Bulk Fermi surfaces of the Dirac Type-II Semimetallic Candidates VAl3, NbAl3 and TaAl3

We report a de Haas-van Alphen (dHvA) effect study on the Dirac type-II semimetallic candidates \emph{M}Al$_3$ (where, \emph{M} = V, Nb and Ta). The angular-dependence of their Fermi surface (FS) cross-sectional 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 $\varepsilon_F$ for VAl$_3$, NbAl$_3$ and TaAl$_3$ 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 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 implied by the small disagreement between our calculations and the experiments. We suggest that a very small amount of doping could displace $\varepsilon_F$ to produce topologically non-trivial orbits encircling their Dirac node(s).