"DC to THz properties of Metals, Superconductors, Graphene and QHE: Towards a Quantum Standard of Impedance"
DC to THz properties of Metals, Superconductors, Graphene and QHE: Towards a Quantum Standard of Impedance (QSI)
Shakil A. Awan
Wolfson Nanomaterials & Devices Laboratory, School of Engineering, Computing and Mathematics, University of Plymouth, Plymouth, Devon, PL4 8AA, UK
Web: www.plymouth.ac.uk/staff/shakil-awan
Research Group: www.plymouth.ac.uk/research/nanotechnology-electronics
Email: shakil.awan@plymouth.ac.uk
Direct current (DC) based measurements of metals, superconductors, graphene, quantum Hall effect (QHE) hetrostructures and a variety of other materials and systems, using two-probe or four-probe techniques, are well established in the literature [1]. Such measurements, spanning the last couple of centuries, have not only revolutionised our understanding of the physics of such materials but have also led to a plethora of applications. Here, we discuss alternating current (AC) measurement techniques we have been developing over the last two-decades for a range of materials (Metals, Superconductors, Graphene and quantum Hall effect hetrostructures) where knowledge of their dynamic properties play a crucial role in a range of radio-frequency (RF), microwave and THz applications [2]. However, AC (compared to DC) measurements over such a broad range of frequencies require significantly more complex experimental set-up to measure the dynamic properties of materials and these will detailed in the presentation.
We find impedance of metals is dominated by resistive losses (proportional to ω2 when skin-effect is negligible, where ω = 2πf in rads-1) and reactance proportional to ω. When skin-effect is not negligible the losses and reactance are found to scale with ω1/2 . In contrast, high temperature superconductors (HTS), such as BiSrCaCuO-2223/Ag tapes (at 77 K) are found to show linear frequency dependence (over 32 – 256 Hz power frequencies) and a β3 and β4 dependence for a cylindrical or an elliptical tape and a thin conductor, respectively, where β = I/IC is the ratio of applied current to the critical current of the HTS [3]. High quality exfoliated Graphene, in contrast, shows no frequency dependence of its conductivity σ(ω) = σ1(ω) +iσ2 (ω) such that the real part of the conductivity σ1(ω) between DC and 13.5 GHz is found to be identical to the DC conductivity of Graphene at room temperature, with the imaginary part σ2 (ω)=0 at frequencies up to 13.5 GHz, in agreement with the theory based on the Kubo formalism [4]. Similar conductivity properties are also found in our 0.1 – 1.1 THz measurements of chemical vapour deposition (CVD) Graphene. We briefly also describe how the dynamic frequency response of Graphene can also be utilized to developing novel biosensors to enable early diagnosis of Alzheimer’s, Cancer and Cardiovascular diseases using patient samples [5]. In contrast, QHE has been investigated using precision four-terminal-pair bridge systems up to ~10 kHz [6], which originally showed a 0.1ppm/kHz dependence, from the DC resistance value of R = h/νe2 (or ~25.8 kΩ/ν) at the ν=2 and ν=4 quantised plateaux, where h is the Planck constant and e is the electronic charge. Recent measurements using gates above or below the QHE device to shield capacitive current charging can reduce the frequency-dependence to within 1-2x10-8 /kHz, which is at the limit of current experimental uncertainty [7]. Finally, we detail efforts currently underway, to extend the above experimental and theoretical approaches, to establish a Quantum Standard of Impedance (QSI) through precision measurements at frequencies up to few MHz.
References
[1] Janezic M. D., Kaiser R. F., Baker-Jarvis J. and Free G., “DC Conductivity measurement of metals”, NIST technical Note 1531, 2004.
[3] Awan S. A. and Sali S., “Self-field AC power dissipation in high-Tc superconducting tapes and a prototype cable”, IEE Proc.-Sci. Meas. Technol., 149 (1), 2-8, 2002.
[4] Awan S. A., Lombardo A., Colli., Privitera G., Kulmala T. S., Kivioja J. M., Koshino M., Ferrari A. C., “Transport Conductivity of Graphene at RF and Microwave Frequencies”, 2D Mater., 3 (1), 015010-1-11, 2016.
[5] Bungon T., Haslam C., Damiati S., O’Driscoll B., Whitley T., Davey P., Siligardi G., Charmet J. and Awan S. A., “Graphene FET Sensors for Alzheimer’s Disease Protein Biomarker Clusterin Detection”, Front. Mol. Biosci., 8:651232, 2021.
[6] Klitzing K. V., Dorda G. and Pepper M., “New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance,” Phys. Rev. Lett., 45, 494–497, 1980.
[7] Schurr J, Kibble B. P., Hein G., and Pierz K.,”Controlling losses with gates and shields to perfect a Quantum Hall Impedance Standard”, IEEE Trans. Instrum. Meas., 58(4), 973-979, 2009.
Links:
WEBEX-MEETING BEITRETEN
metrology.webex.com/metrologyj.php
Meeting-Kennnummer (Zugriffscode): 2742 652 9793
Meeting Passwort: JYtsWWTb962