$\pi$ Berry phase and Zeeman splitting of Weyl semimetal TaP

The recent breakthrough in the discovery of Weyl fermions in monopnictide semimetals provides opportunities to explore the exotic properties of relativistic fermions in condensed matter. The chiral anomaly-induced negative magnetoresistance and $\pi$ Berry phase are two fundamental transport properties associated with the topological characteristics of Weyl semimetals. Since monopnictide semimetals are multiple-band systems, resolving clear $\pi$ Berry phase for each Fermi pocket remains a challenge. We report the determination of Berry phases of multiple Fermi pockets of Weyl semimetal TaP through high field quantum transport measurements. We show our TaP single crystal has the signatures of a Weyl state, including light effective quasiparticle masses, ultrahigh carrier mobility, as well as negative longitudinal magnetoresistance. Furthermore, we have generalized the Lifshitz-Kosevich (LK) formula for multiple-band Shubnikov-de Haas (SdH) oscillations and extracted the Berry phases of $\pi$ for multiple Fermi pockets in TaP through the direct fits of the modified LK formula to the SdH oscillations. In high fields, we also probed signatures of Zeeman splitting, from which the Land\'{e} \textit{g}-factor is extracted.