Response function and plasmon dispersion for strongly coupled Coulomb liquids: Two-dimensional electron liquid

We employ the recently established formalism for the calculation of the dielectric response function for strongly coupled Coulomb liquids to obtain the dispersion of the plasmon mode in a two-dimensional one-component plasma in the strong-coupling domain. This formalism is based on the physical picture of particles being quasilocalized at strong coupling. The analytical and numerical calculations are carried out over a range of liquid-state coupling parameters up to Γ=${\mathit{e}}^2$ √πn /${\mathit{k}}_{\mathit{B}}$T=120 and for arbitrary wave numbers. When the slow thermal migration of the quasisites (around which the particles are localized) is neglected, the plasmon dispersion is oscillatory and the oscillations become more pronounced with increasing Γ. When the coupling is very strong (Γ=120, e.g.), the distance to the first minimum in ω(k) and the spacing between successive minima approaches ${\mathit{K}}_0$=3.3/a, the lattice spacing in the reciprocal lattice. The ‘‘direct’’ thermal effects due to the slow migration are represented by a phenomenological modification of the dielectric function. This modification leaves the plasmon dispersion almost entirely unaffected up to ka≊1. For ka>1, however, changes in the dispersion due to the direct thermal motion are as follows: (i) the dispersion is no longer oscillatory; ω(k) rises from zero to a maximum and then cuts off beyond that at a value k=${\mathit{k}}_{\max }$(Γ), which approaches an asymptotic limit ${\mathit{k}}_{\max }$(${\mathrm{\Gamma }}_{\mathit{m}}$) close to ${\mathit{K}}_0$ as Γ approaches ${\mathrm{\Gamma }}_{\mathit{m}}$=137±15; (ii) the plasmon frequency is increased especially at the lower coupling values where one expects the thermal motion to play a more significant role; (iii) the dispersion exhibits two branches: the upper branch corresponds to the plasmon mode and the heavily damped lower soundlike branch is already identified in random-phase-approximation calculations.