Josephson effect in a triple-quantum-dot ring with one dot coupled to superconductors: Numerical renormalization group calculations

• We study the Josephson effect in a triple-dot ring with one dot coupled to superconductors.
• The results are based on the numerical renormalization group calculations.
• Two phase transitions arise, differentiated from sharp or smooth changes of current direction.
• The phase transitions are determined by the variation of interdot spin correlations.
• A spin singlet can form between two lateral dots, decoupled from the main channel.

We investigate the Josephson effect in a triple-quantum-dot ring in which only one dot is coupled to the superconductors, by performing the numerical renormalization group calculations. As a result, two kinds of Josephson phase transitions arise. One is the phase transition accompanied by the sharp change of the current direction, whereas the other phase transition is only accompanied by the smooth change of the current direction. Our analysis shows that in this structure, the phase transitions are determined by the variation of interdot spin correlations. The geometry of triple-dot ring induces various spin-correlation modes, leading to the complicate phase transitions. What's notable is that a spin singlet can form between the two lateral dots, which is decoupled from the main channel of this structure. It is certain that such a structure provides an alternative proposal to manipulate the spin correlation between the lateral dots.