Exact many-electron scattering states in a parallel-coupled double quantum-dot system

We study a parallel-coupled double quantum-dot (PDQD) system with both intradot and interdot Coulomb interactions by constructing many-electron scattering eigenstates explicitly. We obtain exact solutions of the two-electron scattering eigenstates whose incident states are plane-wave states. We find that, as a result of the Coulomb interactions, many-body bound states appear in the scattering eigenstates. The binding strength of the many-body bound states is shown to depend on the difference of gate energies of the two quantum dots, which is interpreted as an effect of geometrical interference.