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Abstract: The one-loop polarization function of graphene has been calculated at zerotemperature for arbitrary wavevector, frequency, chemical potential doping,and band gap. The result is expressed in terms of elementary functions and isused to find the dispersion of the plasmon mode and the static screening withinthe random phase approximation. At long wavelengths the usual square rootbehaviour of plasmon spectra for two-dimensional 2D systems is obtained. Thepresence of a small compared to a chemical potential gap leads to theappearance of a new undamped plasmon mode. At greater values of the gap thismode merges with the long-wavelength one, and vanishes when the Fermi levelenters the gap. The screening of charged impurities at large distances differsfrom that in gapless graphene by slower decay of Friedel oscillations $1-r^2$instead of $1-r^3$, similarly to conventional 2D systems.



Author: P.K. Pyatkovskiy

Source: https://arxiv.org/







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