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We study the density driven symmetry breaking in holographic superconductorsby considering the positive mass squared case. We show that even for thepositive $m^2$, a scalar condensation still forms, provided the chemicalpotential is high enough. As $m^2$ increases, the phase space folds due to thenon-linearity of the equations of motion, and two nearby points in the phasespace can represent symmetry breaking and preserving configurationsrespectively. The phase space defined by the set of initial conditions of fieldvariables at the horizon undergoes a non-linear radial evolution to result inthe phase space folding, a characteristic phenomenon in a non-linear system. Wethen calculate the specific heat, which characterizes superconductors and hasbeen measured in experiments.We observe a discontinuity in the specific heat atthe transition point and compare our results with experimentally observednumbers. The electrical conductivity for various $m^2$ is also calculated.

Density driven symmetry breaking and Butterfly effect in holographic superconductors