Vortices and Quantum tunneling in Current-Biased 0-π-0 Josephson Junctions of d-wave Superconductors

We study a current-biased 0-\pi-0 Josephson junction made by high-T_c superconductors, theoretically. When a length of the \pi junction is large enough, this junction contains a vortex-antivortex pair at both ends of the \pi junction. Magnetic flux carried by the vortices is calculated using the sine-Gordon equation. The result shows that the magnetic flux of the vortices is suppressed to zero as the distance between the vortices is reduced. By applying an external current, the orientation of the vortices is reversed, and a voltage pulse is generated. The current needed for this transition and generated pulse energy are calculated. Macroscopic quantum tunneling (MQT) in this transition is also studied. The tunneling rate has been evaluated by an effective Hamiltonian with one degree of freedom.