Figure 1

Nanoabacus resonators. (a) Schematic cross section of the device. Suspended carbon nanotubes were grown bridging source and drain electrodes $(\mathrm{Pt}∕\mathrm{Cr})$ (Refs. 3, 4) with a local gate lying on the bottom of the trench (Ref. 5). An evaporation of materials such as indium on to the nanotube forms the abacus structure. (b) Scanning electron micrograph of a nanoabacus made by evaporating nominal $2.5\mathrm{nm}$ thick indium onto a CNT. Scale bar: $100\mathrm{nm}$.Reuse & Permissions

Figure 2

(a) Schematic circuit diagram of the experimental setup for the $2\omega$ mixing method. An actuation voltage signal of amplitude $\delta {\mathrm{V}}_g$ at a frequency $\omega$ is applied to the gate G, while a carrier voltage signal of amplitude $\delta {\mathrm{V}}_d$ is applied to the drain D at a frequency $2\omega -\Delta \omega$. The current flow through the source S at the frequency $\Delta \omega$ (typically set at $7\mathrm{KHz}$) is monitored using a lock-in amplifier with a time constant of $300\mathrm{ms}$. The lock-in reference at the frequency $\Delta \omega$ is obtained through a frequency doubler and a mixer. The effective driving frequency on the resonator is $2\omega$, the frequency of the electrostatic force induced by the gate voltage signal. (b) Illustration of actuation gate signal $\delta {\mathrm{V}}_g$ and the corresponding response in charge $q$, force $F$, conductance $G$, and Fourier transform of conductance ${\chi }_G$ under ideal conditions with no accumulated charge (left) and with finite accumulated charge $q_0$ (right).Reuse & Permissions

Figure 3

Amplitude (in logarithmic scale) and phase of the electrical current as a function of effective driving frequency $f$ in a vacuum of ${10}^{-6}\text{Torr}$ (triangles) and in air (circles) for a nanoabacus resonator, measured with a gate signal $\delta {\mathrm{V}}_g=158\mathrm{mV}$ and a drain signal $\delta {\mathrm{V}}_d=70\mathrm{mV}$ by the $2\omega$ mixing method. The resonator was made by coating a suspended carbon nanotube device with thermally evaporated $5\mathrm{nm}$ thick indium (measured by a quartz crystal monitor). The trench between the source and the drain electrodes is $300\mathrm{nm}$ wide and $400\mathrm{nm}$ deep. A metal gate (Pt $20\mathrm{nm}∕\mathrm{Cr}$ $5\mathrm{nm}$) was patterned on the bottom of the trench. The nanotube was grown by chemical vapor deposition (Ref. 6) directly bridging the source and the drain electrodes (Pt $20\mathrm{nm}∕\mathrm{Cr}$ $5\mathrm{nm}$) with electrical contact, and the electrical resistance is $\sim 1\mathrm{M}\Omega$. We also observed other lower-frequency resonance at 0.27, 0.45, and $1.2\mathrm{GHz}$, likely induced by different resonating beam sections.Reuse & Permissions

Figure 4

Schematic diagram of a collision between a gas molecule with velocity $\mathit{V}(v,\theta ,\varphi )$ and a vibrating beam with velocity $V_0$ along the $z$ axis.Reuse & Permissions