Towards a graphene-based quantum impedance standard

Abstract

Precision measurements of the quantum Hall resistance with alternating current (ac) in the kHz range were performed on epitaxial graphene in order to assess its suitability as a quantum standard of impedance. The quantum Hall plateaus measured with alternating current were found to be flat within one part in 10 7 . This is much better than for plain GaAs quantum Hall devices and shows that the magnetic-fluxdependent capacitive ac losses of the graphene device are less critical. The observed frequency dependence of about -8×10 -8 /kHz is comparable in absolute value to the positive frequency dependence of plain GaAs devices, but the negative sign is attributed to stray capacitances which we believe can be minimized by a careful design of the graphene device. Further improvements thus may lead to a simpler and more user-friendly quantum standard for both resistance and impedance.Graphene is probably the most fascinating electronic material discovered in the last decades [1][2][3]. Among its various unique properties, an anomalous 'half-integer' quantum Hall effect (QHE) is most interesting for metrology, where the fact that the Hall resistance is quantized and depends only on fundamental constants is utilized for the representation and maintenance of the resistance unit, the ohm. Typically, twodimensional electron systems (2DES) realized in GaAs/AlGaAs heterostructures [4] are used for this purpose. The required relative measurement uncertainty of better than 1 part in 10 8 is, however, only obtained at strong magnetic fields around 10 tesla and at temperatures of 1.4 kelvin and below. In contrast, in graphene the cyclotron energy splitting between the Landau levels (which is the main factor determining the robustness of the quantized Hall resistance (QHR)) is so large that fingerprints of the QHE are even observed at room temperature [5]. Thus, with graphene a highly precise QHR standard working at low magnetic fields and temperatures above 4 kelvin is conceivable, which would be an enormous advantage for practical metrology. In fact, when measuring with direct current (dc), it has been demonstrated already that the precision of the QHE in high quality graphene devices matches that of GaAs devices [6][7][8][9]. However, in the forthcoming fundamental constant-based redefinition of the Système International d'Unités (SI) [10], also the impedance units (capacitance and inductance) will be traced to fundamental constants [11]. The most direct way to represent the impedance units is to use a quantum Hall resistance measured with alternating current (ac QHR). This has two advantages. Firstly, deriving the resistance and impedance units from the same quantum effect improves the consistency of the SI. And secondly, using the same QHE device at dc and at ac in one and the same cryomagnetic system would constitute a practical and economical advantage. Therefore, the question naturally arises whether graphene can replace GaAs also in the realm of impedance units, leading to an at least equally precise, but more userfriendl...

Ultrasensitive NO2Gas Sensor Based on Epitaxial Graphene

“…The number of graphene layers on top of SiC was evaluated using the method described in [13] and was also found to be about one layer. Observation of half-integer Quantum Hall effect in the epitaxial graphene fabricated by the same technology and conditions and with the similar Raman spectra confirms the presence of single-layer graphene [14]. (exposure periods are marked as grey bands, in 0.2 ppb-2 ppb concentration range) at the room temperature is presented.…”

Nonequilibrium mesoscopic conductance fluctuations as the origin of 1/f noise in epitaxial graphene

“…Low-frequency noise, also referred to as flicker noise or 1/f noise, is a common phenomenon caused by various physical mechanisms and found in numerous systems [4,5], including electronic transport in graphene devices [6][7][8][9]. At low temperature, the noise properties of graphene are of particular interest for its application in metrology as a quantum Hall resistance [10][11][12][13] and impedance [14] standard. In low-temperature diffusive transport in a disordered conductor like graphene, quantum interference effects arise due to the phase-coherent transport of electrons.…”

Mini array of quantum Hall devices based on epitaxial graphene

“…The accurate mini-array of 4 or 8 Hall bars connected in series could be applied in ac impedance metrology to improve, e.g., traceability of 1 nF capacitance standards at frequencies near 1 kHz. Our experiments concentrated on dc properties of graphene-based QHR arrays, but recent ac measurements of the quantum Hall resistance in single graphenebased Hall bars demonstrated promising ac performance and low capacitive losses in the kHz range [19]. A major benefit of graphene-based QHARS devices compared to GaAs-based devices is that graphene-based devices can be operated in much more easily achievable experimental conditions: higher temperatures and lower magnetic fields.…”

“…Series-connected QHARS devices would also be needed in ac calibration of impedance standards. In recent experiments with single graphene-based Hall devices, the QHE plateaux measured with alternating current were found to be flat within one part in 10 7 , which is much better than for plain GaAs quantum Hall devices [19]. By using a QHARS instead of a single QHR device, the quantized resistance value can be tailored to a level that is suitable for direct use as a reference in quadrature bridge for calibration of capacitance standards.…”