Fermi surface topology and large magnetoresistance in the topological semimetal candidate PrBi

We report a detailed magnetotransport study on single crystals of PrBi. The presence of $f$ electrons in this material raises the prospect of realizing a strongly correlated version of topological semimetals. PrBi shows a magnetic-field-induced metal-insulator-like transition below $T\sim 20\mathrm{K}$ and a very large magnetoresistance ($\approx 4.4\times {10}^4\%$) at low temperatures ($T=2\mathrm{K}$). We have also probed the Fermi surface topology by de Haas–van Alphen and Shubnikov–de Haas quantum oscillation measurements complimented with density functional theory (DFT) calculations of the band structure and the Fermi surface. Angle dependence measurements of the Shubnikov–de Haas oscillations have been carried out to probe the possible signature of surface Dirac fermions. We find three frequencies corresponding to one electron ($\alpha$) and two hole ($\beta$ and $\gamma$) pockets in experiments, consistent with DFT calculations. The angular dependence of these frequencies is not consistent with a two-dimensional Fermi surface, suggesting that the transport is dominated by bulk bands. We estimate high mobility and small effective mass for carriers in PrBi that are comparable to those of other compounds in this series proposed as topologically nontrivial. A Lifshitz-Kosevich fitting of the quantum oscillation data as well as a Landau fan diagram analysis gave a Berry phase close to $\pi$, suggesting the presence of topological electrons in PrBi.

Figure 1

(a1), (b1) Temperature dependence of ${\rho }_{xx}$ in the two configurations $B\perp I$ and $B\parallel I$, at various magnetic fields. Upper inset of (a1) shows the zero-field behavior of ${\rho }_{xx}$ at low temperature. Lower insets of (a1) and (b1) show enlarged view of ${\rho }_{xx}$ at low temperature, at various fields. (a2) Magnetic field dependence of ${\rho }_{xx}$ in the direction $B\perp I$ at various temperatures. Inset shows the power-law behavior of MR. (b2) Magnetic field dependence of ${\rho }_{xx}$ at 2 K by varying the (out of plane) angle between $B$ and $I$. Inset shows $d{\rho }_{xx}/dT$ vs temperature at various fields. Top right shows an image of the crystal with electrical contacts for magnetotransport measurements.

Figure 2

(a) Background-subtracted SdH oscillations at various angles, at 2 K. (b) The FFT spectra at different angles. (c) The angular dependence of the frequencies $F\left(\alpha \right)$ and $F\left(\beta \right)$. (d) Fitting of the temperature-dependent amplitude in the FFT spectra by the L-K formula (see text for details).

Figure 3

(a) Temperature dependence of the magnetic moment of PrBi in an applied field of 1 T. (b) The temperature-dependent dHvA oscillations obtained after background subtraction. (c) Temperature dependence of the FFT spectra. (d) Fitting of temperature-dependent FFT spectra using L-K formula.

Figure 4

(a) Landau fan diagram extracted from the quantum oscillation data showing the Landau band index $n$ vs reciprocal of the field $1/B$. The extrapolated intercept is close to what is expected (0.5) for a topologically nontrivial system. The lower inset shows an L-K fit to the 2 K dHvA data. (b) The Hall resistivity vs field at various temperatures. The solid curve through the data at $T=2$ K is a fit by a two-band model (see text for details).

Figure 5

(a) Electronic band structure and (b) partial density of states for non-spin-orbit calculation. (c) Electronic band structure and (d) partial density of states with spin-orbit included. Also shown in (b) and (d) is the total density of states (TDOS).

Figure 6

(a)–(c) The Fermi surface of PrBi in the first Brillouin zone for each band crossing the Fermi energy. (d) The total Fermi surface including all crossing bands. (e) The Fermi surface slice for (001) plane. In (a) and (b) we show the two hole pockets of the FS at the $\mathrm{\Gamma }$ point and in (c) we show the electron pockets at each X point of the BZ.