Pressure variation of Rashba spin splitting toward topological transition in the polar semiconductor BiTeI

BiTeI is a polar semiconductor with gigantic Rashba spin-split bands in bulk. We have investigated the effect of pressure on the electronic structure of this material via magnetotransport. Periods of Shubunikov–de Haas (SdH) oscillations originating from the spin-split outer Fermi surface and inner Fermi surface show disparate responses to pressure, while the carrier number derived from the Hall effect is unchanged with pressure. The associated parameters which characterize the spin-split band structure are strongly dependent on pressure, reflecting the pressure-induced band deformation. We find the SdH oscillations and transport response are consistent with the theoretically proposed pressure-induced band deformation leading to a topological phase transition. Our analysis suggests the critical pressure for the quantum phase transition near $P_{\mathrm{c}}=3.5$ GPa.

Figure 1

(a)–(c) Band structure and (e)–(f) three-dimensional Fermi surface of BiTeI under pressure. The red and blue colors in (a)–(c) correspond to Bi-$6p$ and Te-$5p$ orbital characters, respectively, and the enclosed area in (d)–(f) indicates the maximal cross-sectional area of each Fermi surface. $P_{\mathrm{c}}$ is the critical pressure for band inversion. (a), (d) $P\le P_{\mathrm{c}}$; (b), (e) $P=P_{\mathrm{c}}$; (c), (f) $P\ge P_{\mathrm{c}}$.

Figure 2

(a), (b), (d), (e) Pressure dependence of longitudinal resistivity and Hall resistivity. (a) Temperature dependence of ${\rho }_{xx}$ under pressure. The inset shows Hall resistivity at $T=2$ K under each pressure. ${\rho }_{yx}$ and the associated carrier number remain unchanged by pressure. (b) Magnetic field dependence of ${\rho }_{xx}$ at $T=2$ K under each pressure. (c) Inner Fermi surface and outer Fermi surface of a Rashba spin-split band. (d), (e) Oscillatory components of ${\rho }_{xx}$ in a (d) low-field and (e) high-field region.

Figure 3

Landau index plot of (a) IFS oscillations and (b) OFS oscillations. Solid circles indicate the integer index (${\rho }_{xx}$ peak), and open circles denote the half-integer index (${\rho }_{xx}$ valley). Pressure dependence of the extremal cross-sectional area of (c) IFS and (d) OFS.

Figure 4

(a) $(k_{\mathrm{OFS}},k_{\mathrm{IFS}})$ plots of $k_{\mathrm{OFS}}$ and $k_{\mathrm{IFS}}$ for the present measured sample and their pressure dependence. Points for samples A, B, and C in a previous work [25] are also plotted. (b) Comparison of $k_{\mathrm{OFS}}-k_{\mathrm{IFS}}$ values between experiment and calculation. NI and TI stand for the nontopological and topological insulator, respectively, and $P_{\mathrm{c}}$ for the theoretically predicted critical pressure of the topological transition [28].