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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.
We report a de Haas-van Alphen (dHvA) study of the electronic structure of Al doped crystals of MgB$_2$. We have measured crystals with $sim 7.5$% Al which have a $T_c$ of 33.6 K, ($sim 14$% lower than pure MgB$_2$). dHvA frequencies for the $sigma$
We report observations of quantum oscillations in single crystals of the high temperature superconductor MgB_2. Three de Haas-van Alphen frequencies are clearly resolved. Comparison with band structure calculations strongly suggests that two of these
Based on the recently proposed concept of effective gauge potential and magnetic field for photons, we numerically demonstrate a photonic de Haas-van Alphen effect. We show that in a dynamically modulated photonic resonator lattice exhibiting an effe
We report measurements of the de Haas-van Alphen effect for single crystals of MgB$_2$, in magnetic fields up to 32 Tesla. In contrast to our earlier work, dHvA orbits from all four sheets of the Fermi surface were detected. Our results are in good o
The de Haas - van Alphen effect in two-dimensional (2D) metals is investigated at different conditions and with different shapes of Landau levels (LLs). The analytical calculations can be done when many LLs are occupied. We consider the cases of fixe