Study On BCS Model By Using Auxiliary Field Quantum Monte Carlo Method

Superconductor plays an important role in current condensed matter physics. Many efforts have been done on this subject since it was discovered. In this thesis, we have calculated the thermodynamics properties of BCS model by using Auxiliary Field Quantum Monte Carlo (AFQMC) method. The kinds of systems, i.e. macroscopic bulk superconductor and small superconductor grains are investigated.The main conclusions of this thesis are as following:(1). Macroscopic bulk superconductor:The preformed paring phenomenon above the critical temperature is found in both D-wave and S-wave superconductor, in which electron density is10%and25%. Our results also show that, the BCS model could be used to describe preformed paring phenomenon, which is not found in previous studies. Additionally, the preformed paring phenomenon was found to be almost independent on the electron density, while the pseudogap seems to be intimate related with the density.(2). Small superconductor grains with different sizes are also investigated by AFQMC method. We found that,1) the superconductor with finite size also has preformed paring phenomenon;2) the superconductivity is less and less obvious with the reduction of the size, and the superconductivity will disappeared down to a certain size.