Hartree-Fock approximation for Exciton Mott transition in double quantum well: Direct and Indirect exciton diamagnetism

Abstract

Semiconductor to Metal transition due to Excitons i.e., Mott Transition (EMT) in GaAs/Al x Ga 1-x As double quantum well has been demonstrated theoretically by observing the abrupt change in diamagnetic susceptibility (χ Dia ) of direct (indirect) excitons at critical concentration. Variation technique combined with Monte-Carlo method is used to calculate Binding Energy (BE) and exciton diamagnetic susceptibility (χ Dia ) by optimizing <H min > by varying the exciton density. To account for many body interaction, Hartree-Fock dielectric screening is used which manipulates the exchange-correlation effects in our observations. The contribution of phonon interaction in the formation of indirect exciton is involved through size dependent screening. Through this work we demonstrate that Exciton Mott Transition, especially semiconductor to metal transition is a type two phase transition which is attributed by the abrupt fall in the diamagnetic susceptibility of excitons. The critical concentration at T = 4 K is estimated for the direct and indirect excitons for various dimensions of the coupled and decoupled wells. • Exciton Mott Transition due to direct and indirect excitons in double quantum well. • Hartree-Fock approximation is adopted for Exciton-Exciton Interaction. • Critical exciton concentration (N ex C ) is estimated for coupled and decoupled wells. • Abrupt fall in Exciton Diamagnetism (χ Dia ) is observed at N ex C . • Transition occurs at lower N ex C in narrow wells due to indirect excitons.