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We have theoretically investigated the spin- and valley-dependentsuperfluidity properties of indirect momentum space dark dipolar excitons indouble layers with massive anisotropic tilted semi-Dirac bands in the presenceof circularly polarized irradiation. An external vertical electric field isalso applied to the structure and is responsible for tilting and gap openingfor the band structure. For our calculations we used the parameters of a doublelayer of 1T$^\prime$-MoS$_2$. Closed form analytical expressions are presentedfor the energy spectrum for excitons, their associated wave functions andbinding energies. Additionally, we examine the effects which the intensity andfrequency of circularly polarized irradiation has for 1T$^\prime$-MoS$_2$ onthe effective mass of the excitons since it has been demonstrated that theapplication of an external high-frequency dressing field tailors the crucialelectronic including the exciton binding energy, as well as the criticaltemperature for superfluidity. We also calculate the sound velocity in theanisotropic weakly-interacting Bose gas of two-component indirect momentumspace dark excitons for a double layer of 1T$^\prime$-MoS$_2$. We show that thecritical velocity of superfluidity, the spectrum of collective excitations,concentrations of the superfluid and normal component, and mean field criticaltemperature for superfluidity are anisotropic and formed by a two-componentsystem. The critical temperature for superfluidity is increased when theexciton concentration and interlayer separation are increased. We propose theuse of phonon-assisted photoluminescence to experimentally confirm directionalsuperfluidity of indirect momentum space dark excitons in a double layer withmassive anisotropic tilted semi-Dirac bands.

Superfluidity of indirect momentum space dark dipolar excitons in a double layer with massive anisotropic tilted semi-Dirac bands