Quantum Phases of Excitons and Their Detections in Electron-Hole Semiconductor Bilayer Systems

There have been extensive experimental search for possible exciton superfluid in semiconductor electron-hole bilayer (EHBL) systems below liquid Helium temperature. Here we construct a quantum Ginsburg-Landau theory to study the quantum phases and transitions in EHBL. We propose that in the dilute limit as distance is increased, there is a first order transition from the excitonic superfluid (ESF) to the excitonic supersolid (ESS) driven by the collapsing of a roton minimum, then a 2nd order transition from the ESS to excitonic normal solid. We show the latter transition is in the same universality class of superfluid to Mott transition in a rigid lattice. We then study novel elementary low energy excitations inside the ESS. We find that there are two “supersolidon” longitudinal modes (one upper branch and one lower branch) inside the ESS, while the transverse mode in the ESS stays the same as that inside a exciton normal solid (ENS). We also work out various experimental signatures of these novel elementary excitations by evaluating the Debye-Waller factor, density-density correlation, specific heat and vortex-vertex interactions. For the meta-stable supersolid generated by photon pumping, we show that several unique features of the photoluminescent can be used to detect the metastable ESS state generated by photon pumping without any ambiguity.