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An optical blackbody is an ideal absorber for all incident optical radiation, and the theoretical study of its radiation spectra paved the way for quantum mechanics (Planck’s law). Herein, we propose the concept of an electron blackbody, which is a perfect electron absorber as well as an electron emitter with standard energy spectra at different temperatures. Vertically aligned carbon nanotube arrays are electron blackbodies with an electron absorption coefficient of 0.95 for incident energy ranging from 1 keV to 20 keV and standard electron emission spectra that fit well with the free electron gas model. Such a concept might also be generalized to blackbodies for extreme ultraviolet, X-ray, and γ -ray photons as well as neutrons, protons, and other elementary particles.

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.

The carbon nanotube (CNT) hybrid device composed of a gate-defined quantum dot embedded into a mechanical resonator is investigated under strong actuation condition. The Coulomb peaks are driven to the synchronous and large oscillation by the nonlinear mechanical vibration, and can be coherently modulated to the single-electron shuttle mode. Conversely, the mediated single-electron tunnelling current provides an in situ and sensitive characterization strategy for the multi-order mechanical nonlinear resonance. We show that, under the strong modulation applied via gate voltage, the swing and trampoline modes exhibit different nonlinearity behaviour, depending on both the quadratic and cubic coefficients. The nonlinearities in this hybrid system also give rise to coupling modes of quadratic and cubic resonances at combined frequencies and even fractional frequencies. Especially, the subharmonic resonance due to quadratic nonlinearity is predicted to enable the excitation of the coherent coupling state between two modes. Our theoretical mode of the intra- and intermodal nonlinearities shows a good agreement of our experimental observations quantitatively.

We study the collinear chaotic scattering between an electron and a one-electron ion (e.g., ${\mathrm{He}}^{+})$ with negative total energy. The global dynamics of the unbounded motion in phase space can be illustrated by introducing two submanifolds of critical injecting and critical escaping. We find a type of bifurcation of chaotic scattering resulted from the tangency between these two submanifolds, which explains the emergence or disappearance of an extra zeroth-order chaotic band in the scattering functions as the nuclear charge Z is changed.