Vortices in a superconducting two-band disk: Role of the Josephson and bi-quadratic coupling

•Ab inition and two bands GL model.•Found a novel and interesting behavior in the order parameter.•Two component superconductor and Cooper and Josephson coupling.•Magnetic response. 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 γ 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 MgB2. 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.