  We study a minimally coupled charged scalar field in a charged Lifshitz
background. For z=2, we find an analytic expression for the corresponding low
energy retarded Green's function. Unlike the RN-AdS case, the position of the
superfluid surfaces depends on the charge of the scalar field only through the
IR scaling dimension. We show that by increasing the dynamical exponent, the
dual theory becomes more stable. We also show that the background could suffer
from an instability of the IR geometry leading to a bifurcating critical point.
It also allows the existence of scalar hair, causing hybridized critical point.
We have investigated stable an unstable regions in the parameter space.
