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$\mathrm{\Omega }$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 $2.5\times {10}^7$ $\mathrm{\%}$ under $\mu_{0}H = 35$Tat$T = 0.35$ 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${}_2$.