Ultrasensitive and Wide-Bandwidth Thermal Measurements of Graphene at Low Temperatures

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Ultrasensitive and Wide-Bandwidth Thermal Measurements of Graphene at Low Temperatures

Kin Chung Fong and K. C. Schwab

Phys. Rev. X 2, 031006 – Published 30 July 2012; Erratum Phys. Rev. X 2, 039903 (2012)

Abstract

At low temperatures, the electron gas of graphene is expected to show both very weak coupling to thermal baths and rapid thermalization, properties which are desirable for use as a sensitive bolometer. We demonstrate an ultrasensitive, wide-bandwidth measurement scheme based on Johnson noise to probe the thermal-transport and thermodynamic properties of the electron gas of graphene, with a resolution of $2 mK / \sqrt{Hz}$ and a bandwidth of 80 MHz. We have measured the electron-phonon coupling directly through energy transport, from 2–30 K and at a charge density of $2 \times 10^{11} {cm}^{- 2}$ . We demonstrate bolometric mixing and utilize this effect to sense temperature oscillations with a period of 430 ps and determine the heat capacity of the electron gas to be $2 \times 10^{- 21} J / (K \cdot μ m^{2})$ at 5 K, which is consistent with that of a two-dimensional Dirac electron gas. These measurements suggest that graphene-based devices, together with wide-bandwidth noise thermometry, can generate substantial advances in the areas of ultrasensitive bolometry, calorimetry, microwave and terahertz photo-detection, and bolometric mixing for applications in fields such as observational astronomy and quantum information and measurement.

Received 9 April 2012
Corrected 3 August 2012

DOI:https://doi.org/10.1103/PhysRevX.2.031006

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Corrections

3 August 2012

Erratum

Publisher’s Note: Ultrasensitive and Wide-Bandwidth Thermal Measurements of Graphene at Low Temperatures [Phys. Rev. X 2, 031006 (2012)]

Kin Chung Fong and K. C. Schwab

Phys. Rev. X 2, 039903 (2012)

Authors & Affiliations

Kin Chung Fong^* and K. C. Schwab

Applied Physics, California Institute of Technology, MC 128-95, Pasadena, California 91125, USA

^*kcfong@caltech.edu

Popular Summary

Physicists’ fascination with graphene—single atomic layers of carbon atoms—has stemmed largely from the material’s unique electronic properties such as pseudorelativistic charge carriers and remarkably good electric conductivity. Although graphene is also known to conduct heat well at room temperature through phonons, its thermodynamic properties at low temperatures are largely determined by its electrons and their interaction with phonons, and have been little explored experimentally due to the challenge of sensitively measuring the electronic temperature of such a delicate material. As reported in this experimental paper, we have overcome this challenge and succeeded in measuring, for the first time, both the electronic thermal conductance and the heat capacity of graphene, which turns out to be among the smallest heat capacities ever measured. Our device is the first graphene-based hot-eletron bolometer for sensitive microwave detection.

The key to our successful measurements is a microwave-frequency, low-temperature electrical circuit with ultrahigh sensitivity, into which a micron-sized graphene flake is integrated. The thermal agitations, or noise, of the electrons in the graphene are then picked up as noisy electrical signals in the ultrasensitive circuit, giving clues to the electronic temperature. Raising the electronic temperature by heating up the circuit leads to measurements of thermal conductance and, in principle, heat capacity. Using high-frequency heating and measurement techniques in particular, we are able to detect a fast 430-picosecond oscillation in the electronic temperature and derive from the oscillation the tiny heat capacity. We also reveal that graphene’s thermal conductance at low temperatures is dominated by the heat transfer from the electrons to phonons, confirming theoretical models from other research groups.

By our estimate, a cleaner graphene at lower temperatures should be able to detect the quantum fluctuations of an incident microwave field and even one single GHz photon through their heating effect on the electrons in the graphene. Imagine how very useful such an ultrasensitive detector can be in quantum information as well as in sub-millimeter astronomy.

