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Abstract
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In this work we investigate the effect of relativistic degeneracy on different
properties of low-dimensional quantum plasmas. Using the dielectric response from
the conventional quantum hydrodynamic model, including the quantum diffraction
effect (Bohm potential) on free electrons, we explore the existence of the Shukla–
Eliasson attractive screening and possibility of the ion structure formation in lowdimensional, completely degenerate electron–ion plasmas. A generalized degeneracy
pressure expression for arbitrary relativity parameter in two-dimensional case is
derived, indicating that change in the polytropic index (change in the equation of
state) for the two-dimensional quantum fluid takes place at the electron numberdensity of n0 1.1 × 1020 cm−2 whereas this is known to occur for the threedimensional case in the electron density of n0 5.9 × 1029 cm−3. Also, a generalized
dielectric function valid for all dimensionalities and densities of a degenerate electron
gas is calculated, and distinct properties of electron–ion plasmas, such as static
screening, structure factor and Thomson scattering, are investigated in terms of
plasma dimensionality.
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