Shubnikov–de Haas oscillations in the bulk Rashba semiconductor BiTeI

Bulk magnetoresistance quantum oscillations are observed in high quality single crystal samples of BiTeI. This compound shows an extremely large internal spin-orbit coupling, associated with the polarity of the alternating Bi, Te, and I layers perpendicular to the $c$ axis. The corresponding areas of the inner and outer Fermi surfaces around the A point show good agreement with theoretical calculations, demonstrating that the intrinsic bulk Rashba-type splitting is nearly 360 meV, comparable to the largest spin-orbit coupling generated in heterostructures and at surfaces.

Figure 1

(a) BiTeI crystal structure. (b) Corresponding Brillouin zone. (c) Calculated energy bands along the H-A-L direction. Local minima are offset from $k=0$ by $\Delta k_{\mathrm{R}}\sim 0.05$ Å${}^{-1}$, the Rashba splitting. The energy splitting $\Delta E_{\mathrm{R}}\sim 0.360$ eV, at the Fermi level $E_{\mathrm{F}}$, corresponding to the density of sample no. 1.

Figure 2

Calculated Fermi surfaces around the A point for sample no. 1. (a) An opened view of the outer and inner Fermi surfaces. The inclination ($\theta$) and azimuthal ($\varphi$) angles are also shown. (b), (c) Outer and inner Fermi surfaces, respectively, along the $k_z$ axis, and (d), (e), along the $k_y$ axis.

Figure 3

$\rho \left(H\right)$ for various values of $\theta$ at $T=2$ K for sample no. 1. Data are offset vertically for clarity. Inset: Three representative data sets with a linear background subtracted. Down (up) arrows indicate the local maximum (minimum) used to calculate the SdH oscillation frequencies for the respective data sets.

Figure 4

Theoretical variation (solid lines) of the effective mass (right ordinate axis), and the Fermi surface area (left ordinate axis) as a function of $\theta$, for the IFS. Plots for theoretical azimuthal angles of $\varphi =0^{\circ }$ and ${30}^{\circ }$, corresponding to the extremal values in the plane perpendicular to the $c$ axis, show no significantly different $\theta$ dependences. Circles (triangles) show the experimental $A_k^{\mathrm{IFS}}$ values extracted for sample no. 1 (no. 2). Ordinate error bars are smaller than the point size.

Figure 5

Sample no. 1. (a) Higher frequency OFS SdH oscillations at various temperatures at $\theta =0^{\circ }$. (b) SdH oscillations at various inclination angles for $T=2$ K. $\Delta \rho$ is the resistivity change after quartic background subtraction. Inset in (a): $T=2$ K, $\theta =0^{\circ }$, $\ln \left(A_p\right)$ vs $1/B_p$ data. The solid line is a best fit, used to determine $T_{\mathrm{D}}$.

Figure 6

Theoretical variation (solid and dashed lines) of the effective mass (right ordinate axis), and the Fermi surface area (left ordinate axis) as a function of $\theta$, for the OFS. Theoretical azimuthal angles are $\varphi =0^{\circ }$ and ${30}^{\circ }$, corresponding to the extremal values in the plane perpendicular to the $c$ axis. Circles (triangles) show the experimental values extracted from the angular- and temperature-dependent SdH data for sample no. 1 (no. 2). Ordinate error bars are smaller than the point size. Datum point for sample no. 2 at $\theta ={45}^{\circ }$ is calculated from SdH data up to 57 T.