Static and rf magnetic field effects on fluxon dynamics in semiannular Josephson junctions

Long semiannular Josephson junctions coupled to in-plane external static and rf magnetic fields are investigated analytically and numerically. A spatially homogeneous dc magnetic field applied in the plane of the dielectric barrier and perpendicular to a plane containing the junction boundaries induces a potential well in which trapped fluxons are pinned in the absence of a bias current. An applied rf field produces phase-locked fluxon motion manifesting constant voltage steps in the current-voltage characteristics. Analytical expressions obtained for depinning current, power-balance velocity, phase-locking range, and constant voltage steps using perturbational analysis are found to be in very good agreement with the numerical results. The proposed device is suitable for studying quantum dynamics of fluxons trapped in a potential well and in the fabrication of devices like submillimeter-wave local oscillators and constant-voltage standard devices, etc.

Figure 1

A sketch of a semiannular LJJ with an applied magnetic field $b$ parallel to the plane of the dielectric barrier of uniform thickness and perpendicular to a plane containing the junction boundaries (not drawn to scale). $\overline{n}$ represents the direction of the magnetic moment of a trapped fluxon.

Figure 2

The potential well $U\left(x_0\right)∕C$ in the junction as a function of the fluxon coordinate $x_0\left(●\right)$ and the field-induced bias term ${\gamma }_b\left(x\right)∕b\left(엯\right)$ in a junction of $l=10$ at $\gamma =0$. Inset shows spatial profile $\left({\phi }_x\right)$ of a trapped fluxon pinned at the center of the junction.

Figure 3

(a) Applied dc bias $\gamma$ versus the average velocity $⟨u⟩=l∕2\pi ⟨{\phi }_t⟩$ at different values of the magnetic fields. The parameters of the junction are $l=10$, $\alpha =0.05$, and $\beta =0.01$. (b) Magnetic field intensity $b$ versus zero-voltage bias current ${\gamma }_0$ showing linearity of ${\gamma }_0$ with $b$ on two junctions with parameters $\alpha =0.05$ and $\beta =0$. Solid lines represent values computed using Eq. (23) and symbols represent numerical results with a single fluxon trapped in the junction.

Figure 4

Critical current $\left({\gamma }_c\right)$ versus static magnetic field $(2B∕B_{c1}=b∕k)$ of a semiannular LJJ $\left(엯\right)$ and that of a rectangular LJJ $\left(●\right)$ of $l=10$, $\alpha =0.05$, and $\beta =0$ without any trapped fluxons.

Figure 5

IVC at different rf magnetic field intensities showing constant voltage steps. The parameters are $l=12$, $\alpha =0.05$, $\beta =0.01$, and $\omega =0.2$.

Figure 6

PL range $\Delta \gamma ∕b$ as function of velocity parameter $u_0=\omega ∕k$. Theoretical values computed using Eq. (40) are shown (solid lines) along with numerically obtained values $\left(●\right)$ for different length junctions. The parameters are $\alpha =0.05$, $\beta =0.01$, and $b=0.2$.

Figure 7

rf magnetic field frequency $\omega$ as a function of the PL velocity $u_0$. The parameters are $\alpha =0.05$, $\beta =0.01$, $b=0.3$, and $\gamma =0.2$. Solid lines represent values computed using Eq. (42) and symbols represent numerically obtained values.