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Microscopic derivation of two-component Ginzburg-Landau model and conditions of its applicability in two-band systems

We report a microscopic derivation of two-component Ginzburg-Landau (GL) field theory and the conditions of its validity in two-band superconductors. We also investigate the conditions when microscopically derived or phenomenological GL models fail and one should resort to a microscopic description. We show that besides being directly applicable at elevated temperatures, a version of a minimal two-component GL theory in certain cases also gives accurate description of certain aspects of a two-band system even substantially far from $T_c$. This shows that two-component GL model can be used for addressing a wide range of questions in multiband systems, in particular vortex physics and magnetic response. We also argue that single Ginzburg-Landau parameter cannot in general characterize magnetic response of multiband systems.