Extended Data Fig. 9: The effect of gating on the quantum oscillations in device 1.

a–e, Magnetoresistance (MR ≡ (R(B) – R₀)/R₀) curves taken at selected V_tg (V_bg = 0 V). f, Colour map of the normalized oscillating component, R_osc/R₀, under varying B and V_tg. g, FFT map of the same data. h, A zoomed-in plot of the FFT map at V_tg > 1 V, highlighting the weak peak that features a gate-tunable frequency. i, Gate-dependent FFT amplitudes of all visible peaks. j, A sketch summarizing the observed peaks. The solid black line (α_H peak, corresponding to the α peak mentioned in the main text) is the most pronounced peak and the focus of our discussion. Dashed coloured lines are weak features, whose amplitudes are shown in i. In the insulating regime, a lower-frequency peak (α_L) emerges together with the α_H peak. Towards the hole side, the α_H peak splits into two peaks (α_H′ and s). Towards the electron side, a new peak (e) emerges from almost zero frequency with an amplitude that decreases monotonically. Coincident with the emergence of the e peak, the amplitudes of the α_H and α_L peaks drop abruptly. Careful studies of these weak modes under higher magnetic fields and lower temperatures may provide further information to help the understanding of this system. Data were recorded from a pair of contacts in device 1, at 1.8 K.