Fermi surface of the Weyl type-II metallic candidate WP2

Weyl type-II fermions are massless quasiparticles that obey the Weyl equation and which are predicted to occur at the boundary between electron- and hole-pockets in certain semi-metals, i.e. the (W,Mo)(Te,P)$_2$ compounds. Here, we present a study of the Fermi-surface of WP$_2$ \emph{via} the Shubnikov-de Haas (SdH) effect. Compared to other semi-metals WP$_2$ exhibits a very low residual resistivity, i.e. $\rho_0 \simeq 10$ n$\Omega$cm, which leads to perhaps the largest non-saturating magneto-resistivity $(\rho(H))$ reported for any compound. For the samples displaying the smallest $\rho_0$, $\rho(H)$ is observed to increase by a factor of $2.5 \times 10^{7}$ $\%$ under $\mu_{0}H = 35$ T at $T = 0.35$ K. The angular dependence of the SdH frequencies is found to be in very good agreement with the first-principle calculations when the electron- and hole-bands are slightly shifted with respect to the Fermi level, thus supporting the existence of underlying Weyl type-II points in WP$_2$.