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We reexamine the charged AdS domain wall solution to theEinstein-Abelian-Higgs model proposed by Gubser et al as holographicsuperconductors at quantum critical points and comment on their statement aboutthe uniqueness of gravity solutions. We generalize their explorations from 3+1dimensions to arbitrary $n+1$Ds and find that the $n+1\geqslant5$D charged AdSdomain walls are unstable against electric perturbations.

n+1 Dimensional Gravity duals to quantum criticalities with spontaneous symmetry breaking