Josephson and thermophase effect in interacting T-shaped double quantum dots system

This article theoretically analyzes the phase and thermal driven transport properties in a T-shaped double quantum dot Josephson junction. We began by investigating the Josephson current for different on-dot Coulomb interaction on central quantum dot and interdot-tunneling between quantum dots. Josephson current exhibits $0-\pi$ phase transition for intermediate Coulomb interaction to dot-lead coupling ratio with quantum dots energy level below the Fermi level. The Josephson current exhibits complete $\pi$-phase in doublet regime for relatively large Coulomb interaction to dot-lead coupling ratio. The interdot-tunneling destroys the $\pi$ region and shifts the $0-\pi$ transition points depending on the position of quantum dot energy levels. Further, depending on the position of central quantum dot energy level and Coulomb interaction strength, Josephson current shows Fano types symmetric and asymmetric line shapes with a Fano dip at the Fermi level of side dot. Next, we demonstrated that with increasing thermal energy, the discontinuity in the Josephson current smeared and becomes sinusoidal. Finally, the total current (Josephson current+quasi-particle current) is analyzed by applying a finite temperature biasing across the junction. The system is examined in electrically open circuit configuration, where phase driven Josephson current and thermal driven quasi-particle cancels each other, and analyze the thermophase Seebeck effect in linear response region. At the $0-\pi$ transition points, where the Josephson current shows discontinuities, the thermal gradient produces abrupt thermophase Seebeck coefficient (TPSC) peaks, and the strength of interdot-tunneling provides great control over these abrupt TPSC peaks.