The theory for spontaneous coherence of short-lived quasiparticles in two-dimensional excitonic systems is reviewed, in particular, quantum wells (QWs) and graphene layers (GLs) embedded in microcavities. Experiments with polaritons in an optical microcavity have already shown evidence of Bose-Einstein condensation (BEC) in the lowest quantum state in a harmonic trap. The theory of BEC and superfluidity of the microcavity excitonic polaritons in a harmonic potential trap is presented. Along the way, we determine a general method for defining the superfluid fraction in a two-dimensional trap, within the angular momentum representation. We discuss BEC of magnetoexcitonic polaritons (magnetopolaritons) in a QW and GL embedded in an optical microcavity in high magnetic field. It is shown that Rabi splitting in graphene is tunable by the external magnetic field B, while in a QW the Rabi splitting does not depend on the magnetic field in the strong B limit.
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