Josephson transport across T-shaped and series-configured double quantum dots system at infinite- $$\textit{U}$$ 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- $$\textit{U}$$ U limit. It has been shown that Andreev bound states 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 energy level $$\epsilon _{d1}=\epsilon _{d2}=0$$ ϵ d 1 = ϵ d 2 = 0 , the energy of Andreev bound states crosses at Fermi energy, and Josephson current shows a discontinuity at phase difference $$\phi =\pm \pi $$ ϕ = ± π . On the other hand, for coupled quantum dots the lower and upper Andreev bound states have a finite spacing, the Josephson current exhibits a sinusoidal nature and its magnitude suppresses with increasing interdot tunneling strength. While in the series configuration, with increment in interdot tunneling, Josephson current increases and shows a discontinuity at phase difference $$\phi =\pm \pi $$ ϕ = ± π , once the system gets resonant tunneling for $$t=0.5\Gamma $$ t = 0.5 Γ with quantum dots energy level $$\epsilon _{d1}=\epsilon _{d2}=0.5\Gamma $$ ϵ d 1 = ϵ d 2 = 0.5 Γ . Further, we also analyze the nature of the energy of Andreev bound states and Josephson current with the quantum dots energy level in both configurations. Graphical Abstract