UC Berkeley

Understanding the interactions of excitons has been central to the development of technolo-gies such as solar cells and light-emitting diodes. To improve quantum yields and design materials with desired optoelectronic properties, researchers require an understanding of how multiple electron-hole pairs interact. From a fundamental perspective, excitons display rich phase behavior; as composite bosons, they can support both Bose-Einstein condensation as well as quantum Fermi liquids such as Keldysh’s electron-hole liquid. Additionally, since they are analogous to hydrogen atoms, excitons can form molecules in the form of biexcitons and ions in the form of trions. Recent studies on the interactions and phase behavior of excitons have considered indi- rect excitons whose constituents are constrained to reside in distinct planes separated by a distance d. By separating the electrons from the holes, both radiative and non-radiative recombination lifetimes are extended by orders of magnitude, making it easier to study and probe their equilibrium phase behavior. Additionally, indirect excitons possess permanent electric dipole moments, introducing a repulsion between particles. This interaction inhibits the formation of biexcitons and provides more favorable conditions for Bose-Einstein con- densation. Furthermore, there is experimental and theoretical evidence for new emergent phases not previously observed when considering spatially-direct excitons, such as a classical liquid of individual excitons. In this dissertation, we use a broad range of theoretical techniques to study the phase be- havior of indirect excitons. First, we examine the interaction between two indirect excitons using diffusion Monte Carlo, finding long-range dipole-dipole repulsion in addition to short- range attraction for relatively small d. In order to study the effects of introducing a third exciton, we construct basis sets for indirect excitons and apply the full configuration inter- action method, typically used for three-dimensional electronic systems. For very small d, 2 the lowest energy state of the triexciton is a weakly-bound exciton-biexciton van der Waals complex. Because the three-body potential is so weak and not pair-wise decomposable, we find no evidence for a driving force towards the classical condensation of indirect excitons. In order to explain recent observations of a condensed phase of indirect excitons, we consider Keldysh’s electron-hole liquid in a bilayer geometry. Working within the random-phase approximation, we calculate the ground state energy of a dense degenerate phase of unbound carriers, finding good agreement with experimental measurements. Taking the Green’s- function approach to finite temperatures, we evaluate free energies for electrons and holes in a bilayer geometry using the linked-cluster expansion. By solving the law of mass action, we investigate how the exciton Mott transition from bound excitons to free carriers varies with d. Finally, using Maxwell equal-area constructions, we map the quantum liquid-gas phase diagram in the plane of temperature and total carrier density. These diagrams are in close agreement with the aforementioned experimental observations.