Electron energy-loss spectroscopy study of electron-doping in MgB$_2$

The electronic structure of electron-doped polycrystalline Mg$_{1-x}$Al$_{x}$(B$_{1-y}$C$_{y}$)$_2$ was examined by electron energy-loss spectroscopy (EELS) in a scanning transmission electron microscope (STEM) and first-principle electronic structure calculations. We found significant changes in the boron $K$ edge fine structure, suggesting the two bands of the B $K$ edge, the $\sigma$ and the $\pi$ band are being simultaneously filled as the electron doping concentration of Mg$_{1-x}$Al$_{x}$(B$_{1-y}$C$_{y}$)$_2$ was increased. Our density-functional theory calculations confirm the filling of the $\sigma$ band states close to the Fermi level, which is believed to cause the loss of superconductivity in highly doped MgB$_2$, since the electron-phonon coupling of these states is thought to be responsible for the high superconducting transition temperature. Our results do not show significant differences in the electronic structure for electron doping on either the Mg or the B site, although many superconducting properties, such as $T_c$ or H$_{c_2}$ differ considerably for C- and Al- doped \MB. This behavior can not be satisfactorily explained by band filling alone, and effects such as interband scattering are considered.