Superfluidity of dipolar excitons in a double layer of alpha-T3 with a mass term

We predict the Bose-Einstein condensation and superfluidity of dipolar excitons, formed by electron-hole pairs in spatially separated gapped hexagonal α-T3 (GHAT3) layers. The two possible model Hamiltonians of charge carriers in a GHAT3 monolayer include two possible expressions for an effective mass term, which can be generated either (1) by the effective magnetic field or (2) the site energy difference on different sublattices, which has been found in photonic crystals and optical lattices. This effective mass term opens a gap between the valence and conduction bands. We calculate the binding energy for a single dipolar exciton in a GHAT3 double layer for both Hamiltonians (1) and (2). For a weakly interacting Bose gas of dipolar excitons in a GHAT3 double layer, we obtain the energy dispersion of collective excitations, the sound velocity, the superfluid density, and the temperature of the Kosterlitz-Thouless (KT) phase transition. We compare the exciton binding energies and KT temperatures for both mechanisms of the gap opening to predict which mechanism will result in the formation of more stable excitons and the creation of the superfluid at higher temperatures at the same interlayer separations and exciton concentrations.