Collective excitations and quantum incompressibility in electron-hole bilayers

We apply quantum continuum mechanics to the calculation of the excitation spectrum of a coupled electron-hole bilayer. The theory expresses excitation energies in terms of ground-state intra- and inter-layer pair correlation functions, which are available from Quantum Monte Carlo calculations. The final formulas for the collective modes deduced from this approach coincide with the formulas obtained in the quasi-localized particle approximation by Kalman et al., and likewise, the theory predicts the existence of gapped excitations in the charged channels, with the gap arising from electron-hole correlation. An immediate consequence of the gap is that the static density-density response function of the charged channel vanishes as $q^2$ for wave vector $q to 0$, rather than linearly in $q$, as commonly expected. In this sense, the system is {it incompressible}. This feature, which has no analogue in the classical electron-hole plasma, is consistent with the existence of an excitonic ground state and implies the existence of a discontinuity in the chemical potential of electrons and holes when the numbers of electrons and holes are equal. It should be experimentally observable by monitoring the densities of electrons and holes in response to potentials that attempt to change these densities in opposite directions.