DOI: 10.5061/dryad.z08kprrn8
title: Easy-to-configure zero-dimensional valley-chiral modes in a graphene point junction

description: The valley degree of freedom in 2D materials can be manipulated for
 low-dissipation quantum electronics called valleytronics. At the boundary
 between two regions of bilayer graphene with different atomic or
 electrostatic configurations, a valley-polarized current has been
 realized. However, the demanding fabrication and operation requirements
 limit device reproducibility and scalability toward more advanced
 valleytronics circuits. We demonstrate a new device architecture of a
 point junction where a valley-chiral 0D PN junction is easily configured,
 switchable, and capable of carrying valley current with an estimated
 polarization of ~80%. This work provides a new building block in
 manipulating valley quantum numbers and scalable valleytronics.
description: # Easy-to-configure zero-dimensional valley-chiral modes in a graphene
 point junction
 [https://doi.org/10.5061/dryad.z08kprrn8](https://doi.org/10.5061/dryad.z08kprrn8) The data is structured in the following way: the data is divided into folders corresponding to the figures where the data was visualized. Some folders have subfolders that correspond to a particular panel of the figure. The names of the folders and subfolders unambiguously tell which panel the data corresponds to. For each subfolder, there are details below on how to access the data and what experimental parameters the values in the data correspond to. The electrical transport data can be accessed via MATLAB (recommended versions: MATLAB Release 2018a and newer). The data about the gates' topography can be accessed via software (e. g. Gwyddion) that can analyze atomic force microscope topography results. ## Description of the data and file structure ## Subfolder "Fig1-BC" The software called Gwyddion can be used to analyze the scan topography. ## Subfolder "Fig1-H" All .mat files need to be opened in Matlab using the "load" command. The AC excitation voltage was 0.1 mV. For the "1H_data" file: data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC current through the sample (R-channel) (in A), data{1,3} is the silicon back gate voltage (in V), data{1,4} and date{1,5} are the gate voltages V_{t2} (in V), data{1,6} is the gate voltage V_{t1} (in V), data{1,7} and date{1,8} are the gate voltages V_{b2} (in V), data{1,9} is the gate voltage V_{b1} (in V). ## Subfolder "Fig1-I" All .mat files need to be opened in Matlab using the "load" command. For the M12, M14, M16, M18 files: data{1,1} is AC the current through the sample (R-channel) (in \muA), data{1,2} is AC the current through the sample (X-channel) (in \muA), data{1,3} is AC the voltage across the sample (R-channel) (in V), data{1,4} is AC the voltage across the sample (X-channel) (in V), data{1,5}, data{1,7} is the gates V_{t1} voltages (in V), data{1,6} is the gate V_{t2} voltage (in V), data{1,8}, data{1,10} is the gates V_{b2} voltages (in V), data{1,9} is the gate V_{b1} voltage (in V), data{1,11} is the global silicon back gate's voltage (in V). The magnetic field is zero. For the rest of the files: data{1,1} is AC the current through the sample (R-channel) (in \muA), data{1,2} is AC the current through the sample (X-channel) (in \muA), data{1,3} is AC the voltage across the sample (R-channel) (in V), data{1,4} is AC the voltage across the sample (X-channel) (in V), data{1,5} is the gates V_{t1} voltages (in V), data{1,6} is the gate V_{t2} voltage (in V), data{1,7}, data{1,9} is the gates V_{b2} voltages (in V), data{1,8} is the gate V_{b1} voltage (in V), data{1,10} is the global silicon back gate's voltage (in V). The magnetic field is zero. Displacement fields (V/nm) (one for a single data file, higher magnitudes of V_{t1} correspond to higher displacement fields) = [0.141000000000000 0.150400000000000 0.159800000000000 0.169200000000000 0.178600000000000 0.188000000000000 0.197400000000000 0.206800000000000 0.216200000000000 0.225600000000000 0.235000000000000 0.244400000000000 0.253800000000000 0.263200000000000]. ## Subfolder "Fig1-J" All .mat files need to be opened in Matlab using the "load" command. The AC excitation was 1nA. data{1,1} is the voltage across the sample (R-channel) (in V). data{1,2} is the voltage across the sample (X-channel) (in V). data{1,4}, data{1,9} is the gates V_{t1} voltages (in V). data{1,3} is the gate V_{t2} voltage (in V). data{1,6} is the gates V_{b2} voltages (in V). data{1,5} is the gate V_{b1} voltage (in V). data{1,7} is the DC current bias (in 2*\muA). The global silicon back gate was parked at 40V. The magnetic field is zero. We considered that a PJ was formed when the resistance reached a peak under changing V_{b2} at zero DC current bias.