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Weakly damped acoustic plasmon mode in transition metal dichalcogenides with Zeeman splitting

We analyze the effect of a strong Zeeman field on the spectrum of collective excitations of monolayer transition metal dichalcogenides. The combination of the Dresselhaus type spin orbit coupling and an external Zeeman field result in the lifting of the valley degeneracy in the valence band of these crystals. We show that this lifting of the valley degeneracy manifests in the appearance of an additional plasmon mode with linear in wavenumber dispersion along with the standard square root in wavenumber mode. Despite this novel mode being subject to the Landau damping, it corresponds to a well defined quasiparticle peak in the spectral function of the electron gas.