  Coulomb screening and excitation spectra of electrons in a graphene layer
with spin-orbit interaction (SOI) is studied in the random phase approximation.
The SOI opens a gap between the valence and conduction bands of the semi-metal
Dirac system and reshapes the bottom and top of the bands. As a result, we have
observed a dramatic change in the long-wavelength dielectric function of the
system. An undamped plasmon mode emerges from the inter-band electron-hole
excitation continuum edge and vanishes or merges with a Landau damped mode on
the edge of the intra-band electron-hole continuum. The characteristic
collective excitation of the Dirac gas is recovered in a system with high
carrier density or for a large wave vector.