\ Displacement fields (V/nm) (one for a single data file, higher magnitudes of V_{t1} correspond to higher displacement fields) = [0.141000000000000 0.150400000000000 0.159800000000000 0.169200000000000 0.178600000000000 0.188000000000000 0.197400000000000 0.206800000000000 0.216200000000000 0.225600000000000 0.235000000000000 0.244400000000000 0.253800000000000 0.263200000000000]. ## Subfolder "Fig2-D" All .mat files need to be opened in Matlab using the "load" command. The AC excitation was 1nA. data{1,1} is the voltage across the sample (R-channel) (in V). data{1,2} is the voltage across the sample (X-channel) (in V). data{1,3} is the global silicon back gate's voltage (in V). data{1,5} is the gates V_{t1} voltages (in V). data{1,4} is the gate V_{t2} voltage (in V). data{1,6} is the gates V_{b2} voltages (in V). data{1,7} is the gate V_{b1} voltage (in V). The magnetic field is zero. ## Subfolder "Fig2-E-G-H" All .mat files need to be opened in Matlab using the "load" command. For the M13, M15, M17 files: data{1,1} is AC the current through the sample (R-channel) (in \muA), data{1,2} is AC the current through the sample (X-channel) (in \muA), data{1,3} is AC the voltage across the sample (R-channel) (in V), data{1,4} is AC the voltage across the sample (X-channel) (in V), data{1,5}, data{1,7} is the gates V_{t1} voltages (in V), data{1,6} is the gate V_{t2} voltage (in V), data{1,8}, data{1,10} is the gates V_{b2} voltages (in V), data{1,9} is the gate V_{b1} voltage (in V), data{1,11} is the global silicon back gate's voltage (in V). The magnetic field is zero. For the rest of the files: data{1,1} is AC the current through the sample (R-channel) (in \muA), data{1,2} is AC the current through the sample (X-channel) (in \muA), data{1,3} is AC the voltage across the sample (R-channel) (in V), data{1,4} is AC the voltage across the sample (X-channel) (in V), data{1,5} is the gates V_{t1} voltages (in V), data{1,6} is the gate V_{t2} voltage (in V), data{1,7}, data{1,9} is the gates V_{b2} voltages (in V), data{1,8} is the gate V_{b1} voltage (in V), data{1,10} is the global silicon back gate's voltage (in V). The magnetic field is zero. Displacement fields (V/nm) (one for a single data file, higher magnitudes of V_{t1} correspond to higher displacement fields) = [0.141000000000000 0.150400000000000 0.159800000000000 0.169200000000000 0.178600000000000 0.188000000000000 0.197400000000000 0.206800000000000 0.216200000000000 0.225600000000000 0.235000000000000 0.244400000000000 0.253800000000000 0.263200000000000]. ## Subfolder "Fig2-F" All .mat files need to be opened in Matlab using the "load" command. The AC excitation was 1nA. data{1,1} is the voltage across the sample (R-channel) (in V). data{1,2} is the voltage across the sample (X-channel) (in V). data{1,4} and data{1,9} are the gates V_{t1} voltages (in V). data{1,3} is the gate V_{t2} voltage (in V). data{1,6} is the gates V_{b2} voltages (in V). data{1,5} is the gate V_{b1} voltage (in V). data{1,7} is the DC current bias (in 2*\muA). The global silicon back gate was parked at 40V. The magnetic field is zero. We considered that a PJ was formed when the resistance reached a peak under changing V_{b2} at zero DC current bias.