The existence and time evolution of charge separation at a plasma edge is studied using a code in which both ions and electrons are described by gyrokinetic equations that include the finite-Larmor-radius correction and the polarization drift. The ion finite-Larmor-radius effect allows the existence of charge separation between ions and electrons, and the polarization drift, which has opposite signs for ions and electrons, has a tendency to accentuate the charge separation in a time-varying electric field. We compare our results with those previously obtained using a code in which the ions were described by using a fluid guiding-centre model, and only the electrons were treated kinetically. In particular, we present results showing excellent agreement between the two codes on the transition of the spectrum of the nonlinear solution from a turbulent spectrum to one dominated by the fundamental mode, where the energy is condensing in the lowest-k modes (inverse cascade).