Dipolar Magnetoexcitons in α-T₃ double layers in a high magnetic field

We consider two parallel α-T₃ layers separated by an insulating slab (e.g. SiO₂ or a hexagonal boron nitride (h-BN) insulating barrier) in a high magnetic field. The equilibrium system of local pairs of electrons and holes, spatially separated in these parallel α-T₃ layers, correspondingly, can be created by varying the chemical potential using a bias voltage between two α-T₃ layers or between two gates located near the corresponding α-T₃ sheets (case 1) (for simplicity, we also call these equilibrium local e-h pairs as dipolar magnetoexcitons). In case 1 a dipolar magnetoexciton is formed by an electron on the Landau level 1 and hole on the Landau level −1. Dipolar magnetoexcitons with spatially separated electrons and holes can be created also by laser pumping (case 2) and by applying a perpendicular electric field. In case 2, a dipolar magnetoexciton is formed by an electron in the Landau level 1 and hole in the Landau level 0. We assume the system is in a quasi-equilibrium state. We study the collective properties and superfluidity of dipolar excitons in α-T₃ double layers in a high magnetic field for both case 1 and case 2.