用G-L理论对二硼化镁超导电性的研究

【作者】 公丕锋；

【导师】 苏希玉；

【作者基本信息】 曲阜师范大学 ， 凝聚态物理， 2006， 硕士

【摘要】 自1911年荷兰物理学家昂尼斯发现超导电性以来,超导研究一直是人们关注的热点问题。特别是1986年发现了高温氧化物超导体以后,在凝聚态物理学界掀起了研究高温超导的热潮。中国在研究高温超导方面也取得了很大的进展。在2001年1月,日本物理学家宣布二硼化镁具有超导电性,而且超导转变温度高达39K。这一发现再次把超导研究推向了高潮。 本论文主要用京兹堡-朗道理论来研究超导体MgB₂的超导电性。在第一章中,我们简要的回顾了超导发展的历程,介绍了BCS理论、京兹堡-朗道理论、G-L方程的解法极其主要结论和二带模型。在第二章中,我们比较详细的介绍了MgB₂超导体正常态和超导态的基本性质,其中包括同位素效应、霍尔效应、压强效应、临界磁场、相干长度、掺杂效应等。研究表明,MgB₂超导体存在两个超导能隙。第一个能隙大约在38.6 K附近,呈现各向异性;第二个能隙大约在12 K附近。由此我们可以用二带模型来描述MgB₂体系的超导特性。在第三章中,通过G-L理论来研究了相干长度ξ（T）、伦敦穿透深度λ（T）以及京兹堡-朗道参量κ（T）=λ（T）/ξ（T）在T_c附近对温度T的依赖关系。理论计算结果与MgB₂样品的实验数据符合的很好。同时与单带G-L理论算出的结果作了对比,对比发现二带G-L理论更能精确描述MgB₂的超导电性,在第四章中,考虑带间相互作用,在弱耦合极限下,得到二带s-波超导体临界温度T_c的公式及同位素效应指数。在这里,耦合相互作用在每一个带中包括两部分:电子-声子相互作用和非电子-声子相互作用,当T_c≈40K时,在弱耦合机制中得到MgB₂的同位素效应指数α=0.3,并且带间电子-声子相互作用比非电子-声子相互作用对同位素效应指数的影响大。更多还原

【Abstract】 Since the discovery of superconductivity by Onnes in 1911, researches on superconductivity are always a hot problem. Especially, since the discovery of high critical temperature cooper oxide superconductors in 1986, superconductivity research reached a high level. In China, superconductivity researches were paid more and more attention. In 2001, the superconductivity of magnesium diboride.In this thesis, we study the superconductivity of magnesium diboride based on the two-band Ginzburg-Landau theory. In chapter 1, we review the history of superconductivity research, G-L theory, G-L equation, BCS theory and its main conclusions, and the two-band model. In chapter 2, we present the properties of the system in both the superconductivity state, such as the isotope effect, the Hall effect, the pressure effect, the critical magnetic field, the coherent length and the doping effect. Theory and experiment results show that there are two energy gaps in the superconductor of magnesium diboride, the larger is near 38.5 K, the smaller is by 12 K. Thus, we think that the superconductivity of magnesium system can be described by a two-band model. In chapter 3, the temperature dependence of the coherent length ζ(T), the penetration depth A(T) and the Ginzburg-Landau parameter k(T) = λ(T) / ζ(T) in the vicinity of critical temperature are studied by using two-band G-L model. The calculation results are in better agreement with the experimental results for magnesium diboride than one-band model. In chapter 4, the exact formula of T_c’s equation and the isotope effect exponent of two-band s-wave superconductors in weak coupling limit are derived by considering the influence of interband interaction and non-electron interaction are included in our model. The isotope effect exponent of magnesium diboride, α = 0.3 with T_c ≈40K can be found in the weak coupling regine andinterband interaction of electron-phonon interaction show more effect on isotope effect exponent than of non-electron-phonon interaction.更多还原