Studying the electronic structure in pure and electron doped MgB$_{2}$

We use high-energy electrons to reveal electronic structure information to understand the effects of electron doping in MgB$_{2}$ superconductors. Angle-resolved electron energy-loss spectroscopy was used to investigate the difference in the excited states, while image-coupled quantitative electron diffraction was used to map the valence electron distribution, in pure and Al-doped MgB$_{2}$. The results were compared with density functional theory calculations. We found significant changes in the B K-edge fine structure as a function of electron doping concentration, suggesting the corresponding $\sigma $ and $\pi $ bands are being filled simultaneously. The filling of the $\sigma $-band states near the Fermi level reduces the critical temperature T$_{c}$ of highly doped MgB$_{2}$ to a level comparable to that of other $\pi $-band superconductors such as intercalated graphite. Valence electron maps reveal that electron doping causes considerable charge transfer and accumulation in charge density between both Al-B and B-B bonds. This results in a shortened c-axis of the unit cell and higher phonon frequency, which eventually quenches superconductivity altogether. The relationship between charge transfer and inter-band scattering are also examined.