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Vol. 2, Iss. 3 — July - September 2012

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Figure 1
(a) The measurement circuit: graphene (represented by a resistor), impedance matched with a 1.161 GHz resonant, lithographic LC network (NbTiN film, $T_{c} = 13.5 K$ ), and connected to a HEMT amplifier. (b) The expected thermal conductances ( $G_{WF}, G_{ep}, G_{rad}$ ) and heat capacity versus temperature for a bandwidth of 80 MHz, $n = 10^{11} {cm}^{- 2}$ , and $A = 10^{- 10} m^{2}$ . The inset shows an optical micrograph of the graphene sample. The scale bar is $15 μ m$ long. (c) The two-terminal resistance of the graphene versus gate voltage, taken from 1.65–12 K. (d) The reflected microwave response versus gate voltage. The absorption dip at 1.161 GHz shows that the graphene is well matched to $50 Ω$ in an 80-MHz band. (e) Spectra of the measured noise power taken at various sample temperatures, demonstrating the Johnson-noise signal of the graphene in the impedance-matching band.Reuse & Permissions
Figure 2
(a) The integrated noise power versus refrigerator temperature, demonstrating the expected temperature dependence of the Johnson-noise signal. The deviation at temperatures above 8 K are due to the temperature dependence of the NbTiN inductor. The inset shows the precision of the noise thermometry taken with two measurement bandwidths, 4 and 80 MHz, versus integration time. A resolution of 100 ppm is achieved, in agreement with the Dicke radiometer formula (shown as lines). (b) The results of the differential thermal-conductance measurements. The inset shows a time trace, taken at 4 K, of the small heating current at 17.6 Hz, and the resulting 12-mK temperature oscillations at 35.2 Hz detected with the noise thermometer. The red curve is a power-law fit with exponent $2.7 \pm 0.3$ . (c) The results of applying large dc heating currents at various sample temperatures, $T_{p}$ (points). The expected form is shown as the blue line. Also shown is the heating of the electron gas versus applied microwave power at 1.161 GHz, also showing a similar heating curve and demonstrating the microwave bolometric effect with graphene.Reuse & Permissions
Figure 3
Panel (a) shows the power spectral density, at the input of the HEMT, due to bolometric mixing. The central, 600-pV red tone is due to a heating signal at $ω_{heat} / 2 π = 1.161 GHz$ , which produces a temperature response at 2.322 GHz, which is then mixed down to $ω_{bolo} = ω_{heat} + 2 π \cdot 1 kHz$ using a small modulation tone at $ω_{\mod} = ω_{heat} - 2 π \cdot 1 kHz$ . The blue spike, shifted down by 100 Hz, is the result of increasing the modulation tone by 100 Hz. The green spike, shifted up by 200 Hz, is due to increasing the heating tone by 100 Hz, validating the expected relationship: $ω_{bolo} = 2 ω_{heat} - ω_{\mod}$ . (b) A plot of the measured bolometric mixing tone normalized by our expected signal under the assumption that the graphene thermal time constant $τ = 0$ . The red points are measured with a heating tone of $ω_{heat} / 2 π = 1.161 GHz$ , the blue points are measured with $ω_{heat} / 2 π = 17.6 Hz$ , and both are measured with a modulation tone of 1.161 GHz–1 kHz. The dashed line shows the expected roll-off of the bolometric signal when $2 ω_{heat} / 2 π = 2.32 GHz$ and $τ = C_{e} / G_{ep}$ .Reuse & Permissions
Figure 4
(a) The expected sensitivity of graphene as a bolometer assuming $n = 10^{9} {cm}^{2}$ and $A = 10^{- 11} m^{2}$ versus the coupling bandwidth, for various cryogenic operating temperatures, with (b) the optimal value of NEP versus temperature. (c) The expected energy sensitivity to single photons. (d) The threshold for detection of shot noise of an incident microwave field of various frequencies.Reuse & Permissions

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