DOI: 10.7795/720.20240314
title: Additional data for the publication "Zero External Magnetic Field Quantum Standard of Resistance at the 10^−9 Level"

description: Experimental study on the quantization accuracy of the quantum anomalous Hall effect.
description: The archive contains 14 data files corresponding to the graphs shown in the publication. The data elaboration and graphs creation were performed with the software tool “Origin” and the data tables have been subsequently exported in a tabular format.

Filename: Fig1c.tsv
Parent Figure: Figure 1 c) of main text
Data description: Processed data for the plot (1st line: Physical quantity; 2nd line: Physical unit; 3rd line: Comment; Next lines: Numerical data).
Device basic characterization: Hall resistance R_xy versus normal-to-plane magnetic field H. The Hall voltage is measured at contact pair 4-5 (during up and down sweep of the magnetic field) using standard low-frequency lock-in characterization techniques, at temperature T = 34 mK, current I = 5 nA, and applied top gate voltage U_Gate = 5.8 V.

Filename: Fig2b.tsv
Parent Figure: Figure 2 b) of main text
Data description: Processed data for the plot (1st line: Physical quantity; 2nd line: Physical unit; Next lines: Numerical data).
Typical Allan deviation plot of the bridge readings ∆U (the average difference of the bridge voltage U, obtained from a series of measurements with alternating current directions) of a 5 h measurement on contact pair 2-3 with I = 160 nA. The curve follows a τ^−1/2 relation, demonstrating the dominance of white noise up to at least about one hour of measurement (integration) time.

Filename: Fig3a.tsv
Parent Figure: Figure 3 a) of main text
Data description: Processed data for the plot (1st line: Physical quantity; 2nd line: Physical unit; 3rd line: Comment; Next lines: Numerical data).
Precision measurement results: Current-dependent CCC measurements for various contact pairs at fixed gate voltage U_Gate = 5.8 V, temperature 34 mK and at zero external magnetic field. Each data point corresponds to 192 measurement cycles (in total 64 minutes). Error bars shown correspond to measurement uncertainty analysis according to the uncertainty budget provided in section “Uncertainty Budget Analysis” (Table S1) of the Supplementary Information. 
Data are for the relative deviation ∆R/R_K from R_K for measurements on the three orthogonal contact pairs (2-3, 4-5, 6-7) and on the two diagonal contact pairs (2-7, 6-3), as a function of the applied current. 

Filename: Fig3b.tsv
Parent Figure: Figure 3 b) of main text
Data description: Processed data for the plot (1st line: Physical quantity; 2nd line: Physical unit; 3rd line: Comment; Next lines: Numerical data).
Precision measurement results: Current-dependent CCC measurements for various contact pairs at fixed gate voltage U_Gate = 5.8 V, temperature 34 mK and at zero external magnetic field. Each data point corresponds to 192 measurement cycles (in total 64 minutes). Error bars shown correspond to measurement uncertainty analysis according to the uncertainty budget provided in section “Uncertainty Budget Analysis” (Table S1) of the Supplementary Information. 
Data are for the current dependence of the longitudinal resistivity ρ_xx for the high and low potential edge, and for an exponential fit to ρ_xx(low) following the relation ρ_xx = ρ_xx0 exp(I/I_0), where ρ_xx0 = 915 ± 59 µΩ and I_0 = 55.4 ± 0.7 nA. 

Filename: Fig3c.tsv
Parent Figure: Figure 3 c) of main text
Data description: Processed data for the plot (1st line: Physical quantity; 2nd line: Physical unit; Next lines: Numerical data).
Precision measurement results: Current-dependent CCC measurements for various contact pairs at fixed gate voltage U_Gate = 5.8 V, temperature 34 mK and at zero external magnetic field. Each data point corresponds to 192 measurement cycles (in total 64 minutes). Error bars shown correspond to measurement uncertainty analysis according to the uncertainty budget provided in section “Uncertainty Budget Analysis” (Table S1) of the Supplementary Information. 
Data are for the same data as in Figure 3 b), plotted on a logarithmic ρ_xx scale.

