  Holographic superconductor model represents various inhomogeneous solutions
with homogeneous sources. In this paper, we study inhomogeneous structures in
the presence of the homogeneous current and chemical potential. We find single
complex kink condensates, multiple-kink condensates and twisted kink crystal
condensates in which both the amplitude and the phase of the order parameter
modulates in space. Analyzing the gauge-invariant phase difference in the
single complex kink condensates, we find that it can be non-monotonic with
respect to the current. We also analyze the thermodynamic stability of the
single complex kink condensate by computing the free energy.
