IA–C in the outer perimeter, whereas the inner perimeter was grounded through contact 1. The dark blue colour indicates the high electrochemical potential part of the circuit, whereas light grey shows the low potential. b, A measurement of VB–D/IA–C for this configuration as a function of current IA–C. c,d, Same for the Hall resistance VB–D/IA–C measured with electrochemical potential balancing: circuit diagram (c) and measurements (d). An additional d.c. I3–1 (of the same magnitude as IA–C) was passed at the inner perimeter to balance the electrochemical potentials along the ring. e–h, Analogous, but for the longitudinal resistance VB–C/IA–D: circuit diagram (e) and measurements (f) without and circuit diagram (g) and measurements (h) with electrochemical potential balancing. The horizontal dashed lines in b, d, f and h show the expected values for ideal quantum anomalous Hall edge states. All data were collected at zero external magnetic field, a temperature of 30 mK and an applied gate voltage of 4 V to tune the Fermi level so that we could observe the quantization plateau.
