  We explore the behaviors of the holographic superconductors at zero
temperature for a charged scalar field coupled to a Maxwell field in
higher-dimensional AdS soliton spacetime via analytical way. In the probe
limit, we obtain the critical chemical potentials increase linearly as a total
dimension $d$ grows up. We find that the critical exponent for condensation
operator is obtained as 1/2 independently of $d$, and the charge density is
linearly related to the chemical potential near the critical point.
Furthermore, we consider a slightly generalized setup the
Einstein-Power-Maxwell field theory, and find that the critical exponent for
condensation operator is given as $1/(4-2n)$ in terms of a power parameter $n$
of the Power-Maxwell field, and the charge density is proportional to the
chemical potential to the power of $1/(2-n)$.
