We show that in presence of an applied external field the two-component order parameter superconductor falls in two categories of ground states, namely, in the traditional Abrikosov ground state or in a new ground state fitted to describe a superconducting layer with texture, that is, patched regions separated by a phase difference of $pi$. The existence of these two kinds of ground states follows from the sole assumption that the total supercurrent is the sum of the two individual supercurrents and is independent of any consideration about the free energy expansion. Uniquely defined relations between the current density and the superfluid density hold for these two ground states, which also determine the magnetization in terms of average values of the order parameters. Because these ground state conditions are also Bogomolny equations we construct the free energy for the two-component superconductor which admits the Bogomolny solution at a special coupling value.
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