We present detailed calculations for several significant properties of the kagome lattice in the presence of irradiation. We employ the Floquet-Magnus perturbation expansion to obtain the energy bands and the corresponding wave functions near the Dirac points for the kagome lattice in the presence of circularly or linearly polarized irradiation. In contrast with linearly polarized irradiation, for which the energy bands do not get modified, a band gap is opened up near the Dirac points, between the valence and conduction bands in the presence of circularly polarized irradiation. We calculated the exciton binding energy and the exciton energy for gapped kagome lattice as a function of the frequency and intensity of the irradiation. We compare the exciton binding energy and exciton energy in a monolayer with those in a double layer consisting of electrons in one layer and holes in a parallel layer, separated by an insulator to inhibit recombination. We predict that a phase transition in the kagome lattice from the semiconducting phase to the excitonic insulating phase can be induced by applying circularly polarized irradiation. We examine the conditions for such a phase transition. Superfluidity of dipolar excitons was investigated, as well as the collective properties of the kagome lattice by calculating the sum of ladder diagrams for the vertex, describing the dipole-dipole repulsion between excitons. We propose observation of Bose-Einstein condensation and superfluidity of quasi-two-dimensional dipolar excitons in two-layer kagome lattices in the presence of pumping by circularly polarized light. The energy spectrum of collective excitations and the sound velocity, as well as the effective mass of dipolar excitons, are obtained in the regime of pumping by circularly polarized light. The superfluid density $n_s$ and the temperature of the Kosterlitz-Thouless phase transition $T_c$ are shown to be monotonic increasing functions of the excitonic density $n$ and the interlayer separation $D$. We have also analyzed the dependence of superfluid density $n_s$ and the Kosterlitz-Thouless phase transition temperature on the parameters of circularly polarized light. We explore opportunities to tune exciton binding energy, the spectrum of collective excitations, and the critical temperature of superfluidity by applying circularly polarized irradiation.

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• Excitons
• Flat bands
• Superfluidity
• 2-dimensional systems
• Two-dimensional electron system
• Critical phenomena
• Effective mass theory
• Tight-binding model