Extended Data Fig. 4: Numerical simulation demonstrating current imaging by measuring \({{B}}_{{z}}^{{\rm{ac}}}\).
From: Mapping the twist-angle disorder and Landau levels in magic-angle graphene
a, Current distribution Jy(x – x0) of a Δx = 50-nm-wide channel carrying Iy = 1 μA in the \(\hat{{\bf{y}}}\) direction. b, Calculated −Bz(x – x0) at a height of 70 nm above the sample, convoluted with a 220-nm-diameter SOT sensing area. c, Calculated \({B}_{z}^{{\rm{ac}}}(x-{x}_{0})\) for an r.m.s. \({x}_{0}^{{\rm{ac}}}\) = 54 nm spatial modulation of the channel position. The dashed profile corresponds to a current strip of width Δx = 150 nm carrying the same current, showing that the spatial resolution is limited by the SOT diameter. d–f, As in a–c but for three counter-propagating currents spaced 150 nm apart. g, Analysis of the \({B}_{z}^{{\rm{ac}}}\) peak of an incompressible strip. \({B}_{z}^{{\rm{ac}}}(x)\) signal (blue) acquired along the line indicated in Fig. 3a for Vbg = −10.54 V (a single vertical line from Fig. 2a) showing the ν = −12 incompressible peak, along with a numerical fit (red). The fit uses the experimental values of \({V}_{{\rm{bg}}}^{{\rm{ac}}}\), hSOT and the SOT diameter with a single fitting parameter of the total current in the incompressible strip resulting in IT = 1.3 μA. An incompressible strip of width Δx = 50 nm was used for the fit. The mean value of \({B}_{z}^{{\rm{ac}}}(x)\) was subtracted from the data. The asymmetry in \({B}_{z}^{{\rm{ac}}}(x)\) away from the peak is caused by the presence of counterflowing nontopological currents INT of lower density in the adjacent compressible strips.