Filename: Fig3d.tsv
Parent Figure: Figure 3 d) of main text
Data description: Processed data for the plot (1st line: Physical quantity; 2nd line: Physical unit; Next lines: Numerical data).
Precision measurement results: Current-dependent CCC measurements for various contact pairs at fixed gate voltage U_Gate = 5.8 V, temperature 34 mK and at zero external magnetic field. Each data point corresponds to 192 measurement cycles (in total 64 minutes). Error bars shown correspond to measurement uncertainty analysis according to the uncertainty budget provided in section “Uncertainty Budget Analysis” (Table S1) of the Supplementary Information. 
Data are for the relative deviation of the Hall resistance from R_K for the three orthogonal contact pairs, plotted as a function of the applied current, and for exponential fits following the relation ∆R_xy/R_K = α exp(I/I_0) + ∆R_xy/R_K (I = 0), where ∆R_xy/R_K (I = 0) is the deviation from quantization when extrapolated to zero current. 

Filename: Fig3e.tsv
Parent Figure: Figure 3 e) of main text
Data description: Processed data for the plot (1st line: Physical quantity; 2nd line: Physical unit; Next lines: Numerical data).
Precision measurement results: Current-dependent CCC measurements for various contact pairs at fixed gate voltage U_Gate = 5.8 V, temperature 34 mK and at zero external magnetic field. Each data point corresponds to 192 measurement cycles (in total 64 minutes). Error bars shown correspond to measurement uncertainty analysis according to the uncertainty budget provided in section “Uncertainty Budget Analysis” (Table S1) of the Supplementary Information. 
Data are for the relative deviation of the Hall resistance from R_K for the three orthogonal contact pairs, plotted as a function of the applied current, and for exponential fits following the relation ∆R_xy/R_K = α exp(I/I_0) + ∆R_xy/R_K (I = 0), where ∆R_xy/R_K (I = 0) is the deviation from quantization when extrapolated to zero current. 

Filename: Fig3f.tsv
Parent Figure: Figure 3 f) of main text
Data description: Processed data for the plot (1st line: Physical quantity; 2nd line: Physical unit; Next lines: Numerical data).
Precision measurement results: Current-dependent CCC measurements for various contact pairs at fixed gate voltage U_Gate = 5.8 V, temperature 34 mK and at zero external magnetic field. Each data point corresponds to 192 measurement cycles (in total 64 minutes). Error bars shown correspond to measurement uncertainty analysis according to the uncertainty budget provided in section “Uncertainty Budget Analysis” (Table S1) of the Supplementary Information. 
Data are for the relative deviation of the Hall resistance from R_K for the three orthogonal contact pairs, plotted as a function of the applied current, and for exponential fits following the relation ∆R_xy/R_K = α exp(I/I_0) + ∆R_xy/R_K (I = 0), where ∆R_xy/R_K (I = 0) is the deviation from quantization when extrapolated to zero current. 

Filename: Fig3g.tsv
Parent Figure: Figure 3 g) of main text
Data description: Processed data for the plot (1st line: Physical quantity; 2nd line: Physical unit; Next lines: Numerical data).
Precision measurement results: Current-dependent CCC measurements for various contact pairs at fixed gate voltage U_Gate = 5.8 V, temperature 34 mK and at zero external magnetic field. Each data point corresponds to 192 measurement cycles (in total 64 minutes). Error bars shown correspond to measurement uncertainty analysis according to the uncertainty budget provided in section “Uncertainty Budget Analysis” (Table S1) of the Supplementary Information. 
Data are for a parametric plot of the Hall resistance deviation from quantization ∆R_xy for the same orthogonal contact pairs, plotted against the longitudinal resistivity ρ_xx (along the low potential edge), and for a linear fit following the relation ∆R_xy = sρ_xx + ∆R_xy(ρ_xx = 0), where s is the admixing parameter and ∆R_xy(ρ_xx = 0) is the deviation from Hall resistance quantization when extrapolated to zero longitudinal resistivity. 

