This paper shows the effect of the Josephson and bi-quadratic coupling types on the vortex state, the magnetization in a two-band superconducting disk in the presence of an external magnetic field and the effect that the $\gamma$ value has on the vortex state. This study is based on the two bands Ginzburg-Landau time dependent theory, and the main properties are presented via Ab-Initio of MgB${}_2$. The superconducting electron density and the magnetic response of the material are also calculated for several temperatures and we present the state of unconventional vortices for each superconductor band. Finally, it is shown that there is a predominant band in this type material for weak coupling, this is also supported by the ab-initio study.

本文展示了约瑟夫森和双二次耦合类型对涡旋状态的影响，在存在外部磁场的情况下两波段超导盘中的磁化强度以及 $\gamma$值具有涡旋状态。这项研究基于金兹堡-朗道的两个波段随时间变化的理论，其主要性质通过MgB的Ab-Initio给出。${}_2$。还在几个温度下计算了材料的超导电子密度和磁响应，我们给出了每个超导带的非常规涡旋状态。最后，表明在这种类型的材料中存在一个主要带，用于弱耦合，从头算起的研究也支持这一点。