Superfluidity of a two-component Bose gas of dipolar excitons in a double layer of gapped hexagonal alpha-T3

We present the conditions for Bose-Einstein condensation and superfluidity of a two-component weakly interacting Bose gas of  dipolar excitons, formed by electron-hole pairs in spatially separated gapped hexagonal alpha-T3 (GHAT3) layers. An applied magnetic field to this pseudospin-1 monolayer system results in a Zeeman-type splitting of the energy subbands.   This  dispersion relation consists of three bands: conductivity (CB), intermediate (IB) and valence bands (VB). We consider two types of dipolar excitons  in double-layer of GHAT3: (a)  “A excitons,” which are  bound states of electrons in CB and holes in IB and (b)  “B excitons,” which are bound states  of electrons in CB and holes in VB.  The binding energy of A and B dipolar excitons is calculated. For a two-component  weakly interacting Bose gas of dipolar excitons in a GHAT3 double layer, we obtain the  energy dispersion of collective excitations, two sound velocities for two branches of the collective excitation spectrum, the superfluid density, and the mean-field critical temperature Tc for superfluidity. We found the optimal ranges for the hoping parameter alpha, the gap in the single particle spectrum, the interlayer separation that correspond to higher exciton binding energy, higher Tc, lower critical concentrations of A and B excitons.