两带模型与二硼化镁的超导电性

【作者】 张宪科；

【导师】 苏希玉；

【作者基本信息】 曲阜师范大学 ， 凝聚态物理， 2007， 硕士

【摘要】 自1911年荷兰物理学家昂尼斯首先发现超导电性以来，超导研究一直是人们关注的热点问题。特别是1986年发现了氧化物高温超导体以后，更是在全世界掀起了超导研究的热潮。2001年1月10日，日本青山学院秋光纯教授宣布二硼化镁材料具有超导电性，超导转变温度高达39K。MgB₂超导电性的发现掀起了对简单化合物超导体研究的热潮。人们使用各种现代化的研究手段，对二硼化镁超导体及相关材料的物理性质进行了重点研究。本论文在弱耦合条件和两带模型的基础上，通过在配对势引入非电声作用，研究了新型超导体MgB₂的超导电性，得到了与实验一致的结果。在第一章，我们简要回顾了超导电性的发现及超导理论发展的历程、超导体的基本性质、BCS理论及其主要结论和两带模型。在第二章，我们详细介绍了世界各国研究人员对二硼化镁超导体研究的成果，其中包括超导体MgB₂的结构、同位素效应、压力影响、霍尔效应、元素替代、临界磁场、超导机制，同时也介绍了研究MgB₂超导体的意义及其它相关化合物的研究。结果表明，MgB₂具有声子媒介超导体的基本特征，可以在BCS理论的框架内讨论它的超导电性。与此同时，我们注意到，与其它具有相似晶格结构的化合物相比，MgB₂并没有什么特殊之处，但它却拥有远高于其它金属间化合物，高达39K的超导转变温度；另外，实验还表明，MgB₂超导体总的同位素效应指数仅为0.3，明显偏离BCS的理论值1／2。所有这些都告诉我们，MgB₂并非一个纯粹的BCS超导体，单纯的电子-声子耦合机制不能很好地解释它的超导电性，还需要考虑到某种非电子-声子相互作用的贡献。于是在第三章和第四章，我们利用考虑了非电子-声子相互作用的两带模型对二硼化镁的超导电性进行了研究。在第三章，我们通过引入非电子-声子相互作用，利用两带模型来解释MgB₂的超导电性，并且使同一组参数分别计算了MgB₂超导体的临界温度、同位素效应指数、零温能隙及比热的跃变，所有计算结果都与实验基本一致。同时也说明，讨论二硼化镁超导电性的时候，考虑到非电子-声子相互作用是必要的。在第四章，我们通过在配对势中引入非电子-声子相互作用，在BCS理论框架下，推导出MgB₂超导体临界温度和同位素效应指数的方程，计算得到MgB₂超导体的临界温度T_c=38K以及同位素效应指数α_B=0.27，这与实验结果是一致的，并且指出带内非电子-声子作用比带间非电子-声子作用对同位素效应的影响要大。在第五章，我们在配对势中唯象地引入非电子-声子作用，在弱耦合条件下研究了电子-声子作用、非电子-声子作用和直接库仑作用共存超导体的同位素效应。在（a）ω_np＜ω_D和（b）ω_np＞ω_D两种情况下，讨论了非电子-声子作用对同位素效应的影响，ω_np和ω_D分别是电声作用和非电声作用的截止频率。结果表明，在情况（a）中非电声作用λ_np只能改变α的大小，而不能改变α的符号，当α＜0时，超导体中非电声机制占统治地位，电声机制处于次要地位；在情况（b）中非电声作用λ_np既能够改变α的大小，又能够改变α的符号，当α＜0时，超导体中电声机制占统治地位，非电声机制处于次要地位。更多还原

【Abstract】 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.更多还原