  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.
