Magnesium Diboride Superconductivity

Since the discovery of superconductivity by H. Kamerlingh Onnes in 1911, researches on superconductivity are always a hot problem. Especially, since the discovery of superconductivity of Copper oxide superconductors in 1986, superconductivity studies reached a high level. On January 10th 2001, the superconductivity of MgBa system was discovered by J. Akimitsu et. al., the researches on superconductivity reached a new high level.In this thesis, we study the superconductivity of MgBi system based on the two-band model and a self-consistent method.In chapter 1, we review briefly the history of superconductivity study, BCS theory and its main conclusions, and the two-band superconductivity model. In chapter 2, we present the properties of the system in both the superconducting state and normal state, such as the isotope effect, the hall effect, the pressure effect and the doping effect. Theory results show that superconductor MgBz is a BCS superconductor in substance, but there appear two energy gaps. The first gap is near 38.5K, and the other is by 12K. The relation between the gaps and temperature is close to a BCS like one. Thus, we think the superconductivity of MgB2 system can be described by a two-band superconductivity model. In chapter 3, by introducing the non electron-phonon interaction on the basis of the two-band model, andusing a self-consistent method we solve the gap equation at 7C, and the isotope effect coefficient will be obtained. The obtained results show that the isotope coefficient is close to 0.30 at Tc = 39K, and the value of the non-electron-phonon interaction is about 0.43. In the meantime, we discover the non-electron-phonon interaction plays an important role in enhancing the transition temperature. In chapter 4, we calculate the energy gaps at different temperatures. The ratio andm are derived. Obviously, one ratio is larger than the BCS value , and the other is smaller than that. These results are in agreement with the tunneling experiments. In chapter 5, we discuss the doping properties of the system by introducing the chemical potential on the basis of the two-band model. The relation between superconductivity transition temperature and doping is obtained. The calculated results show that doping may not only decrease but also increase the superconducting transition temperature, and there exists the best doping value at which the superconducting transition temperature may be greatly enhanced.In summary, by introducing the non electron-phonon interaction on the basis of the two-band model ,and using a self-consistent method we discuss the isotope effect, the relation between the gaps and the temperature and the doping effect for MgB2 system. Our results are in agreement with experiments.