Collective excitations and quantum incompressibility in electron-hole bilayers

TL;DR

This paper uses quantum continuum mechanics and Monte Carlo data to analyze collective excitations in electron-hole bilayers, revealing a gapped, incompressible state linked to excitonic correlations.

Contribution

It introduces a novel application of quantum continuum mechanics combined with Monte Carlo data to predict collective modes and incompressibility in electron-hole bilayers.

Findings

Existence of gapped excitations due to electron-hole correlations

Incompressibility characterized by quadratic vanishing of response function at small q

Predicted discontinuity in chemical potential when electron and hole numbers are equal

Abstract

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.