\ Displacement fields (V/nm) (one for a single data file, higher magnitudes of V_{t1} correspond to higher displacement fields) = [0.141000000000000 0.150400000000000 0.159800000000000 0.169200000000000 0.178600000000000 0.188000000000000 0.197400000000000 0.206800000000000 0.216200000000000 0.225600000000000 0.235000000000000 0.244400000000000 0.253800000000000 0.263200000000000]. ## Subfolder "Fig3-A" All .mat files need to be opened in Matlab using the "load" command. The AC excitation was 1nA. data{1,1} is the voltage across the sample (R-channel) (in V). data{1,2} is the voltage (with a minus sign) across the sample (X-channel) (in V). data{1,3} is the global silicon back gate's voltage (in V). data{1,7} is the gates V_{t1} voltages (in V). data{1,6} is the gate V_{t2} voltage (in V). data{1,5} is the gates V_{b2} voltages (in V). data{1,4} is the gate V_{b1} voltage (in V). data{1,8} is the magnetic field. data{1,9} is a dummy variable (used for averaging the resistance at a constant magnetic field). Displacement fields (V/nm) (one for a single data file, higher magnitudes of V_{t1} correspond to higher displacement fields) = [0.188000000000000 0.197400000000000 0.206800000000000 0.216200000000000 0.225600000000000]. ## Subfolder "Fig3-F" All .mat files need to be opened in Matlab using the "load" command. The AC excitation was 1nA. data{1,1} is the voltage across the sample (R-channel) (in V). data{1,2} is the voltage (with a minus sign) across the sample (X-channel) (in V). data{1,3} is the global silicon back gate's voltage (in V). data{1,7} is the gates V_{t1} voltages (in V). data{1,6} is the gate V_{t2} voltage (in V). data{1,5} is the gates V_{b2} voltages (in V). data{1,4} is the gate V_{b1} voltage (in V). data{1,8} is the magnetic field. data{1,9} is a dummy variable (used for averaging the resistance at a constant magnetic field). Displacement fields (V/nm) (one for a single data file, higher magnitudes of V_{t1} correspond to higher displacement fields) = [0.188000000000000 0.197400000000000 0.206800000000000 0.216200000000000 0.225600000000000]. ## Folder "FigS1" The simulation data was obtained separately for the top and bottom gates for three displacement fields (0.11 V/nm, 0.23 V/nm, 0.45 V/nm) in the bulk insulating region with the smaller bandgap. Each data file has four columns (x-coordinate (in m), y-coordinate (in m), z-coordinate (in m), displacement field (in V/m)). ## Folder "FigS3" The simulation data was obtained separately for the top and bottom gates for 0.23 V/nm displacement field in the bulk insulating region with the smaller bandgap. Each data file has four columns (x-coordinate (in m), y-coordinate (in m), z-coordinate (in m), displacement field (in V/m)). ## Subfolder "FigS4-A" data{1,1} is AC the voltage across the sample (R-channel) (in V), data{1,2} is AC the voltage across the sample (X-channel) (in V), data{1,3} is AC the current through the sample (R-channel) (in \muA), data{1,4} is AC the current through the sample (X-channel) (in \muA), data{1,7} is the gates V_{t1} voltages (in V), data{1,6} is the gate V_{t2} voltage (in V), data{1,8} is the gates V_{b2} voltages (in V), data{1,9} is the gate V_{b1} voltage (in V), data{1,5} is the global silicon back gate's voltage (in V). The magnetic field is zero. ## Subfolder "FigS4-B" All .mat files need to be opened in Matlab using the "load" command. The AC excitation voltage was 0.1 mV. For the "S4B_data" file: data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC current through the sample (R-channel) (in A), data{1,3} is the silicon back gate voltage (in V), data{1,4} and date{1,5} are the gate voltages V_{t2} (in V), data{1,6} is the gate voltage V_{t1} (in V), data{1,7} and date{1,8} are the gate voltages V_{b2} (in V), data{1,9} is the gate voltage V_{b1} (in V). ## Subfolder "FigS4-C" All .mat files need to be opened in Matlab using the "load" command. The AC excitation voltage was 0.1 mV. For the "S4C_data" file: data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC voltage across the sample (X-channel) (in V), data{1,3} is the AC current through the sample (R-channel) (in A), data{1,4} is the AC current through the sample (X-channel) (in A), data{1,5} is the silicon back gate voltage (in V), data{1,6} is the gate voltage V_{b1} (in V), data{1,7} is the gate voltage V_{b2} (in V), data{1,8} is the gate voltage V_{t1} (in V), data{1,9} is the gate voltage V_{t2} (in V), data{1,10} is the magnetic field (in T). ## Subfolder "FigS4-D" All .mat files need to be opened in Matlab using the "load" command. The AC excitation voltage was 0.1 mV. For the "S4D_data" files: data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC