Third-frequency-moment sum rule for electronic multilayers

The authors establish the third-frequency-moment sum rules for the density-density reponse matrix of electronic multilayer structures modeled as an array of N parallel two-dimensional (2D) electron-plasma monolayers. Layer densities and spacings between adjacent layers need not be equal. Contact is made with previously established sum rules for the isolated 2D electron liquid and type-1 infinite superlattices. The case of the equal-density bilayer is considered and its third frequency-moment-sum-rules for the in-phase and out-of-phase inverse dielectric functions are formulated.