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Strong Coulomb interactions in 2D materials results in a wide variety of correlated many body states. In this talk we present optical spectroscopy results and theoretical results on strongly correlated electron states in Landau levels in bi-layer graphene and on trions and trion-polaritons in transition metal dichalcogenides. Our results show a rich variety of features exhibited by these correlated states in 2D materials. In the case of Landau levels, we observe valley-dependent optical transitions that violate the conventional optical selection rules. At low magnetic fields, the oscillator strengths of forbidden transitions are as large as those of the allowed transitions. Moreover, we can tune the relative oscillator strength by tuning the bandgap of bilayer graphene. Our findings provide new insights into the interplay between magnetic field, band structure and many-body interactions in tunable semiconductor systems, and the experimental technique paves the way to studying symmetry-broken states and low energy magneto-optical properties of novel materials. In the case of trions and trion-polaritons, despite the nomenclature, our results show that the actual quantum states are many body states involving at least four or five particles. A trion state in n-doped 2D materials consists of two electrons, one valence band hole, and one conduction band hole. The conduction band hole is weakly bound to the other three particles. However, inside an optical microcavity the hole becomes strongly bound to the other three particles because of strong light-matter interaction. Our results shed new light on the nature of trions and trion-polaritons in 2D materials. We will discuss the connections of our models with the recently proposed exciton-polaron picture of trions.
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