current through the sample (R-channel) (in A), data{1,3} is the gates V_{t1} voltages (in V), data{1,4} is the gates V_{t2} voltages (in V), data{1,5} is the gates V_{b1} voltages (in V), data{1,6} is the gates V_{b2} voltages (in V). ## Subfolder "FigS4-E" All .mat files need to be opened in Matlab using the "load" command. The AC excitation was 1nA. data{1,1} is the voltage across the sample (R-channel) (in V). data{1,2} is the voltage across the sample (X-channel) (in V). data{1,3} is the global silicon back gate's voltage (in V). data{1,5} is the gates V_{t1} voltages (in V). data{1,4} is the gate V_{t2} voltage (in V). data{1,6} is the gates V_{b2} voltages (in V). data{1,7} is the gate V_{b1} voltage (in V). The magnetic field is zero. ## Subfolder "FigS4-F" All .mat files need to be opened in Matlab using the "load" command. The AC excitation voltage was 0.1 mV. For the "S4F_data" file: data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC current through the sample (R-channel) (in A), data{1,3} is the silicon back gate voltage (in V), data{1,4} and date{1,5} are the gate voltages V_{t2} (in V), data{1,6} is the gate voltage V_{t1} (in V), data{1,7} and date{1,8} are the gate voltages V_{b2} (in V), data{1,9} is the gate voltage V_{b1} (in V). ## Subfolder "FigS4-G" All .mat files need to be opened in Matlab using the "load" command. The AC excitation current was 10 nA. For the "S4G_data" file: data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC voltage across the sample (X-channel) (in V), data{1,3} is the silicon back gate voltage (in V), data{1,4} is the gate voltage V_{b1} (in V), data{1,5} is the gate voltage V_{b2} (in V), data{1,6} is the gate voltage V_{t1} (in V), data{1,7} is the gate voltage V_{t2} (in V), data{1,8} is the magnetic field (in T), data{1,9} is the DC offset (in V), data{1,10} is the dummy number (irrelevant to this measurement). ## Subfolder "FigS4-H" All .mat files need to be opened in Matlab using the "load" command. The AC excitation voltage was 0.1 mV. For the "S4H_data" files: data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC current through the sample (R-channel) (in A), data{1,3} is the gates V_{t1} voltages (in V), data{1,4} is the gates V_{t2} voltages (in V), data{1,5} is the gates V_{b1} voltages (in V), data{1,6} is the gates V_{b2} voltages (in V). ## Subfolder "FigS4-I" All .mat files need to be opened in Matlab using the "load" command. The AC excitation voltage was 0.1 mV. For the "S4I_data" files: data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC current through the sample (R-channel) (in A), data{1,3} is the silicon back gate voltage (in V), data{1,5} is the gate voltage V_{t1} (in V), data{1,4} and date{1,6} are the gate voltages V_{t2} (in V), data{1,8} is the gate voltage V_{b1} (in V), data{1,7} and date{1,9} are the gate voltages V_{b2} (in V). ## Subfolder "FigS4-J" All .mat files need to be opened in Matlab using the "load" command. data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC voltage across the sample (X-channel) (in V), data{1,3} is the AC current through the sample (R-channel) (in \muA), data{1,4} is the AC current through the sample (X-channel) (in \muA), data{1,5} is the gates V_{t2} voltages (in V), data{1,6} is the gate V_{t1} voltages (in V), data{1,7} is the gates V_{b2} voltages (in V), data{1,8}, data{1,9} are the gate V_{b1} voltages (in V). Global Si back gate is parked at +60V. ## Subfolder "FigS4-K" All .mat files need to be opened in Matlab using the "load" command. data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC voltage across the sample (X-channel) (in V), data{1,3} is the AC current through the sample (R-channel) (in \muA), data{1,4} is the AC current through the sample (X-channel) (in \muA), data{1,5} is the gates V_{t2} voltages (in V), data{1,6} is the gate V_{t1} voltages (in V), data{1,7} is the gates V_{b2} voltages (in V), data{1,8}, data{1,9} are the gate V_{b1} voltages (in V). Global Si back gate is parked at +60V. ## Subfolder "FigS4-L" All .mat files need to be opened in Matlab using the "load" command. The AC excitation voltage was 0.1 mV. For the "S4L_data" files: data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC