Dielectric functions and collective excitations in MgB 2

The frequency- and momentum-dependent dielectric function $\ensuremath{\epsilon}(\mathbf{q},\ensuremath{\omega})$ as well as the energy loss function $\mathrm{Im}[\ensuremath{-}{\ensuremath{\epsilon}}^{\ensuremath{-}1}(\mathbf{q},\ensuremath{\omega})]$ are calculated for intermetallic superconductor ${\mathrm{MgB}}_{2}$ by using two ab initio methods: the plane-wave pseudopotential method and the tight-binding version of the linear muffin-tin orbital method. We find two plasmon modes dispersing at energies $\ensuremath{\sim}2\char21{}8 \mathrm{eV}$ and $\ensuremath{\sim}18\char21{}22 \mathrm{eV}.$ The high energy plasmon results from a free electron like plasmon mode while the low energy collective excitation has its origin in a peculiar character of the band structure. Both plasmon modes demonstrate clearly anisotropic behavior of both the peak position and the peak width. In particular, the low energy collective excitation has practically zero width in the direction perpendicular to boron layers and broadens in other directions.