Plasmon mass and Drude weight in strongly spin-orbit-coupled two-dimensional electron gases

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 Galilean 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 focused 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.