Due to the Coulomb interaction exciton eignestates in monolayer transitional metal dichalcogenides are coherent superposition of two valleys. The exciton band which couples to the transverse electric mode of light has parabolic dispersion for the center of mass momentum, whereas the one which couples to the transverse magnetic mode has both parabolic and linear components. In this work we present an experimental proposal to observe the signatures of linear component of the dispersion. In particular, it is demonstrated that by pumping the system with linearly polarized light the exciton transport is anisotropic compared to circularly polarized pump. We show that the results persist for moderate level of disorder present in realistic systems. Finally, we demonstrate that similar effects can be obtained for positively detuned exciton-polaritons, in less stringent experimental requirements compared to bare exciton case.
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