0-π junction transition in the Josephson junction of parallel double quantum dots: Bistable junction behavior induced by Majorana bound states

By employing the exact diagonalization method and the zero-bandwidth approximation, we conducted a theoretical study on the 0-n junction transition in a Josephson junction composed of coupled Majorana bound states (MBSs) in parallel double quantum dots (QDs). We examined the effects of system parameters such as the dot-MBSs coupling coefficient VM and the QDs energy level Ed on the Josephson current and inter-dot spin correlation function under different lengths of topological superconducting wires. In the limit of long wires, we found that due to the degenerate ground states arising from coupling MBSs, quasi-particle excitations between these ground state levels at electron-hole symmetric points open up a new channel for Kondo effect, significantly impacting the Josephson junction transition in the system; namely, a new bistable junction behavior appears in the 0-n transition diagram, and we analyzed its underlying physical mechanism. In the case of finite-length topological quantum wire, new Kondo effect channels caused by quasi-particle excitations between the degenerate ground state levels at electron-hole symmetric points disappear, as well as the bistable junction behavior. However, under different Emvalues, we found that both current curves and inter-dot spin correlation functions exhibit completely different characteristics in the system, demonstrating profound impacts of MBSs on quantum states and n junction transition in superconducting systems.