Tuning of phase diffusion in small Josephson junctions by magnetic field

We report experimental and theoretical study of low-voltage resistive states in submicrometer Josephson tunnel junctions placed in an external magnetic field $H$. The junctions display a low-voltage Josephson phase diffusion branch characterized by small but finite resistance and hysteretic switching to higher voltages. Depending on the junction area, we observe two different effects of the external magnetic field on the low-voltage part of current-voltage characteristics. In the first case, the maximum voltage $V_m$ of the phase-diffusion branch increases with magnetic field. In the second case, we find $V_m$ to be nearly independent of magnetic field. These resistive states depend on the ratio between the Josephson energy $E_J\left(H\right)$ and energy of thermal fluctuations $k_{B}T$. A theoretical analysis based on a diffusion of the ”center mass“ of the Josephson phase is in good accord with experimental observations.

Figure 1

(Color online) Typical $I\text{−}V$ curve of a Josephson tunnel junction of the area $0.47\times 0.47\mu {\mathrm{m}}^2$ measured at zero magnetic field at a temperature $T=4.2\mathrm{K}$. Notice small but finite resistance of the critical current branch close to origin.

Figure 2

(Color online) Magnetic-field dependence of the low-voltage part of $I\text{−}V$ curves: (a) moderate junction size $1\times 1\mu {\mathrm{m}}^2$; (b) small junction size $0.47\times 0.47\mu {\mathrm{m}}^2$. Legend refers to magnetic flux in the junction in units of magnetic flux quantum ${\Phi }_0$. Current decreases with an external magnetic field.

Figure 3

(Color online) Magnetic-field dependence of parameters $V_m$ (open symbols) and $I_m$ (solid symbols) for two Josephson junctions of different areas. The moderate-size junction $1\times 1\mu {\mathrm{m}}^2$ data are shown by circles. Squares correspond to a junction of smaller size $0.47\times 0.47\mu {\mathrm{m}}^2$. Lines are just to guide the eye.

Figure 4

(Color online) Theoretical magnetic-field dependences of the low-voltage part of the $I\text{−}V$ curve: (a) using Eq. (7) for a Josephson junction of moderate size, $E_J\left(0\right)\simeq 8k_{B}T$; (b) using Eq. (8) for a Josephson junction of smaller size, $E_J\left(0\right)=2k_{B}T$. Legend refers to magnetic flux in the junction in units of magnetic flux quantum ${\Phi }_0$. Current decreases with an external magnetic field.