  We analytically study the critical phase of a mixed system of the U(2) gauge
fields and global symmetry on the boundary using gauge/gravity. A variational
minimization problem has been formulated. The numerical results pertinently
show that there exists a minimum chemical potential in which both scalar
(s-wave) and vector (p-wave) condensates exist in a mixture, as well as in the
distinct s- and p-phases. This result is obtained by breaking the symmetry into
U(1) symmetry and rotational symmetry. While the analytical solutions of
condensates and charge densities are achieved in both cases: the balanced and
unbalanced holographic superconductors. This is the first an- alytical study of
the coexistence of two modes of the superconductivity with different order
parameters. The realistic model consists of two different phases of the
superfluidity in Helium.

High Energy Physics - Theory