Compared with the semiconductors such as silicon and gallium arsenide which have been used widely for decades, semimetals have not received much attention in the field of condensed matter physics until very recently. The realization of electronic topological properties has motivated interest of investigations on Dirac semimetals and Weyl semimetals, which are predicted to show unprecedented features beyond the classical electronic theories of metals. In this letter for the first time we report the electric transport properties of a robust Weyl semimetal candidate proposed by recent theoretical calculations, TaAs. Our study shows that this bulk material manifests ultrahigh carrier mobility ($mathrm{5times10^5 cm^2/Vcdot{s}}$) accompanied by an extremely large, unsaturated linear magnetoresistance ($mathrm{MR}$), which reaches 5400 at 10 Kelvins in a magnetic field of 9 Teslas and 2.47$times$10$^4$ at 1.5 Kelvins in a magnetic field of 56 Teslas. We also observed strong Shubnikov-de Haas (SdH) oscillations associated with an extremely low quantum limit ($sim$8 Teslas). Further studies on TaAs, especially in the ultraquantum limit regime, will help to extend the realization of the topological properties of these exotic electrons.
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