@article{Wang2021, 
author = {Xinhe Wang and Lin Cong and Dong Zhu and Zi Yuan and Xiaoyang Lin and Weisheng Zhao and Zaiqiao Bai and Wenjie Liang and Ximing Sun and Guang-Wei Deng and Kaili Jiang},
title = {Visualizing nonlinear resonance in nanomechanical systems via single-electron tunneling},
year = {2021},
journal = {Nano Research},
volume = {14},
number = {4},
pages = {1156-1161},
keywords = {carbon nanotube, quantum dot, coupling, mechanical resonator, nonlinear},
url = {https://www.sciopen.com/article/10.1007/s12274-020-3165-2},
doi = {10.1007/s12274-020-3165-2},
abstract = {Numerous reports have elucidated the importance of mechanical resonators comprising 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 device has been investigated, which comprises 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 vibration amplitude of the CNT versus its frequency can be directly visualized via detecting the time-averaged single-electron 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.}
}