Impurity effect and vortex cluster phase in mesoscopic type-1.5 superconductors

Based on two-band time-dependent Ginzburg-Landau theory, we study the electromagnetic properties of two-band mesoscopic superconductors. We perform the numerical simulations with the finite element method, and determine the minimum sample size L_c <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> for the existence of the type-1.5 superconductivity from the obtained phase diagram in the absence of impurity. Meanwhile in the presence of an isotropic impurity, our numerical results reveal that the vortex cluster state induced by the attractive defect potential will gradually appear in the mesoscopic system with the sample size L &lt; L_c <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>L</mml:mi> <mml:mo>&lt;</mml:mo> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:mrow> </mml:math> , and the critical defect strength is about 0.2 in the T_c <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> disorder model. In addition, we also investigate the effect of anisotropic defect structures and multiple correlated disorders on the patterns of magnetic vortex distributions. Our theoretical study thus indicates that the diversity of impurity depositions has a significant influence on the semi-Meissner state in mesoscopic type-1.5 superconductors.