Vibrating Superconducting Island in a Josephson Junction

We consider a combined nanomechanical-supercondcuting device that allows the Cooper pair tunneling to interfere with the mechanical motion of the middle superconducting island. Coupling of mechanical oscillations of a superconducting island between two superconducting leads to the electronic tunneling generates a supercurrent that is modulated by the oscillatory motion of the island. This coupling produces alternating finite and vanishing supercurrent as function of the superconducting phases. Current peaks are sensitive to the superconducting phase shifts relative to each other. The proposed device may be used to study the nanoelectromechanical coupling in case of superconducting electronics.

Figure 1

Schematic view of the mechanically and electronically coupled superconducting island (SC I) to the superconducting leads (SC L and SC R). The cantilever superconducting island is modeled as a harmonic oscillator with spring constant $k_c$ and mass $m_c$, placed between the infinitely massive superconducting leads. The device is biased with voltage $V$.

Figure 2

Fourier transform of the Josephson current ${log}_{10}|2I_S(\omega )/J_S{|}^2$ in the symmetrically biased and undamped system as a function of the frequency $\omega$ and the phase ${\varphi }_L$, for a fixed phase ${\varphi }_R=0$. Here we have taken $\tilde{\alpha }=0.1$, $K=0.6$, and the oscillating frequencies (a) ${\omega }_0=0.4{\omega }_J$ and (b) ${\omega }_0=1.4{\omega }_J$.

Figure 3

Zero bias Josephson current ${log}_{10}|2I_S(\omega )/J_S{|}^2$ in the symmetrically biased and undamped system as a function of the frequency $\omega$ and the phase ${\varphi }_L$, for a fixed phase ${\varphi }_R=\pi /2$. Here we have taken ${\omega }_0=1$, while other parameters are as Fig. 2.