Andreev bound states and π-junction transition in a superconductor / quantum-dot / superconductor system

We study Andreev bound states and π-junction transition in a superconductor / quantum-dot / superconductor (S-QD-S) system by Green function method. We derive an equation to describe the Andreev bound states in S-QD-S system, and provide a unified understanding of the π-junction transition caused by three different mechanisms: (1) Zeeman splitting. For QD with two spin levels E↑ and E↓, we find that the surface of the Josephson current I(φ = π2 ) vs the configuration of (E↑, E↓) exhibits interesting profile: a sharp peak around E↑ = E↓ = 0; a positive ridge in the region of E↑ ·E↓ > 0; and a negative, flat, shallow plain in the region of E↑ ·E↓ < 0. (2) Intra-dot interaction. We deal with the intra-dot Coulomb interaction by Hartree-Fock approximation, and find that the system behaves as a π-junction when QD becomes a magnetic dot due to the interaction. The conditions for π-junction transition are also discussed. (3) Non-equilibrium distribution. We replace the Fermi distribution f(ω) by a non-equilibrium one 12 [f(ω − Vc) + f(ω + Vc)], and allow Zeeman splitting in QD where E↑ = −E↓ = h. The curves of I(φ = π2 ) vs Vc show the novel effect of interplay of non-equilibrium distribution with magnetization in QD. 1 PACS numbers: 74.50.+r, 73.40.Gk, 73.20.Dx, 72.15.Nj.