  We prove that the predicted charge transfer state in symmetric bilayers of
two dimensional electron gases is always unstable at zero bias voltage, due to
interlayer correlation and/or tunneling. This is most easily seen by resorting
to a pseudospin formalism and considering coherent states obtained from the
charge transfer state through rotations of the pseudospins. Evidently, the
charge transfer state is stabilized by a sufficiently strong gate voltage, as
found in recent experiments. We show that a simple model, in which the layers
are strictly two dimensional, is able to account quantitatively for such
experimental findings, when correlation is properly included.
