Nonlinear Oscillations: Exact Solutions and their Approximations

A single-electron transistor embedded in a nanomechanical oscillator realises an extreme limit of electron-phonon coupling. It performs fast and sensitive electromechanical measurements but also introduces backaction forces, due to the tunnelling of individual electrons, which randomly perturb the mechanical state. Despite the stochastic nature of this backaction, under conditions of strong coupling it is predicted to create a self-sustained state of coherent mechanical oscillations. I will show how we verify this prediction using time-resolved measurements of a vibrating carbon nanotube transistor. This electromechanical oscillator has intriguing similarities with a laser, with the population inversion provided by the electrical bias and the resonator acting as a phonon cavity. I will show that the resulting emission has the same coherence as a laser, and demonstrate other laser behaviour including injection locking and feedback narrowing of the emitted signal.

A coherent nanomechanical oscillator driven by single-electron tunneling

The spin filtering effect, negative differential resistance, spin Seebeck effect and spin diode effect are found in homogeneous and heterogeneous 1T-FeCl2 nanotubes, which suggest their potential applications in spintronic devices. 

Promising spin caloritronics and spin diode effects based on 1T-FeCl<sub>2</sub> nanotube devices

Controllable single‐molecule logic operations will enable development of reliable ultra‐minimalistic circuit elements for high‐density computing but require stable currents from multiple orthogonal inputs in molecular junctions. Utilizing the two unique adjacent conductive molecular orbitals (MOs) of gated Au/S‐(CH2)3‐Fc‐(CH2)9‐S/Au (Fc = ferrocene) single‐electron transistors (≈2 nm), a stable single‐electron logic calculator (SELC) is presented, which allows real‐time modulation of output current as a function of orthogonal input bias (Vb) and gate (Vg) voltages. Reliable and low‐voltage (ǀVbǀ ≤ 80 mV, ǀVgǀ ≤ 2 V) operations of the SELC depend upon the unambiguous association of current resonances with energy shifts of the MOs (which show an invariable, small energy separation of ≈100 meV) in response to the changes of voltages, which is confirmed by electron‐transport calculations. Stable multi‐logic operations based on the SELC modulated current conversions between the two resonances and Coulomb blockade regimes are demonstrated via the implementation of all universal 1‐input (YES/NOT/PASS_1/PASS_0) and 2‐input (AND/XOR/OR/NAND/NOR/INT/XNOR) logic gates.

Stable Universal 1‐ and 2‐Input Single‐Molecule Logic Gates

We investigate electronic transport in Josephson junctions formed by single-walled carbon nanotubes coupled to superconducting electrodes. We observe enhanced zero-bias conductance (up to 10e^2/h) and pronounced sub-harmonic gap structures in differential conductance, which arise from the multiple Andreev reflections at superconductor/nanotube interfaces. The voltage-current characteristics of these junctions display abrupt switching from the supercurrent branch to resistive branch, with a gate-tunable switching current ranging from 50 pA to 2.3 nA. The finite resistance observed on the supercurrent branch and the magnitude of the switching current are in good agreement with calculation based on the model of classical phase diffusion.

Phase Diffusion in Single-Walled Carbon Nanotube Josephson Transistors

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.

Ximing Sun

Papers

Visualizing nonlinear resonance in nanomechanical systems via single-electron tunneling