EMRP-SIB51: Quantum Resistance Metrology based on Graphene

• Forschungsstelle: METAS
• Projektnummer: F-5010.30023
• Projekttitel Englisch: EMRP-SIB51: Quantum Resistance Metrology based on Graphene

Schlüsselwörter (Englisch)

Graphene, electrical metrology, quantum Hall effect

Kurzbeschreibung (Englisch)

Graphene was discovered in 2004 by A. Geim and K. Novoselov who both received the Nobel prize in 2010. Soon after the discovery, the quantum Hall effect was observed in this new material. This observation has triggered a considerable interest in the metrology community and with the progress in the device fabrication graphene was soon identified as a good candidate to replace the traditional GaAs devices. The major advantage of graphene over GaAs is that it will be possible to make measurement at higher temperature (4.2 K instead of 0.3 K) and lower magnetic fields (2 T instead of 10T). This change of the operational parameters will have a profound impact on the equipment needed to perform the experiment. The whole set up will become simpler and much cheaper to operate.

Quantum resistance metrology makes use of the quantum Hall Effect (QHE) to reproduce the unit of electrical resistance with unprecedented precision. However, up to now the complexity of quantum standards precludes a widespread use and necessitates a hierarchy of secondary standards to disseminate the electrical quantities to end-users. A simpler to use primary standard of electrical resistance, short-cutting tedious present-day calibration chains, is the key goal of this project.
This goal came into reach by the discovery of graphene. Graphene is the first material being truly two-dimensional by nature and as such it exhibits the QHE. Among numerous unique properties its extraordinary high cyclotron energy splitting allows higher temperature operation than any other material, predestining it as perfect for a simplified primary standard. Adapted instrumentation to make full use of the offered advantages also needs to be developed.

This project is part of the European Metrology Research Programme (EMRP, http://www.euramet.org/index.php?id=emrp); it is partly funded by the European Union on the basis of Decision No 912/2009/EC.

Projektziele (Englisch)

METAS is mainly involved in workpackage 3 of the project. This WP specifically addresses the objective: “To investigate the potential of quantum devices for ac-metrology”. The aim is to provide detailed insight into the potential use of graphene QHE devices as an ac-resistance standard. At METAS, the graphene devices will be measured in an environment that minimises the losses to the external world. In this way the losses intrinsic to the device will be studied in detail and will be compared to a phenomenological model that successfully explained the ac-measurements of GaAs heterostructures.
The main objectives in this WP are: 

• to fabricate samples with a design and a quality appropriate for ac-QHE measurements. 
• to perform precision ac-QHE measurements at kHz-frequencies on adapted ac-QHE devices.
• to understand the physics of the ac-QHE in this new material.

Abstract (Englisch)

METAS' task in the project was to study the Quantum Hall Effect (QHE) at audio frequencies. To this end a fully automated digitally assisted bridge was developed and fully characterized.  Using this bridge, ac measurements of graphene samples at frequencies up to 10 kHz were carried out. A close to linear, negative frequency dependence of the ac quantized Hall resistance (QHR) has been observed with considerable differences between individual samples. In one of the samples, the ac QHR only increased by less than one part in 10⁷ from 0 to 10 kHz, which demonstrates the potential of the ac QHE in epitaxial graphene to realize a primary standard of impedance. The wide i = 2 plateau shown at dc is preserved at ac with a flatness which depends on the level of ac dissipation. Relating R_H to R_xx at ac reveals a linear relationship with a negative slope for a typical epitaxial graphene device. However, the extrapolation to zero dissipation shows a very good agreement with R_K/2, in full agreement with previous measurements in GaAs devices. In addition, one sample has shown almost negligible frequency dependence both in R_xy and R_xx. A sample with vanishing ac dissipation represents the ideal candidate to realize a new graphene impedance standard where the ac resistance can be measured without any additional active shielding or further extrapolation method. However, the low ac dissipation demonstrated in this particular sample already allows for a realization of the ac QHR at a precision level sufficient for most applications. Finally, measurements with two dedicated devices having a particular geometry confirm the understanding of capacitive losses affecting the ac QHE. According to this model, positive and negative contributions to the measured ac R_xy depend on the device geometry. This geometrical dependence opens the way to design graphene Hall bars with vanishing dependence of ac R_xy on ac dissipation thus making the extrapolation procedure obsolete. In particular, in a asymmetric device, the dependence of the capacitive losses on the current direction is a convincing demonstration of the dependence of the capacitive losses on the device dimensions.

Umsetzung und Anwendungen (Englisch)

The results obtained so far are very interesting and extremely promising. As mentioned in the previous paragraph, graphene really has the potential to realize an AC standard of resistance much easier to use than its GaAs counterpart. This new standard will work at 4 K, instead of 0.3 K, in reduced magnetic fields. In addition, neither the extrapolation of the Hall resistance to zero dissipation nor the complicated double active shielding technique will be needed. However, additional measurements are needed to better understand the details of the frequency behaviour in order to optimize the design of the device. This will be carried out in future projects.

Publikationen / Ergebnisse (Englisch)

1. F. Lüönd, DC and AC QHE measurements with graphene, Poster presented at the Graphene Week, Chalmers University of Technology, Gothenburg, June 2014.
2. F. Lüönd, DC and AC QHE measurements with graphene, Poster presented at the Graphene and 2D Materials Conference, NPL, Teddington, November 2014.
3. F. Overney, F. Lüönd and B. Jeanneret, Digitally Assisted Coaxial Bridge for Automatic Quantum Hall Effect Measurements at Audio Frequencies, Proceedings of the Conference on Precision Electromagnetic Measurements, pp. 226-227, 2014.
4. F. Overney, Digitally Assisted Coaxial Bridge for Automatic Quantum Hall Effect Measurements at Audio Frequencies, Talk presented at the Conference on Precision Electromagnetic Measurements, Rio de Janeiro, August 2014.
5. F. Lüönd, AC Quantum Hall effect in epitaxial graphene, Talk presented at the EURAMET DC-QM Expert meeting, Bern, May 2015.
6. F. Lüönd, AC quantum Hall effect in epitaxial graphene, Poster presented at the Graphene Week, University of Manchester, Manchester, June 2015.
7. F. Overney, F. Lüönd and B. Jeanneret, Broadband Fully Automated Digitally Assisted Coaxial Bridge for High Accuracy Impedance Ratio Measurements, Metrologia 53, pp. 918–926, 2016.
8. F. Lüönd, F. Overney, B. Jeanneret, A. Müller, M. Kruskopf and K. Pierz, AC Quantum Hall Effect in Epitaxial Graphene, Proceedings of the Conference on Precision Electro-magnetic Measurements, 2016.
9. F. Lüönd, C. C. Kalmbach, F. Overney, J. Schurr, B. Jeanneret, A. Müller, M. Kruskopf, K. Pierz and F.-J. Ahlers, AC Quantum Hall Effect in Epitaxial Graphene, submitted to IEEE Trans. Instrum. Meas. , 2016.
10. F. Lüönd, AC Quantum Hall Effect in Epitaxial Graphene, Talk presented at the Conference on Precision Electromagnetic Measurements, Ottawa, July 2016.