Figure 1

(a) Aerial view in a scanning electron microscope of two coupled electron shuttles. The two nanopillars’ gold tops have diameters of $\cong 65\mathrm{nm}$ with a total nanopillar height of around 250 nm. The inset gives a top view of the coupled nano-electromechanical pendula. The scale bars are 200 nm in both graphs. Below: Sketch of the measurement setup. An applied ac and dc bias voltage ($V_{\mathrm{DS}}$) displaces the two pendula by $x_1$, $x_2$ and the resulting current $I_{\mathrm{DS}}$ is amplified. (b) Direct current $I_{\mathrm{DS}}$ vs bias voltage $V_{\mathrm{DS}}$ in the case of pure self-excitation, i.e., $V_{\mathrm{ac}}=0$ at room temperature. The upper inset shows low bias regime with the dashed lines indicating the occurrence of Coulomb charging effects (see text for details). The lower inset gives a finite-element simulation of the electric field distribution under an applied bias voltage (top view). The field intensity is maximal between the two pillars.Reuse & Permissions

Figure 2

(a) Spectrum of drain current $I_{\mathrm{DS}}$ vs $f$ the excitation frequency of the coupled nanopillars. The current resonances are labeled according to the commensurate mode numbers $p/q$ where the fundamental mode is found to be at ${\omega }_o/(2\pi )=504\mathrm{MHz}$ from finite-element simulations. The externally applied power of the radio frequency source was $P=4\mathrm{dBm}$. Note the seven distinct current peaks in the reverse current (blue triangles). This electromechanical pumping mechanism pushes electrons against the dc bias of $V_{\mathrm{DS}}=0\mathrm{mV}$. The low-frequency region ($\star$) is plotted in detail in (b). The red (light gray) line indicates fits to the resonances taking into account different line shapes. (c) Finite-element simulation based on COMSOL showing the fundamental mode of the coupled pendula in a 3D (left) and top view (right). The color coding indicates the displacement within the nanopillars.Reuse & Permissions

Figure 3

(a) Current response on and off resonance: at 589 MHz ($\delta$) with an ac radio frequency excitation of $-3\mathrm{dBm}$ a strong mechanical response of the coupled pendula is obtained, while at off resonance ($\eta$) only a weak current shows. (b) Bias dependence of the coupled nanopillars on resonance $\delta$ and off resonance $\eta$. While we find an ohmic response for both cases the red (light gray) $\delta$ trace is offset from the blue (dark gray) $\eta$ trace. This offset results from the rectification through the coupled nanomechanical shuttles.Reuse & Permissions

Figure 4

Arnold tongues: (a) mechanical resonances at around 80 MHz under increased ac power. (b) The dc bias dependence with gradually increased ac-power, from $-20\mathrm{dBm}$ (bottom) to $-15\mathrm{dBm}$ (top). Inset shows the linear dependence of the rectified direct current upon increasing ac-power. (c) Color scale plot of the total power dependence, revealing Arnold’s tongues with the whited dashed lines being guides to the eye. Inset shows a devil’s staircase plot depicting the width of each bistable region.Reuse & Permissions