Abstract
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 an accurate description of certain aspects of a two-band system, even substantially far from ${T}_{c}$. This shows that a 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 a single Ginzburg-Landau parameter cannot in general characterize the magnetic response of multiband systems.
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