Visualizing nonlinear resonance in nanomechanical systems via single-electron tunneling

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Numerous reports have elucidated the importanca of mechanical resonators oomprising quantum-dot-embedded carbon nanotubes(CNTs) for studying the effects of single-electron transport.However,there is a need to investigate the single-electron transport that drives a large amplitude into a nonlinear regime.Herein,a CNT hybrid devioe has been investigated,which oomprises a gate-defined quantum dot that is embedded into a mechanical resonator under strong actuation conditions.The Coulomb peak positions synchronously oscillate with the mechanical vibrations,enabling a single-electron “chopper” mode.Conversely,the wibration amplitude of the CNT versus its frequenoy can be directly visualized via detecting the time-averaged single-eiectron tunneling current.To understand this phenomenon,a general formula is derived for this time-averaged single-electron tunneling current,which agrees well with the experimental results.By using this visualization method,a variety of nonlinear motions of a CNT mechanical oscillator have been directly recorded,such as Duffing nonlinearity,parametric resonance,and double-,fractional-,mixed-frequency excitations.This approach opens up burgeoning opportunities for investigating and understanding the nonlinear motion of a nanomechanical system and its interactions with electron transport in quantum regimes.
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