Third-frequency-moment sum rule and long-wavelength plasmon dispersion in layered electron liquids

Abstract

We derive the third-frequency-moment (${\mathrm{\ensuremath{\omega}}}^{3}$) sum rule and exact high-frequency dielectric response function for the layered electron liquid in zero magnetic field. The latter is examined in the kd\ensuremath{\rightarrow}0 and kd\ensuremath{\rightarrow}\ensuremath{\infty} limits characteristic of bulk behavior and two-dimensional (2D) single-layer behavior, respectively (k is the 2D wave number, d is the distance between any two adjacent layers). We incorporate the correlational part of the ${\mathrm{\ensuremath{\omega}}}^{3}$ sum rule into a mean-field-theory description of the long-wavelength dispersion of the in-phase and out-of-phase plasmon modes in the presence of very strong correlations.