Dynamical polarization function, plasmons, their damping and collective effects in semi-Dirac bands

We have calculated the dynamical polarization, plasmons and damping rates in semi-Dirac bands (SDB's) with zero band gap and half-linear, half-parabolic low-energy spectrum. The obtained plasmon dispersions are strongly anisotropic and demonstrate some crucial features of both two-dimensional electron gas and graphene. Such gapless energy dispersions lead to a localized area of undamped and low-damped plasmons in a limited range of the frequencies and wave vectors. The calculated plasmon branches demonstrate an increase of their energies for a finite tilting of the band structure and a fixed Fermi level which could be used as a signature of a specific tilted spectrum in a semi-Dirac band.