Dynamical theory of classical surface plasmas

Abstract

The authors present a self-consistent approximation scheme for the calculation of the dynamical polarizability \ensuremath{\alpha}(k\ensuremath{\rightarrow},\ensuremath{\omega}) and plasmon dispersion at long wavelengths in electron films trapped on the free surface of liquid helium. The principal building blocks to the construction of the approximation scheme are the nonlinear fluctuation-dissipation theorem and linearized equations for the plasma density, fluid velocity, pressure tensor, and heat-flow tensor moments. Equilibrium three-point correlations, quadratic polarizability response functions, and the Navier-Stokes hypothesis linking the pressure tensor to its trace are all central elements in the development of the theory. At frequencies high compared with the collision frequency, the Golden-Lu (GL) formula for \ensuremath{\alpha}(k\ensuremath{\rightarrow},\ensuremath{\omega}) exactly satisfies the ${\ensuremath{\omega}}^{\mathrm{\ensuremath{-}}4}$ moment sum rule. Analysis of ${\ensuremath{\alpha}}_{\mathrm{GL}(\mathrm{k}\ensuremath{\rightarrow}}$,\ensuremath{\omega}) at \ensuremath{\omega}\ensuremath{\simeq}(2\ensuremath{\pi}${\mathrm{ne}}^{2}$k/m${)}^{1/2}$\ensuremath{\gg}${\mathrm{kv}}_{\mathrm{th}}$ leads to the description of the long-wavelength plasmon structure over the range of couping strengths spanning the entire fluid regime. The GL theory predicts that the transition from plasmonlike to longitudinal-phonon-like dispersion occurs at the critical value of the coupling parameter ${\ensuremath{\Gamma}}_{\mathrm{crit}}$=3.22; this transition is inextricably linked to the onset of a ``liquid-state'' short-range order signaled by the development of oscillations in the equilibrium pair correlation function somewhere in the range 2.2\ensuremath{\Gamma}2.9. In the infinite coupling (\ensuremath{\Gamma}\ensuremath{\rightarrow}\ensuremath{\infty}) limit, the GL long-wavelength dispersion relation very nearly reproduces the zero-temperature Bonsall-Maradudin longitudinal-phonon dispersion for the two-dimensional hexagonal lattice.