  We study the electronic properties of dual-gated electron-hole bilayers in
which the two layers are separated by a perfectly opaque tunnel barrier.
Combining an electrostatic and thermodynamic analysis with mean-field theory
estimates of interacting system chemical potentials, we explain the dependence
of the electron and hole densities on the two gate voltages. Because chemical
potential jumps occur for both electrons and holes at neutrality, there is a
finite area in gate voltage parameter space over which electron and hole
densities are equal. In that regime the electron-hole pair density depends only
on the sum of the two gate voltages. We are able to explain a recent
experimental study of electrically controlled bilayers by allowing for
interlayer tunneling and using a non-equilibrium steady-state transport
picture.
