We present ab initio time-dependent density-functional theory calculation results for low-energy collective electron excitations in ${\text{MgB}}_2$. The existence of a long-lived collective excitation corresponding to coherent charge density fluctuations between the boron $\sigma$ and $\pi$ bands ($\sigma \pi$ mode) is demonstrated. This mode has a sine-like oscillating dispersion for energies below 0.5 eV. At even lower energy we find another collective mode ($\sigma \sigma$ mode). We show the strong impact of local-field effects on dielectric functions in ${\text{MgB}}_2$. These effects account for the long $q$-range behavior of the modes. We discuss the physics that these collective excitations bring to the energy region typical for lattice vibrations.

• Received 28 July 2009

DOI:https://doi.org/10.1103/PhysRevB.80.054521