current through the sample (R-channel) (in A), data{1,3} is the silicon back gate voltage (in V), data{1,5} is the gate voltage V_{t1} (in V), data{1,4} and date{1,6} are the gate voltages V_{t2} (in V), data{1,8} is the gate voltage V_{b1} (in V), data{1,7} and date{1,9} are the gate voltages V_{b2} (in V). ## Subfolder "FigS4-M" All .mat files need to be opened in Matlab using the "load" command. data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC voltage across the sample (X-channel) (in V), data{1,3} is the AC current through the sample (R-channel) (in \muA), data{1,4} is the AC current through the sample (X-channel) (in \muA), data{1,5} is the gates V_{t2} voltages (in V), data{1,6} is the gate V_{t1} voltages (in V), data{1,7} is the gates V_{b2} voltages (in V), data{1,8}, data{1,9} are the gate V_{b1} voltages (in V). Global Si back gate is parked at +60V. ## Subfolder "FigS4-N" All .mat files need to be opened in Matlab using the "load" command. data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC voltage across the sample (X-channel) (in V), data{1,3} is the AC current through the sample (R-channel) (in \muA), data{1,4} is the AC current through the sample (X-channel) (in \muA), data{1,5} is the gates V_{t2} voltages (in V), data{1,6} is the gate V_{t1} voltages (in V), data{1,7} is the gates V_{b2} voltages (in V), data{1,8}, data{1,9} are the gate V_{b1} voltages (in V). Global Si back gate is parked at +60V. ## Subfolder "FigS5-A" All .mat files need to be opened in Matlab using the "load" command. The AC excitation current was 10nA. For the "S5A_field1", "S5A_field2", "S5A_field3", "S5A_field4", "S5A_field7", "S5A_field8" files: data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC voltage across the sample (X-channel) (in V), data{1,3} is the silicon back gate voltage (in V), data{1,4} is the gates V_{b1} voltages (in V), data{1,5} is the gates V_{b2} voltages (in V), data{1,6} is the gates V_{t1} voltages (in V), data{1,7} is the gates V_{t2} voltages (in V), data{1,8} is the magnetic field (in T), data{1,9} is the DC offset (in V), data{1,10} is the dummy number (irrelevant to this measurement). The AC excitation voltage was 0.1 mV. For the "S5A_field5" file: data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC voltage across the sample (X-channel) (in V), data{1,3} is the AC current through the sample (R-channel) (in A), data{1,4} is the AC current through the sample (X-channel) (in A), data{1,5} is the silicon back gate voltage (in V), data{1,6} is the gates V_{b1} voltages (in V), data{1,7} is the gates V_{b2} voltages (in V), data{1,8} is the gates V_{t1} voltages (in V), data{1,9} is the gates V_{t2} voltages (in V), data{1,10} is the magnetic field (in T). The AC excitation voltage was 0.1 mV. For the "S5A_field6" file: data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC voltage across the sample (X-channel) (in V), data{1,3} is the AC current through the sample (R-channel) (in A), data{1,4} is the AC current through the sample (X-channel) (in A), data{1,5} is the silicon back gate voltage (in V), data{1,6} is the gates V_{b1} voltages (in V), data{1,7} is the gates V_{b2} voltages (in V), data{1,8} is the gates V_{t1} voltages (in V), data{1,9} is the gates V_{t2} voltages (in V), data{1,10} is the magnetic field (in T), data{1,11} is the DC offset (in V). Displacement fields (one for a single data file, higher displacement fields correspond to higher magnitudes of local gates' voltages, unit: V/nm) = [0.1558 0.1817 0.2077 0.2337 0.2596 0.2856 0.3115 0.3375]. ## Subfolder "FigS5-B" All .mat files need to be opened in Matlab using the "load" command. The AC excitation current was 10nA. For the "S5B_field1", "S5B_field2", "S5B_field3", "S5B_field5", "S5B_field8" files: data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC voltage across the sample (X-channel) (in V), data{1,3} is the silicon back gate voltage (in V), data{1,4} is the gates V_{b1} voltages (in V), data{1,5} is the gates V_{b2} voltages (in V), data{1,6} is the gates V_{t1} voltages (in V), data{1,7} is the gates V_{t2} voltages (in V), data{1,8} is the magnetic field (in T), data{1,9} is the DC offset (in V), data{1,10} is the