de Haas-van Alphen effect investigations of the electronic structure of pure and aluminum-doped MgB_2

Understanding the superconducting properties of MgB_2 is based strongly on knowledge of its electronic structure. In this paper we review experimental measurements of the Fermi surface parameters of pure and Al-doped MgB_2 using the de Haas-van Alphen (dHvA) effect. In general, the measurements are in excellent agreement with the theoretical predictions of the electronic structure, including the strength of the electron-phonon coupling on each Fermi surface sheet. For the Al doped samples, we are able to measure how the band structure changes with doping and again these are in excellent agreement with calculations based on the virtual crystal approximation. We also review work on the dHvA effect in the superconducting state.