DOI: 10.7795/720.20240314

resource type: Dataset / Measurement data

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.

creators:
- Dinesh K. Patel,  Physikalisch-Technische Bundesanstalt (PTB), Fachbereich 2.6 Elektrische Quantenmetrologie,  ORCID: 0000-0002-4934-1039
- Kajetan M. Fijalkowski, Universitt Wrzburg, Wrzburg, Germany, ORCID: 0000-0003-4458-9358
- Mattias Kruskopf, Physikalisch-Technische Bundesanstalt (PTB), Fachbereich 2.6 Elektrische Quantenmetrologie,  ORCID: 0000-0003-2846-3157
- Nan Liu, Universitt Wrzburg, Wrzburg, Germany
- Martin Gtz,      Physikalisch-Technische Bundesanstalt (PTB), Fachbereich 2.1 Gleichstrom und Niederfrequenz, ORCID: 0000-0001-8464-0651
- Eckart Pesel,     Physikalisch-Technische Bundesanstalt (PTB), Fachbereich 2.6 Elektrische Quantenmetrologie,  ORCID: 0000-0003-4112-7377
- Marcelo Jaime,    Physikalisch-Technische Bundesanstalt (PTB), Fachbereich 2.5 Halbleiter-Physik, Magnetismus, ORCID: 0000-0001-5360-5220
- Martin Klement,       Universitt Wrzburg, Wrzburg, Germany
- Steffen Schreyeck,    Universitt Wrzburg, Wrzburg, Germany
- Karl Brunner,         Universitt Wrzburg, Wrzburg, Germany
- Charles Gould,        Universitt Wrzburg, Wrzburg, Germany, ORCID: 0000-0002-6265-6887
- Laurens W. Molenkamp, Universitt Wrzburg, Wrzburg, Germany, ORCID: 0000-0003-4833-5179
- Hansjrg Scherer, Physikalisch-Technische Bundesanstalt (PTB), Fachbereich 2.6 Elektrische Quantenmetrologie,  ORCID: 0000-0002-6287-5107


funding:

- funder name: Free State of Bavaria
  funding program: -
  funding nr: -
  project short + long title: Institute for Topological Insulators

- funder name: Deutsche Forschungsgemeinschaft
  funding program: SFB 1170
  funding nr: 258499086
  project short + long title: ToCoTronics - Topologische und korrelierte Elektronik in Ober- und Grenzflchen
  link to projekt homepage: https://www.physik.uni-wuerzburg.de/en/sfb1170/

- funder name: Deutsche Forschungsgemeinschaft
  funding program: EXC-2123
  funding nr: 390837967
  project short + long title: QuantumFrontiers - Licht und Materie an der Quantengrenze
  link to projekt homepage: https://www.quantumfrontiers.de/en/

- funder name: Deutsche Forschungsgemeinschaft
  funding program: EXC 2147
  funding nr: 39085490
  project short + long title: CT.QMAT - Komplexitt und Topologie in Quantenmaterialien
  link to projekt homepage: https://www.ctqmat.de/

- funder name: European Commission
  funding program: H2020-FETPROACT-01-2018
  funding nr: 824140
  project short + long title: TOCHA - Dissipationless topological channels for information transfer and quantum metrology
  link to projekt homepage: https://tocha-project.eu/

- funder name: European Partnership on Metrology
  funding program: European Partnership on Metrology
  funding nr: 10.13039/100019599
  project short + long title: QuAHMET - Quantum anomalous Hall effect materials and devices for metrology
  link to projekt homepage: https://sites.google.com/inrim.it/quahmet

  funding acknowledgement text: 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), Wrzburg-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 Unions Horizon Europe Research and Innovation Programme and by the Participating States.

license: CC-By (Creative Commons Attribution) 4.0, international

keywords:
electronic devices ; spintronic devices ; quantum metrology ; quantum Hall effect ; topological insulators

classification:
INSPEC B2000 - Components, electron devices and materials
INSPEC B6230H - Photonic switching systems
INSPEC A0365B - Foundations, theory of quantum measurement, miscellaneous quantum theories
INSPEC A7000 - Condensed matter: electronic structure, electrical, magnetic, and optical properties

description of the individual files:

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 ?^?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 ?_xx for the high and low  potential edge, and for an exponential fit to ?_xx(low) following the relation ?_xx = ?_xx0 exp(I/I_0), where ?_xx0 = 915  59 ? 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 ?_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 = ? 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 = ? 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 = ? 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 ?_xx (along the low potential edge), and for a linear fit  following the relation ?R_xy = s?_xx + ?R_xy(?_xx = 0), where s is the admixing parameter and ?R_xy(?_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 ?_xx (along the low potential edge), and for a linear fit following the relation ?R_xy = s?_xx + ?R_xy(?_xx = 0), where s is the admixing parameter and ?R_xy(?_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 ?_xx (along the low potential edge), and for a linear fit following the relation ?R_xy = s?_xx + ?R_xy(?_xx = 0), where s is the admixing parameter and ?R_xy(?_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 T? and 6.9 T?.

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 ? 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.