Josephson Transport across T-shaped and Series-Configured Double Quantum Dots System at Infinite-U Limit

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.