Two Band Model Of Superconductivity In Magnesium Diboride

Since the discovery of superconductivity by H.Kamerlingh Onnes in 1911, researches on superconductivity are always a hot problem. Especially, when the discovery of superconductivity of Copper oxide superconductors in 1986, superconductivity studies reached a high level. On January 10th 2001, the superconductivity of MgB₂ system with Tc as high as 39K was discovered by J. Akimitsu et. al.. The discovery of superconductivity in MgB₂ has generated great interest in simple compounds. Investigators all over the world are researching the properties of MgB₂ and the closely related materials by all kinds of modern means.In this dissertation, we study the superconductivity of MgB₂ by introducing non-electron-phonon interaction in pairing potential on the basis of two band model and weak-coupling limit, and the results are consistent with experimental data.In chapter 1, we review briefly the discovery of superconductivity, the history of superconductivity study, the basic characteristics of superconductors, BCS theory and its main conclusions, and two-band model.In chapter 2, we present in detail the results of investigators all over the world on MgB₂ including the isotope eefect, the Hall effect, the pressure effect, the doping effect, the critical magnet, and the superconducting mechanism. We also discuss the meanings of researching MgB₂ and the research of the closely related material. The results indicate that MgB₂ behaves like a conventional BCS superconductor, and its superconductivity can be discussed within the framework of BCS Theory. At the same time, we take notice that the electronic structure and other normal properties of MgB₂ have few specialties compared with other simple compounds with similar latice structure, but it holds the transition temperature as high as 39K, which is much higher than that of other intermetallic compounds; in addition, the experiments show that the total isotope efect exponent is only about 0.3, which deviates from BCS theoretical value 1/2 obviously. All these tell us that MgB₂ is not a conventional BCS superconductor purely, and only electron-phonon coupling mechanism cannot explain its superconductivity efectively, so some non-electron-phonon interaction should be considered. So in chapter 3 and 4, two-band model with non-electron-phonon interaction are used to investigate the superconductivity of MgB₂.In chapter 3, by introducing non-electron-phonon interaction in two-band model, we investigate the superconductivity of MgB₂. We derive the equations of the critical temperature, the isotope effect exponent, the zero temperature gaps and the specific heat jump of MgB₂ superconductor in weak-coupling limit. We calculate these physical quantities with the same parameters supplied by experiments, and all these results are consistent with experimental data.Our investigation shows that the non-electron-phonon interaction plays an important role in the superconductivity of MgB₂.In chapter 4, the equation of the critical temperature and the isotope effect exponent of two-band superconductor MgB₂ in BCS weak-coupling limit are derived by taking the non-electron-phonon interaction into account.We found that the critical temperature T_C=38K and the isotope effect exponentα_B = 0.27 .The results can be compared with experimental data. Furthermore, we pointed out that intraband non-electron-phonon interaction has more important influence on isotope effect than interband non-electron-phonon interaction.In chapter 5, by introducing non-electron-phonon interaction phenomenally in pairing potential, we investigate the isotope effect of superconductivity in which the electron-phonon, non-electron-phonon and screened Coulomb interaction are coexist in weak-coupling limit.The equations of the critical temperature T_C and isotope effect exponent a are derivrd for cases (a)ω_np<ω_D and (b)ω_np>ω_D,whereω_np ,ω_D is an effective cutoff frequency of the non-electron-phonon and electron-phonon interaction respectively. In case (a),it is found that the non-electron-phonon interactionλ_np only modifies the magnitude ofα, but it can not change the sign ofα; whenα< 0 , non-electron-phonon mechanism is dominant in superconductivity. In case (b), it is found that the non-electron-phonon interaction λ_np can change both the magnitude and sign of α; when α < 0 , electron-phonon mechanism is important in superconductivity.