Optical and Collective Properties of Excitons in 2D Semiconductors

We study the properties of excitons in 2D semiconductors (2DSC) by numerically solving the Schr\ {o}dinger equation for an interacting electron and hole in the effective mass approximation, then calculating optical properties such as the transition energies, oscillator strengths, and absorption coefficients. Our theoretical approach allows us to consider both direct excitons in monolayer (ML) 2DSC and spatially indirect excitons in heterostructures (HS) consisting of two 2DSC MLs separated by few-layer insulating hexagonal boron nitride (h-BN). In particular, we study indirect excitons in TMDC HS, namely MoS2, MoSe2, WS2, and WSe2; both direct and indirect excitons in the buckled 2D allotropes of silicon, germanium, and tin, known as silicene, germanene, and stanene respectively, or collectively as the Xenes; and both direct and indirect excitons in the anisotropic 2DSC phosphorene, the 2D allotrope of black phosphorus. Our study of indirect excitons in TMDC/h-BN HS was one of the first to study the dependence of the properties of spatially indirect excitons in 2DSC HS with respect to the interlayer separation. When considering excitons in the Xenes, we focused on the dependence of the excitonic properties on the magnitude of an external electric field oriented perpendicular to the Xene monolayer(s), which can be used to tune the band gap of the Xenes in-situ, thereby changing the charge carrier effective mass and thus the properties of the excitons themselves. Interestingly, our results for excitons in the Xenes indicate that freestanding ML Xenes may in fact be excitonic insulators in their ground states, that is, when there is zero external electric field. Furthermore, we predict, based on our results, that the freestanding ML Xenes should undergo a phase transition from the excitonic insulator state to a semiconducting state as the external electric field is increased beyond some critical value which is unique to each material. Lastly, our results show that the anisotropic exciton reduced mass, inherited from the anisotropic effective masses of electrons and holes in phosphorene, causes significant deviations in the eigenstates compared to the isotropic 2D model used for TMDCs and Xenes, and that furthermore, this anisotropy leads to enhanced (suppressed) optical absorption compared to the isotropic exciton, under linearly polarized excitations along the in-plane crystal axes with relatively smaller (larger) charge carrier effective masses. In addition, we were able to extend our theoretical framework to consider both exciton-photon and exciton-exciton interactions in a weakly interacting Bose gas of excitons, thereby allowing for the study of exciton-polaritons in an optical microcavity. Using this extended framework, we calculate the Rabi splitting between upper and lower polaritons in a model microcavity, as well as the critical temperature for the Berezinskii-Kosterlitz-Thouless (BKT) phase transition of a weakly interacting Bose gas of lower polaritons. In particular, we applied these methods to study polaritons in the ML Xenes, once again focusing on the dependence of these quantities on the magnitude of the external electric field. Based on our calculations, we predict that, assuming a particular type of open microcavity which maximizes the exciton-photon interaction strength, both freestanding ML silicene and ML silicene encapsulated by h-BN should support polaritons with relatively large Rabi splittings whose BKT critical temperature is greater than room temperature, such that it should be possible to achieve room-temperature superfluidity of polaritons in these materials for a particular range of values of the external electric field