Distinguishing between Direct and Parametric Driving in Nanomechanics using a Vibrating Carbon Nanotube

Dicker, Sam and Laird, Edward (2026) Distinguishing between Direct and Parametric Driving in Nanomechanics using a Vibrating Carbon Nanotube. PhD thesis, Lancaster University.

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Abstract

Carbon nanotubes (CNTs) were discovered in 1952 by L. V. Radushkevich and V.M. Lukyanovich. CNTs have extraordinary mechanical properties being incredibly stiff but lightweight having a tensile strength greater than that of steel. Their electronic properties are also extraordinary allowing measurements in the quantum regime such as quantum blockade and single electron transistors (SETs). CNTs have high quality factors which when paired with their electronic and mechanical properties allows us to view CNT motion in the quantum regime. This can be used for detecting miniscule forces on the CNT possibly allowing the CNT to be used for magnetic resonance force microscopy. CNT motion is usually detected by looking at the change in current through a CNT on resonance, known as the rectification technique. The CNT is prone to unexpected resonances due to parametric motion which can obscure actual harmonics of the CNT, which cannot be differentiated using the rectification technique. In this thesis we show a new technique using a CNT device as an up-conversion RF mixer, which is shown to be able to distinguish between parametrically and directly driven motion. We do this by looking for signals at half the drive frequency which we are able to do using the time dependence on this new mixer technique. We show that the suspected parametric motion in the CNT turns on at a drive power of $\sim-34$~dBm and the signal peak exponentially increases with drive power which agrees with theory on parametric motion. We also show that the directly driven motion follows a linear dependence with drive power. We show that not only is this technique able to tell the difference between parametric and directly driven motion, but is also far more sensitive to CNT motion than the rectification technique. We were able to identify the other resonances seen around the first harmonic of the CNT, but we were unable to identify all harmonics around the 2nd harmonic of the CNT.