Localized Many-Particle Majorana Modes with Vanishing Time-Reversal Symmetry Breaking in Double Quantum Dots

We introduce the concept of spinful many-particle Majorana modes with local odd operator products, thereby preserving their local statistics. We consider a superconductor-double-quantum-dot system where these modes can arise with negligible Zeeman splitting when Coulomb interactions are present. We find a reverse Mott-insulator transition, where the even- and odd-parity bands become degenerate. Above this transition, Majorana operators move the system between the odd-parity ground state, associated with elastic cotunneling, and the even- parity ground state, associated with crossed Andreev reflection. These Majorana modes are described in terms of one, three, and five operator products. Parity conservation results in a 4 pi periodic supercurrent in the even state and no supercurrent in the odd state.