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Abstract
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In this paper, by using a quantum hydrodynamic plasma model which incorporates the important
quantum statistical pressure and electron diffraction force, we the corrected plasmon
dispersion relation for graphene which includes a k4 quantum term arising from the collective electron
density wave interference effects. This correction may well describe the shortcoming of the previous
results based on the classical hydrodynamics and confirms that the quantum hydrodynamic model
may be as effective as the random phase approximation in successful description of the collective
density excitations in quantum plasmas. It is clearly observed that the quantum correction due to the
collective interaction of electron waves gives rise to significant contribution in the dispersion behavior
of the collective plasmon density waves in a wide range of wavelength, as a fundamental property of
the monolayer atom-thick graphene. It is revealed that the plasmon density-perturbation linear
phase-speed in graphene possesses some universal minimum characteristic value, in the absence of an
external magnetic field. It is further remarked that such correction also has important effect on the
dielectric function, hence on the impurity screening, in graphene.
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