Sistema bicamada: formação e condensação de Bose-Einstein de éxcitons indiretos

Abstract

In the present contribution, we have studied the so called indirect excitons in bilayer systems. We separate this work into two parts, in the first one we propose a schematic model to study the formation of excitons from electron - hole pairs and in the second one we study microscopic conditions for the formation of a Bose-Einstein condensate from excitons. The proposed schematic model exhibits a phase transition which is signalized both in the quantum and classical versions of the model. In this work we show that not only the quantum ground state but also higher energy states, up to the energy of the correspondingclassical separatrix orbit, "sense" the transition. We also show two types of one-to-one correspondences in this system: On the one hand, between the changes in the degree of entanglement for these low-lying quantum states and the changes in the density of energy levels; on the other hand, between the variation in the expected number of excitons for agiven quantum state and the behavior of the corresponding classical orbit. In the second part, we have studied microscopic conditions for the occurrence of the condensation. We use the coulomb interaction and an educated guess for the ground state for excitons in the bilayer. The interaction induces the formation of excitons as electron-hole pairs. We show that the ideal condition to condensate formation occurs when the momentum difference in the electron and hole which form the exciton is zero. In this situation, the off-diagonal long-range order (ODLRO) terms of the exciton-exciton correlation function go to a constant in the thermodynamic limit. If the momentum diffrence is not zero, the ODLRO terms go to zero and we have, according to this criterium, no exciton condensation.