Dielectric tensor and shear-mode dispersion for strongly coupled Coulomb liquids: Two-dimensional electron liquid

Similar to the three-dimensional (3D) one-component plasma (OCP), a two-dimensional (2D) OCP (electron film on the surface of liquid He, e.g.) can support transverse shear waves. We adapt the quasilocalized charge formalism of the preceding paper [Golden, Kalman, and Wyns, Phys. Rev. A 46, 3454 (1992)] to the analysis of the 2D transverse dielectric-response function and identify the shear mode, whose existence is unique to the strongly coupled system. We study the dispersion of the shear mode in the 22${\mathit{e}}^2$/${\mathit{ak}}_{\mathit{B}}$T, a is the 2D Wigner-Seitz radius) and compare it with the results of the molecular-dynamics simulations of Totsuji and Kakeya [Phys. Rev. A 22, 1220 (1980)]. Agreement between the theory and simulation results is quite satisfactory. We also establish the correspondence between the shear mode of the strongly coupled 2D OCP and the acoustic phonons of the 2D Wigner crystal.