  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.
