Excitonic Condensates

Excitons are composite bosons like atoms, but with a much lighter mass. This should make excitons to a favorable species for condensation processes. However, there are also the residual fermionic interactions of the electron and hole forming the exciton. The resulting screening of the excitonic binding at high densities leads to a Mott transition to a plasma or a liquid phase which is often more favorable than condensation. Also the finite lifetime of excitons typically prohibits a condensation to the bosonic ground state in k-space. We will first describe in this chapter several types of equilibrium bosonic condensates (BCS Insulator, Bose-Einstein condensate BEC, and BKT superfluid) that could in principle form for different preconditions and consider criteria and methods for an experimental proof for the presence of such a condensate. Equilibrium condensates (this excludes optical excitation) are found in semimetals or semiconductors with inverted bandstructure like mono-layer transition metal dichalcogenides. Optical excitation always evokes a non-equilibrium situation but the exciton system can form a quasi-equilibrium phase and (subsequently) even a condensate. One precondition can be a long lifetime of the excitons. A corresponding long-time candidate have been the dipole-forbidden excitons in bulk Cu \(_2\) O. We shortly review the related intense search for a BEC in this material. Condensation occurs in bilayer systems where inter-layer excitons are formed. We show various realizations of such systems and the differing properties of the respective condensates. We then review the results and discussions on condensation of exciton cavity-polaritons. We clarify used nomenclature and point out required criteria for identification of condensation. We highlight the role of bosonic amplification and describe various realizations of so-called polariton lasers. This chapter also introduces the experimental technique shift interferometry.