Dynamical polarization function, anisotropic plasmon modes, and dephasing rates for interacting electrons in semi-Dirac bands

We have investigated the dynamical polarizability, plasmon dispersion relations, and dephasing in semi-Dirac energy bands. These structures demonstrate zero band gap and a half-linear, half-parabolic low-energy spectrum. We have performed rigorous numerical calculations and discovered some unusual plasmonic and collective properties in these materials. The obtained plasmon dispersion relations are strongly anisotropic and exhibit mixed features associated with both a two-dimensional electron gas and graphene in each specified direction. Such gapless energy dispersions lead to an isolated region for undamped or weakly Landau damped plasmon modes within a limited frequency-wave vector region. With finite tilting, we find two peaks in the polarization function. One plasmon mode is undamped while the other is strongly Landau damped. This feature can be utilized as an indicator for specifying a unique tilted plasmon spectrum from semi-Dirac bands. Additionally, we have presented our calculated density of states for tilted semi-Dirac bands and demonstrated how it could be employed in developing a qualitative model for generating a plasmon spectrum of these materials.