  We investigate the holographic description of a superconductor constructed in
the (2+1)-dimensional AdS soliton background in the probe limit. We study the
holographic properties through both analytical and numerical methods. With
analytical methods, we are the first to obtain the exact formula for critical
phase transition points as $\mu_{c}=1+\sqrt{1+m^2}$. Around the transition
points, we find a correspondence between the value of the scalar field at the
tip and the scalar operator at infinity. We also generalize the front
properties to holographic models in higher dimensional AdS soliton spacetime.
Moreover, we examine effects of the scalar mass on stability of phase
transitions with numerical methods. With $m^{2}\in (-0.38,0]$, we arrive at the
classical second order insulator/superconductor phase transition. Surprisingly,
there is no stable superconducting phases in cases of $m^{2}\in (-1,-0.38]$. In
other words, superconductor only exists in a certain range of the scalar mass
in the (2+1)-dimensional AdS soliton spacetime, which is very different from
properties in other spacetime.