dummy number (irrelevant to this measurement). The AC excitation voltage was 0.1 mV. For the "S5B_field4", "S5B_field6", "S5B_field7" files: data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC voltage across the sample (X-channel) (in V), data{1,3} is the AC current through the sample (R-channel) (in A), data{1,4} is the AC current through the sample (X-channel) (in A), data{1,5} is the silicon back gate voltage (in V), data{1,6} is the gates V_{b1} voltages (in V), data{1,7} is the gates V_{b2} voltages (in V), data{1,8} is the gates V_{t1} voltages (in V), data{1,9} is the gates V_{t2} voltages (in V), data{1,10} is the magnetic field (in T), data{1,11} is the dummy number (irrelevant to this measurement). Displacement fields (one for a single data file, higher displacement fields correspond to higher magnitudes of local gates' voltages, unit: V/nm) = [0.1558 0.1817 0.2077 0.2337 0.2596 0.2856 0.3115 0.3375]. ## Subfolder "FigS6-A" All .mat files need to be opened in Matlab using the "load" command. The AC excitation current was 10nA. data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC current through the sample (R-channel) (in A), data{1,3} is the silicon back gate voltage (in V), data{1,5} is the gate voltage V_{t1} (in V), data{1,4} and date{1,6} are the gate voltages V_{t2} (in V), data{1,8} is the gate voltage V_{b1} (in V), data{1,7} and date{1,9} are the gate voltages V_{b2} (in V). data{1,10} is the dummy number. data{1,11} is the magnetic field (in T). Displacement fields (one for a single data file, higher displacement fields correspond to higher magnitudes of local gates' voltages, unit: V/nm) = [0.1504 0.1773 0.2041 0.2310 0.2578 0.2847 0.3115 0.3384]. ## Subfolder "FigS7-A-B" data{1,1} is AC the voltage across the sample (R-channel) (in V), data{1,2} is AC the voltage across the sample (X-channel) (in V), data{1,3} is AC the current through the sample (R-channel) (in \muA), data{1,4} is AC the current through the sample (X-channel) (in \muA), data{1,6} and data{1,7} are the all top gates voltages (in V), data{1,8} and data{1,9} are the all bottom voltages (in V), data{1,5} is the global silicon back gate's voltage (in V). The magnetic field is zero. ## Subfolder "FigS7-C-D" All .mat files need to be opened in Matlab using the "load" command. The AC excitation voltage was 0.1 mV. For the "S7-C-D_data" file: data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC voltage across the sample (X-channel) (in V), data{1,3} is the AC voltage signal from the current amplifier (amplify 1E6 times) (R-channel) (in V), data{1,4} is the AC voltage signal from the current amplifier (amplify 1E6 times) (X-channel) (in V), data{1,5} is the silicon back gate voltage (in V), data{1,6} is the gate voltage V_{b1} (in V), data{1,7} is the gate voltage V_{b2} (in V), data{1,8} is the gate voltage V_{t} (in V), data{1,9} is the magnetic field (in T). ## Subfolder "FigS7-E-F" All .mat files need to be opened in Matlab using the "load" command. The AC excitation current was 10nA. For the "S7-E-F_data" file: data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC voltage across the sample (X-channel) (in V), data{1,3} is the silicon back gate voltage (in V), data{1,4} is the gate voltage V_{t1} (in V), data{1,5} is the gate voltage V_{t2} (in V), data{1,6} is the gate voltage V_{t3} (in V), data{1,7} is the gate voltage V_{b1} (in V), data{1,8} is the gate voltage V_{b2} (in V), data{1,9} is the gate voltage V_{b3} (in V). ## Subfolder "FigS7-G-H" All .mat files need to be opened in Matlab using the "load" command. For the "FigS7-G-H" file: data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC voltage across the sample (X-channel) (in V), data{1,3}/10^6 is the AC current across the sample (R-channel) (in A), data{1,4}/10^6 is the AC current across the sample (X-channel) (in A), data{1,5} is the left and middle bottom gate V_{bl} and V_{bm} voltages (in V), data{1,6} is the right bottom gate V_{br} voltages (in V), data{1,7} is the lower top gates V_{tl} voltages (in V), data{1,8} is the middle top gates V_{tm} voltages (in V), data{1,9} is the upper top gates V_{tu} voltages (in V), The silicon back gate is parked at +60 V. ## Subfolder "FigS11-A" All .mat files need to be opened in Matlab using the "load" command. The AC excitation was 1nA. data{1,1} is the voltage across the sample (R-channel) (in V). data{1,2} is the voltage (with a minus sign) across the sample (X-channel) (in V). data{1,3} is the global silicon back gate's voltage (in V). data{1,7} is the gates V_{t1} voltages (in V). data{1,6} is the gate V_{t2} voltage (in V). data{1,5} is the gates V_{b2} voltages (in V). data{1,4} is the gate V_{b1} voltage (in V). data{1,8} is the magnetic field. data{1,9} is a dummy variable (used for averaging the resistance at a constant magnetic field). Displacement fields (V/nm) (one for a single data file, higher magnitudes of V_{t1} correspond to higher displacement fields) = [0.1504 0.1598 0.1692 0.1786 0.1880 0.1974 0.2068 0.2162 0.2256 0.2350 0.2444 0.2538 0.2632]. ## Subfolder "FigS11-B" All .mat files need to be opened in Matlab using the "load" command. The AC excitation was 1nA. data{1,1} is the voltage across the sample (R-channel) (in V). data{1,2} is the voltage (with a minus sign) across the sample (X-channel) (in V). data{1,3} is the global silicon back gate's voltage (in V). data{1,7} is the gates V_{t1} voltages (in V). data{1,6} is the gate V_{t2} voltage (in V). data{1,5} is the gates V_{b2} voltages (in V). data{1,4} is the gate V_{b1} voltage (in V). data{1,8} is the magnetic field. data{1,9} is a dummy variable (used for averaging the resistance at a constant magnetic field). Displacement fields (V/nm) (one for a single data file, higher magnitudes of V_{t1} correspond to higher displacement fields) = [ 0.1504 0.1598 0.1692 0.1786 0.1880 0.1974 0.2068 0.2162 0.2256 0.2350 0.2444 0.2538 0.2632]. ## Subfolder "FigS12-A" All .mat files need to be opened in Matlab using the "load" command. The AC excitation current was 10 nA. data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC voltage across the sample (X-channel) (in V), data{1,3} is the silicon back gate voltage (in V), data{1,4} is the gates V_{b1} voltages (in V), data{1,5} is the gates V_{b2} voltages (in V), data{1,6} is the gates V_{t1} voltages (in V), data{1,7} is the gates V_{t2} voltages (in V), data{1,8} is the magnetic field (in T), 2*data{1,9} is the DC current offset (in \muA), data{1,10} is the dummy number (irrelevant to this measurement). Displacement fields (one for a single data file, higher displacement fields correspond to higher magnitudes of local gates' voltages, unit: V/nm) = [0.1558 0.1817 0.2077 0.2337 0.2596 0.2856 0.3115 0.3375]. ## Subfolder "FigS12-B-C" All .mat files need to be opened in Matlab using the "load" command. The AC excitation current was 10 nA. data{1,1} is the AC voltage across the sample (R-channel) (in V), data{1,2} is the AC voltage across the sample (X-channel) (in V), data{1,3} is the silicon back gate voltage (in V), data{1,4} is the gates V_{b1} voltages (in V), data{1,5} is the gates V_{b2} voltages (in V), data{1,6} is the gates V_{t1} voltages (in V), data{1,7} is the gates V_{t2} voltages (in V), data{1,8} is the magnetic field (in T), 2*data{1,9} is the DC current offset (in \muA), data{1,10} is the dummy number (irrelevant to this measurement). Displacement fields (one for a single data file, higher displacement fields correspond to higher magnitudes of local gates' voltages, unit: V/nm) = [0.1558 0.1817 0.2077 0.2337 0.2596 0.2856 0.3115 0.3375]. ## Folder "FigS13" All .mat files need to be opened in Matlab using the "load" command. The AC excitation was 1nA. data{1,1} is the voltage across the sample (R-channel) (in V). data{1,2} is the voltage (with a minus sign) across the sample (X-channel) (in V). data{1,3} is the global silicon back gate's voltage (in V). data{1,7} is the gates V_{t1} voltages (in V). data{1,6} is the gate V_{t2} voltage (in V). data{1,5} is the gates V_{b2} voltages (in V). data{1,4} is the gate V_{b1} voltage (in V). data{1,8} is the magnetic field. data{1,9} is a dummy variable (used for averaging the resistance at a constant magnetic field). Displacement fields (V/nm) (one for a single data file, higher magnitudes of V_{t1} correspond to higher displacement fields) = [0.188000000000000 0.197400000000000 0.206800000000000 0.216200000000000 0.225600000000000].