Transverse dielectric matrix and shear mode dispersion in strongly coupled electronic bilayer liquids

The authors develop a transverse dielectric matrix and from it they calculate the shear mode dispersion in strongly coupled charged-particle bilayer liquids in the T=0 quantum domain. The formulation is based on the classical quasilocalized charge approximation (QLCA) and extends the QLCA formalism into the quantum domain. Its development parallels and complements the development of a similarly extended longitudinal dielectric matrix formalism reported in a recent companion work [K. I. Golden, H. Mahassen, G. J. Kalman, G. Senatore, and F. Rapisarda, Phys. Rev. E 71, 036401 (2005)]. Using pair correlation function data generated from diffusion Monte Carlo simulations, the authors calculate the dispersion of the in-phase and out-of-phase shear modes over a wide range of high-r(s) values and layer separations. Over the coupling range 10 <= r(s)<= 30 and for layer separations 0.2/root pi n <= d <= 0.5 root pi n, the present study predicts the existence of a robust out-of-phase gapped shear mode dispersion in the domain of the q,omega-plane above the left boundary of the RPA single-pair excitation region; under these conditions, the out-of-phase collective excitation is entirely immune to Landau damping and can be safely considered to be mostly unaffected by diffusive-migrational damping.