Interplay of hybrid and unhybrid quantum transport of interacting electron pairs through a short conduction channel

For quantum ballistic transport of electrons through a short conduction channel, the role of Coulomb interaction may significantly modify the energy levels of an electron pair at low temperatures as the channel becomes wide. In this regime, the Coulomb effect on the orbital triplet and singlet electron-pair state is calculated and found to lead to four split energy levels, including two hybrid and two unhybrid states. Moreover, due to the interplay of hybrid and unhybrid Coulomb interactions between two electrons, our calculations reveal that the ground pair-state will switch from one hybrid orbit-triplet state (strong confinement) to the unhybrid orbit-singlet state (intermediate confinement) as the channel width gradually increases and then back to the original hybrid orbit-triplet state (weak confinement), due to larger total spin of the orbit-singlet state, as the channel width becomes larger than a threshold value. This switching behavior leaves a footprint in the conductance as well as in the diffusion thermoelectric power of electrons. Here, the predicted reoccurrence of the hybrid orbit-triplet state (spin-$0$ state) as a ground state is shown to relate to the higher spin degeneracy of the spin-$1$ state as well as to the strong Coulomb repulsion in the central region of the channel, which separates two electrons away and pushes them to different channel edges. The conductance reoccurrence region expands from the weak to the intermediate confinement regime with increasing linear electron density.