Fig. 1: Chiral edge current detection scheme under an alternating current bias.

a and b Illustration of the direction of chiral edge current in a quantum anomalous Hall (QAH) insulator. The chirality of the edge current is clockwise and counter-clockwise under opposite out-of-plane magnetization M, respectively. c Optical image of a MnBi₂Te₄ device consisting of a 7-septuple layer (SL) which potentially hosts QAH. There is also a 10-SL flake that has no net M and zero Chern number. d Waveform of a pure alternating current (AC) bias applied to QAH with period T. It has positive (negative) chemical potential \({\mu }_{{{\rm{AC}}}}\) relative to ground during the first (second) half-cycle. e and f Current flow in the first and second half of the cycle, respectively, under the AC current bias in (d). Since the instantaneous current \({I}_{1,2}=\left|{\mu }_{{{\rm{L}}}}-{\mu }_{{{\rm{R}}}}\right|\frac{e}{h}\) always flows from the higher potential to the lower, the chirality of the edge state forces the current \({I}_{2}\) during the second half-cycle (when \({\mu }_{{{\rm{L}}}} > {\mu }_{{{\rm{R}}}}\)) to flow on the top edge. \({\mu }_{{{\rm{L}}}}\) (\({\mu }_{{{\rm{R}}}}\)) is the chemical potential on the left (right) electrode; \(e\) and \(h\) are the electron charge and Planck’s constant, respectively. g A lock-in amplifier adds a \(\pi\) phase shift to the current flux signal from the second half-cycle, which makes the currents from the top and bottom edges appear to be propagating in the same direction with demodulated current \({I}_{{{\rm{AC}}}}=\frac{{\mu }_{{{\rm{AC}}}}}{2}\frac{e}{h}\) on both. In the presence of edge–bulk scattering, the ‘co-propagating’ edge currents due to the chiral edge state appear similar to non-chiral bulk flow. h–k Illustration of the situation when a direct-current (DC) offset is added to the AC bias. If the DC offset is larger than the AC amplitude, the chemical potential is higher on the right electrode during the entire period. The current flows unidirectionally on the bottom edge with \({I}_{{{\rm{AC}}}}={\mu }_{{{\rm{AC}}}}\frac{e}{h}\), because the demodulated flux signal is proportional to the amplitude of the AC amplitude and independent of the DC offset (twice the area of the pink region and thus twice the edge current in g).