多带超导体的表面临界磁场和穿透深度随温度的变化具有一系列的特点，引起实验和理论研究者很多兴趣。研究表明，通过对表面临界磁场和穿透深度的研究，可以知道多带超导体的能隙特点，因此开展对表面临界磁场和穿透深度的研究是很有意义的。唯象的GL理论模型简单、易于理解、计算量小、参数的物理意义明确，因此在研究第II类超导体时，唯象的GL理论是最常用的理论。但是到目前为止，用唯像的三带GL理论研究多带超导体表面临界磁场和穿透深度的文献还尚未见报导。本项目就以此为选题，用三带GL理论研究多带超导体的表面临界磁场和穿透深度，用变分法获得表面临界磁场和穿透深度的相图，研究GL方程中参数对多带超导体电磁性质的影响，讨论改善多带超导体电磁性质的方法，揭示多带超导体的超导机理，解释实验现象，希望对以后的实验工作具有一定的指导作用。

The depending of the surface critical field and the penetration depth of the multi-band superconductors on the temperature has a series of characteristics, which caused by the experimental and theoretical researchers a lot of interest. Research shows that, through the research on the surface critical field and the penetration depth , can know the multi-band superconductor gap characteristics. Therefore the research on the surface critical field and the penetration depth is great significance. For the II type superconductors the phenomenological GL theory is the most commonly used theory, because that the model is simple and easy to understand, the calculation amount is small and the physical meaning of the parameters in GL model is clear. The research on the surface critical field and the penetration depth of multi-band superconductor with the three-band GL theory has not been reported. This project just research on this topic, obtains the phase diagram of the surface critical field and the penetration depth using the variational method, studies the influence of the parameters in GL equation on the electromagnetic properties of multi-band superconductor, discusses the improvement of multi-band superconductor electromagnetic properties method, reveals the mechanism of superconductivity of the multi-band superconductor, explains the experimental phenomena. And we hope that this work has certain direct effect on the experimental work in the future.