Two-band superconducting square with a central defect: role of the deGennes extrapolation length

We present the influence of the deGennes extrapolation length on the vortex matter in a two band superconducting square with a central defect. This is determined by considering different values of the de Gennes extrapolation length b on the lateral surface of the sample. Our investigation was carried out by solving the two-dimensional time-dependent Ginzburg-Landau equations for a two-band system (2B-TDGL). We studied the density, magnetization, vorticity, and critical fields of the superconducting electrons as functions of the external applied magnetic field for different values of b on the surfaces of the sample and different sizes of the internal square defect. We show an unconventional vortex state due to the repulsive (attractive) short- (long-) range potential between the vortices. Finally, we show that at the limit of the thin film, a two-band system behaves like a three-band system. Graphical abstract