Fermi Surfaces and Topological Character of Dirac and Weyl Type-II Semimetals as Revealed by the de Haas-van Alphen Effect*

The texture of the Berry phase curvature has led to the observation of novel, but controversial, electrical transport properties
in the so-called topological semimetals. Examples include the so-called Weyl orbits that explore the Fermi arcs on the surfaces of Weyl semimetals, the observation a planar Hall-effect in non-magnetic compounds, or the observation of a negative magnetoresistivity ascribed to the axial current between Weyl points resulting from the suppression of their chiral symmetry. We have studied the transport properties of some of these compounds as well as their Fermi surfaces through quantum oscillatory phenomena, finding both marked disagreements with calculations and photoemission (e.g. MoTe₂ ), as well as good agreements (e.g. PdTe₂). Here, we will focus on the semimetals MAl₃ (where, M = V, Nb and Ta) which were predicted to be candidates for a Dirac type-II state. We find that the angular-dependence of their Fermi surface (FS) crosssectional areas reveals a remarkably good agreement with first-principle calculations. Therefore, dHvA supports the existence of tilted Dirac cones with Dirac type-II nodes located at 100, 230 and 250 meV above the Fermi level for VAl₃, NbAl₃ and TaAl₃ respectively. However, for all three compounds the cyclotron orbits on their FSs, including an orbit nearly enclosing the Dirac type-II node, yield trivial Berry phases. We explain this via an analysis of the Berry phase where the position of this orbit, relative to the Dirac node, is adjusted within the error (of ~10 meV) implied by the small disagreement between our calculations and the experiments.