Low-Energy Charge Excitation in Single Crystal MgB$_{2}$

The charge dynamics of MgB$_{2}$ has been studied at 300K along the {\em c}-axis using inelastic X-ray scattering (IXS) with 65 and 250 meV resolution at 9.886 keV on the Taiwan IXS beamline at SPring-8. [1] An unusual charge excitation has been observed which shows periodic dispersion with momentum transfer {\em q} that follows: $\omega = \omega_{0} - 2{\gamma}{\rm cos}(qc)$, with $\omega_{0} = 3.55$ eV, $\gamma = 0.49$ eV, and $c = 3.52$ {\AA} the lattice constant along the {\em c}-axis. This charge excitation persists even at momentum transfers greater than $q_{c}$, where the conventional bulk plasmon excitation has decayed into the single-particle continuum. This feature may be linked with the predicted sharp collective mode at $q < 0.6$ {\AA}$^{-1}$ [2], but the behavior at higher $q$ is not accounted for. Possible origins and implications of this feature are discussed. This work was supported by the National Science Council of Taiwan. [1] Y.Q. Cai, et al., AIP Conf. Proc. 705, 340 (2004). [2] W. Ku, et al., Phys. Rev. Lett. 88, 057001 (2002).