Measuring carbon nanotube vibrations using a single-electron transistor as a fast linear amplifier

Abstract

We demonstrate sensitive and fast electrical measurements of a carbon nanotube mechanical resonator. The nanotube is configured as a single-electron transistor, whose conductance is a sensitive transducer for its own displacement. Using an impedance-matching circuit followed by a cryogenic amplifier, the vibrations can be monitored at radio frequency. The sensitivity of this continuous displacement measurement approaches within a factor 470 of the standard quantum limit.Suspended carbon nanotubes are mechanical resonators 1 with low mass, high compliance, and high quality factor 2,3 , which makes them sensitive electromechanical detectors for tiny forces 4 and masses 5-7 . The timeaveraged current through a vibrating nanotube probes electron-phonon coupling 8-11 , non-linear dissipation 12 , and mechanical mode mixing 13 on the nanoscale. Timeresolved measurements go further, allowing for the study of transient effects such as spin switching 14,15 , mechanical dephasing 16 , or even force-detected magnetic resonance 17 . Although the low mass favors large electromechanical coupling, the large electrical impedance of nanotube devices makes it difficult to amplify the current signal with high sensitivity and bandwidth, especially since low temperatures are needed to suppress thermal noise.One approach is to downconvert the electromechanical signal to a frequency within the bandwidth of a cryogenic current amplifier, using either two-source mixing or the non-linear conductance of the nanotube itself 18,19 . For fast measurements, parasitic capacitance must be minimised by placing the amplifier close to the resonator. The resulting heat load has usually prevented operation below 1 K 16,19 , although recently such a setup achieved high sensitivity at millikelvin temperatures and with a bandwidth of 87 kHz 20 . A second approach, with higher bandwidth, is to detect the changing capacitance between the vibrating nanotube and a pickup antenna 21 . However, the small size of the pickup antenna means that a large electric field is needed to generate an appreciable signal. A third approach, used for other kinds of nanoscale resonator 22,23 , is to connect the resonator's output directly to a fast amplifier matched to the cable impedance (typically 50 Ω). However, the electrical divider formed between the large impedance of the device and the small impedance of the cable degrades the signal.Here, we demonstrate a circuit that combines sensitivity with high speed by monitoring the electromechanical signal directly, while requiring only a DC bias voltage. The circuit exploits a single-electron transistor (SET) dea) Electronic mail: e.a.laird@lancaster.ac.uk fined within the nanotube as the initial stage of displacement amplification 2,[9][10][11][24][25][26][27] . The SET output current, which depends linearly on displacement, is monitored directly at radio frequency using a low-noise cryogenic radio-frequency (RF) amplifier with MHz bandwidth. To improve the coupling between the SET and the cryogenic amplifier, we use an impe...

Ultrastrong coupling between electron tunneling and mechanical motion

“…( 9). The amplitude of motion, z(0) 0.1 nm, is consistent with the values estimated in previous experiments [40,45]. The value of z(0) only significantly affects the width of the dip in the resonance frequency when z(0) is larger than (Γ tot /g m )z ZPM , i.e z(0) > ∼ 0.6 nm (see Supplemental Material [47]).…”

“…The quantum dot is defined in the nanotube through a combination of Schottky barriers at the contacts and the voltages applied to five gate electrodes (labelled V G1-G5 ) beneath the nanotube. These gate electrodes are also used to actuate the nanotube's motion [40,44,45]. A current I is driven by a bias voltage V s .…”

A coherent nanomechanical oscillator driven by single-electron tunnelling

“…To explore these dynamic effects, we implemented an electromechanical circuit for measuring the nanotube's vibrations directly 12 (Fig. 1b).…”

Self-driven oscillation in Coulomb blockaded suspended carbon nanotubes

“…However, these oscillations may exhibit narrower linewidths than the intrinsic resonator linewidth [22], and a properly tailored electromechanical coupling can provide a pathway to active cooling of the mechanical state [4]. Additionally, with sensitive frequency-resolved readout [9], self-driven oscillations may be useful for sensitive mass/force detection without the need for high-frequency external excitation at the device [23]. These self-driving devices could also FIG.…”

“…The suspended nanotube devices were fabricated by a process in which the CNT is grown separately from the device wafer, then transferred onto predefined contacts by stamping [9,10]. The device consists of 400-nm-thick Ti/Au source/drain electrodes on a SiO 2 /Si substrate.…”