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Abstract
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In this paper the quantum counter-streaming instability problem is studied in planar twodimensional (2D) quantum plasmas using the coupled quantum hydrodynamic (CQHD) model
which incorporates the most important quantum features such as the statistical Fermi-Dirac
electron pressure, the electron-exchange potential and the quantum diffraction effect. The
instability is investigated for different 2D quantum electron systems using the dynamics of
Coulomb-coupled carriers on each plasma sheet when these plasmas are both monolayer doped
graphene or metalfilm (corresponding to 2D Dirac or Fermi electron fluids). It is revealed that
there are fundamental differences between these two cases regarding the effects of Bohmʼs
quantum potential and the electron-exchange on the instability criteria. These differences mark
yet another interesting feature of the effect of the energy band dispersion of Dirac electrons in
graphene. Moreover, the effects of plasma number-density and coupling parameter on the
instability criteria are shown to be significant. This study is most relevant to low dimensional
graphene-based field-effect-transistor (FET) devices. The current study helps in understanding
the collective interactions of the low-dimensional coupled ballistic conductors and the
nanofabrication of future graphene-based integrated circuits.
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