  Spin-orbit-coupled two-dimensional electron gases (2DEGs) are a textbook
example of helical Fermi liquids, i.e. quantum liquids in which spin (or
pseudospin) and momentum degrees-of-freedom at the Fermi surface have a
well-defined correlation. Here we study the long-wavelength plasmon dispersion
and the Drude weight of archetypical spin-orbit-coupled 2DEGs. We first show
that these measurable quantities are sensitive to electron-electron
interactions due to broken Galileian invariance and then discuss in detail why
the popular random phase approximation is not capable of describing the
collective dynamics of these systems even at very long wavelengths. This work
is focussed on presenting approximate microscopic calculations of these
quantities based on the minimal theoretical scheme that captures the basic
physics correctly, i.e. the time-dependent Hartree-Fock approximation. We find
that interactions enhance the "plasmon mass" and suppress the Drude weight. Our
findings can be tested by inelastic light scattering, electron energy loss, and
far-infrared optical-absorption measurements.
