| In this dissertation, we studied weak and nearly ferromagnetic metals around the quantum critical point. The Green function of electrons is calculated by considering the interaction between electrons and spin fluctuations. It is shown that around the quantum critical point the system show Fermi liquid behavior at low temperature and non Fermi liquid behavior at high temperature. The resistivity and specific heat calculations agree with experiment results quite well. Based on the electron's Green function, we solve Eliashberg equations under certain approximation, and get the analytical expression for superconducting transition temperature. We also numerically get superconducting transition temperature and pairing gap around the quantum critical point. Hence the phase diagram around the magnet quantum critical point can be drawn. In the second part, we calculated thermoelectric figure of merit of strongly correlated semiconductors, and present a potential for the application of these strongly correlated materials. In the third part, the full phase structure of the generalized Gross-Neveu model is studied, where we consider the competition between chiral condensate and Cooper pair. We find that there is a first order phase transition from chiral condensate to Cooper pair condensate as chemical potential is increased, and no coexistence of these two phase except at the first order phase transition line. |
