De Haas-Van Alphen Measurements in Topological Metals and Semimetals

This thesis studied the electronic structure at the Fermi level and the topological character of topological semimetals via torque magnetometry. Torque magnetometry measures the anisotropic magnetization of the sample in a tilted magnetic field. In our measurements, the magnetic field is up to 35 T and the temperature is down to 300 mK. The oscillatory signal of the magnetization is detected, which is the so called "de Hass van Alphen (dHvA)" effect. By using dHvA effect, many important parameters such as the geometry of Fermi surfaces, effective masses, quantum mobilities, Land ́e g factors and Berry's phases. It is especially important for the Berry's phase extraction. It is known that if there is a cyclotron orbit encircling a Dirac node, a non-trivial Berry's phase π can be extracted and a trivial Berry's phase 0 is expected for a conventional parabolic band. In the study of MAl3, we provided a detailed study of the dHvA oscillations and provided a comparison with the calculated band structures. The angular dependence of their Fermi surface cross-sectional areas reveals a remarkably good agreement with our first-principles calculations. dHvA supports the existence of tilted Dirac cones with Dirac type-II nodes located at 100, 230 and 250 meV above the Fermi level EF for VAl3,NbAl3 and TaAl3 respectively, in agreement with the prediction of broken Lorentz invariance in these compounds. However, for all three compounds we find that the cyclotron orbits on their FSs, including an orbit nearly enclosing the Dirac type-II node, yield trivial Berry phases. We showed that if one would like to derive a convincing Berry's phase from quantum oscillations one has to take into account the spin dephasing term in the LK formalism, and the precise location between the cyclotron orbit and the Dirac node. M2Te2X is studied via both torque magnetometry and angle-resolved photoemission spectroscopy (ARPES). Bulk two-dimensional Fermi surfaces are well-described by the dHvA oscillations and first principles calculations. Intriguingly, slab electronic structure calculations predict Dirac-like surface states at different locations within the Brillouin zone, which is consistent with ARPES observations.