  We investigate the microphase separation in a membrane composed of charged
lipid, by taking into account explicitly the electrostatic potential and the
ion densities in the surrounding solvent. While the overall (membrane and
solvent) charge neutrality is assumed, the membrane can have a non-zero net
charge. The static structure factor in the homogeneous state is analytically
obtained without using the Debye-Huckel approximation and is found to have a
peak at an intermediate wave number. For a binary membrane composed of anionic
and neutral lipids, the characteristic wave number corresponds to a scale from
several to tens of nanometers. Our numerical calculation further predicts the
existence of nano-domains in charged membranes.
