Extremely Large Magnetoresistance in a Topological Semimetal Candidate Pyrite ${\mathrm{PtBi}}_2$

While pyrite-type ${\mathrm{PtBi}}_2$ with a face-centered cubic structure has been predicted to be a three-dimensional (3D) Dirac semimetal, experimental study of its physical properties remains absent. Here we report the angular-dependent magnetoresistance measurements of a ${\mathrm{PtBi}}_2$ single crystal under high magnetic fields. We observed extremely large unsaturated magnetoresistance (XMR) up to $(11.2\times {10}^6)\%$ at $T=1.8\mathrm{K}$ in a magnetic field of 33 T, which is comparable to the previously reported Dirac materials, such as ${\mathrm{WTe}}_2$, LaSb, and NbP. The crystals exhibit an ultrahigh mobility and significant Shubnikov–de Hass quantum oscillations with a nontrivial Berry phase. The analysis of Hall resistivity indicates that the XMR can be ascribed to the nearly compensated electron and hole. Our experimental results associated with the ab initio calculations suggest that pyrite ${\mathrm{PtBi}}_2$ is a topological semimetal candidate that might provide a platform for exploring topological materials with XMR in noble metal alloys.

Figure 1

(a) The crystal structure of pyrite-type ${\mathrm{PtBi}}_2$ with cubic symmetry and space group of $Pa\stackrel{-}{3}$. Gray and cyan balls represent the Pt atom and Bi atom, respectively. (b) The x-ray diffraction pattern of a pyrite-type ${\mathrm{PtBi}}_2$ single crystal. Inset: Photo of a typical ${\mathrm{PtBi}}_2$ single crystal. (a) Temperature dependence of the longitudinal resistivity ${\rho }_{xx}$ from 2 to 300 K at zero magnetic field. Inset: The zero-field resistivity curve below 20 K can be well fitted by the formula $\rho ={\rho }_0+a{T}^2$. (b) Temperature dependence of resistivity at various magnetic fields applied perpendicular to the (111) plane and current.

Figure 2

(a) MR of ${\mathrm{PtBi}}_2$ under different temperatures with the field applied perpendicular to the high symmetry (111) plane and current. (b) The SdH oscillation $\mathrm{\Delta }{\rho }_{xx}$ plotted as a function of inverse field at different temperatures. The inset shows the Zeeman splitting of an oscillation peak at high field. Data at different temperatures have been shifted for clarity. (c) FFT spectra of SdH oscillations at different temperatures. (d) The amplitudes of the oscillatory component at various temperatures. The solid lines are fitting results of the Lifshitz-Kosevich formula. Inset: Dingle plot of the SdH oscillation associated with the $\alpha$ and $\beta$ bands. (e) The Landau level indices extracted from the SdH oscillation plotted as a function of inverse field.

Figure 3

(a) Magnetoresistence under different angles at $T=2\text{K}$. Inset shows the polar plot for the MR under 16 T and 2 K. (b) SdH patterns at various angles plotted as a function of inverse field. (c) The angular dependence of the oscillation frequency derived from FFT analysis from (b). The solid lines are the fits to the Fermi surfaces using the 2D Fermi surface and 3D ellipsoid Fermi surface models.

Figure 4

(a),(b) Hall resistivity ${\rho }_{xy}$ at several typical temperatures. The red solid lines are numerical fittings to the two-band model. (c) Temperature dependence of the carrier density $n_{e,h}$. Inset: The ratio of $n_h/n_e$ at low temperatures. (d) Temperature dependence of the mobility ${\mu }_{e,h}$.

Figure 5

(a),(b) The ab initio band structure and bulk Fermi surface of pyrite-type ${\mathrm{PtBi}}_2$. (c) Schematic illustration of the semimetal hosted by pyrite-type ${\mathrm{PtBi}}_2$. The pink and yellow colors correspond to (b) and label the electron and hole bands, respectively. “L-e,” “L-h,” and “H-e” label the light electron, light hole, and heavy electron with small and large effective mass, respectively.