Mathematical Physics Seminar, May 19, 2009
After a short review on superconductivity, I will analyze the thermodynamic impact of the Coulomb repulsion on s-wave superconductors via a rigorous study of equilibrium and ground states of the strong coupling BCS-Hubbard Hamiltonian. In particular, I will explain that the one-site electron repulsion can favor superconductivity at fixed chemical potential by increasing the critical temperature and/or the Cooper pair condensate density. If the one-site repulsion is not too large, a first or a second order superconducting phase transition can appear at low temperatures. I will also show that the Meissner effect is rather generic but coexistence of superconducting and ferromagnetic phases can also be feasible, for instance near half-filling and at strong repulsion. Additionally, our proof of a superconductor-Mott insulator phase transition implies a rigorous explanation of the necessity of doping insulators to create superconductors. However, the representation of the kinetic energy of electrons in this specific model is still not satisfactory and I will conclude this talk by explaining how we could generalize these results to translation invariant Fermi systems. |