Extended Data Fig. 3: Correcting for the doping by the tip at finite biases.
From: Imaging the flat bands of magic-angle graphene reshaped by interactions
a,b, The spectroscopy, dI/dVb and the transconductance with respect to the back gate, dI/dVbg, measured as a function of Vb and Vbg with θQTM within the flat-band region. At each integer filling, dI/dVb shows a suppression of conduction and dI/dVbg shows a dipole-like feature. This feature is more prominent at ν = ±4 owing to the gaps to the remote bands. We can see that the position of these features in Vbg shift with increasing magnitude of Vb, making them follow an S-like trajectory. This shift reflects the fact that, because of the parallel capacitor formed by the QTM tip and TBG sample, a relative bias between them leads to doping of the TBG. To correct this, we trace the ν = 4 line by a polynomial fitting and overlay it at each integer filling (black lines). On the basis of this fitting line, we can skew the measurements such that their x-axis becomes the true filling factor (accounting for doping by the back gate as well as the tip) instead of just Vbg. The data presented in Figs. 3 and 4 have been skewed with the above method. The data in Figs. 1 and 2 are measured at a fixed back-gate voltage and can therefore have some deviations with respect to the nominal filling factor at large biases. Figure 5 is measured at zero bias and therefore it does not have any effect of doping by the tip.
