Fermi Surface and Carriers Compensation of pyrite-type PtBi$_{2}$ Revealed by Quantum Oscillations

Large non-saturating magnetoresistance has been observed in various materials and electron-hole compensation has been regarded as one of the main mechanisms. Here we present a detailed study of the angle-dependent Shubnikov -de Haas effect on large magnetoresistance material pyrite-type PtBi$_{2}$, which allows us to experimentally reconstruct its Fermi-surface structure and extract the physical properties of each pocket. We find its Fermi surface contains four types of pockets in the Brillouin zone: three ellipsoid-like hole pockets $alpha$ with C$_4$ symmetry located on the edges (M points), one intricate electron pocket $beta$ merged from four ellipsoids along [111] located on the corners (R points), two smooth and cambered octahedrons $gamma$ (electron) and $delta$ (hole) on the center ($Gamma$ point). The deduced carrier densities of electrons and holes from the volume of pockets prove carrier compensation. This compensation at low temperatures is also supported by fitting the field dependence of Hall and magnetoresistance at different temperatures. We conclude that the compensation is the main mechanism for the large non-saturating magnetoresistance in pyrite-type PtBi$_{2}$. We found the hole pockets {alpha} may contribute major mobility because of their light masses and anisotropy to relatively avoid large-angle scattering at low temperature. This may be a common feature of semimetals with large magnetoresistance. The found sub-quadratic magnetoresistance in high field is probably due to field-dependent mobilities, another feature of semimetals under high magnetic fields.