  The charge transport has been analyzed theoretically across a T-shaped and
series-configured double quantum dots Josephson junction by implementing the
Slave Boson mean field approximation at an infinite-U limit. It has been shown
that Andreev Bound states (ABS) and Josephson current can be tuned by varying
the interdot tunneling (t) and quantum dots energy level. For the T-shape
configuration of the quantum dots, an extra path is available for the transport
of electrons which causes the interference destruction between two paths. For
decoupled quantum dots with $\epsilon_{d1}=\epsilon_{d2}=0$, the energy of ABS
crosses at $\omega=0$ and Josephson current shows a discontinuity at $\phi=\pm
\pi$. On the other hand, for coupled quantum dots the lower and upper ABS has a
finite spacing, the Josephson current exhibits sinusoidal nature and its
magnitude suppresses with increasing interdot tunneling strength. While in the
series configuration, with increment in t, Josephson current increases and
shows a discontinuity at $\phi=\pm \pi$, once the system gets resonant
tunneling for $t=0.5\Gamma$ with $\epsilon_{d1}=\epsilon_{d2}=0.5\Gamma$.
Further, we also analyze the nature of the energy of ABS and Josephson current
with the quantum dots energy level in both configurations.