Filename: Fig3h.tsv
Parent Figure: Figure 3 h) of main text
Data description: Processed data for the plot (1st line: Physical quantity; 2nd line: Physical unit; Next lines: Numerical data).
Precision measurement results: Current-dependent CCC measurements for various contact pairs at fixed gate voltage U_Gate = 5.8 V, temperature 34 mK and at zero external magnetic field. Each data point corresponds to 192 measurement cycles (in total 64 minutes). Error bars shown correspond to measurement uncertainty analysis according to the uncertainty budget provided in section “Uncertainty Budget Analysis” (Table S1) of the Supplementary Information. 
Data are for a parametric plot of the Hall resistance deviation from quantization ∆R_xy for the same orthogonal contact pairs, plotted against the longitudinal resistivity ρ_xx (along the low potential edge), and for a linear fit following the relation ∆R_xy = sρ_xx + ∆R_xy(ρ_xx = 0), where s is the admixing parameter and ∆R_xy(ρ_xx = 0) is the deviation from Hall resistance quantization when extrapolated to zero longitudinal resistivity. 

Filename: Fig3i.tsv
Parent Figure: Figure 3 i) of main text
Data description: Processed data for the plot (1st line: Physical quantity; 2nd line: Physical unit; Next lines: Numerical data).
Precision measurement results: Current-dependent CCC measurements for various contact pairs (abbreviated CP in the legends) at fixed gate voltage U_Gate = 5.8 V, temperature 34 mK and at zero external magnetic field. Each data point corresponds to 192 measurement cycles (in total 64 minutes). Error bars shown correspond to measurement uncertainty analysis according to the uncertainty budget provided in section “Uncertainty Budget Analysis” (Table S1) of the Supplementary Information. 
Data are for a parametric plot of the Hall resistance deviation from quantization ∆R_xy for the same orthogonal contact pairs, plotted against the longitudinal resistivity ρ_xx (along the low potential edge), and for a linear fit following the relation ∆R_xy = sρ_xx + ∆R_xy(ρ_xx = 0), where s is the admixing parameter and ∆R_xy(ρ_xx = 0) is the deviation from Hall resistance quantization when extrapolated to zero longitudinal resistivity. 

Filename: FigS1.tsv
Parent Figure: Figure S1 of supplementary material
Data description: Processed data for the plot (1st line: Physical quantity; 2nd line: Physical unit; 3rd line: Comment; Next lines: Numerical data).
Results of gate leakage measurements: Data for leakage currents as a function of the voltage U_Gate applied to the top gate, measured at base temperature of about 34 mK, with and without a breakout box with additional cables. Also there are data for lines corresponding to leakage resistances of 1.8 TΩ and 6.9 TΩ.

Filename: FigS2.tsv
Parent Figure: Figure S2 of supplementary material
Data description: Processed data for the plot (1st line: Physical quantity; 2nd line: Physical unit; 3rd line: Comment; Next lines: Numerical data).
Results of a gate voltage tuning measurements: Data for longitudinal resistance R_xx measured versus U_Gate at temperatures 34 mK and 100 mK.

Filename: FigS3.tsv
Parent Figure: Figure S3 of supplementary material
Data description: Processed data for the plot (1st line: Physical quantity; 2nd line: Physical unit; Next lines: Numerical data).
Drift behavior of the 100 Ω reference resistor during the measurement campaign: Data for calibration values and their uncertainties ( measurement uncertainty analysis similar to the uncertainty budget as provided in section “Uncertainty Budget Analysis”, Table S1). The data for each data point are generated through 2600 measurement cycles corresponding to total measurement durations of 14.4 hours.
description: We gratefully acknowledge the financial support of the Free State of Bavaria (the Institute for Topological Insulators), Deutsche Forschungsgemeinschaft (SFB 1170, 258499086, and EXC-2123 QuantumFrontiers, 390837967), Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter (EXC 2147, 39085490), the European Commission under the H2020 FETPROACT Grant TOCHA (824140), and by the project 23FUN07 QuAHMET, which has received funding from the European Partnership on Metrology, co-financed from the European Union’s Horizon Europe Research and Innovation Programme and by the Participating States.