  We analyze via theoretical approaches and molecular dynamics simulations the
collective mode structure of strongly coupled two-dimensional binary Yukawa
systems, for selected density, mass and charge ratios, both in the liquid and
crystalline solid phases. Theoretically, the liquid phase is described through
the Quasi-Localized Charge Approximation (QLCA) approach, while in the
crystalline phase we study the centered honeycomb and the staggered rectangular
crystal structures through the standard harmonic phonon approximation. We
identify "longitudinal" and "transverse" acoustic and optic modes and find that
the longitudinal acoustic mode evolves from its weakly coupled counterpart in a
discontinuous non-perturbative fashion. The low frequency acoustic excitations
are governed by the oscillation frequency of the average atom, while the high
frequency optic excitation frequencies are related to the Einstein frequencies
of the systems.
