Tunable spin current due to bulk insulating property in the topological insulator ${\mathrm{Tl}}_{1-x}{\mathrm{Bi}}_{1+x}{\mathrm{Se}}_{2-\delta }$

The surfaces of three-dimensional topological insulators characterized by spin-helical Dirac fermions provide a fertile ground for realizing exotic phenomena, and they have the potential for wide-ranging applications. To realize most of their special properties, the Dirac point must be located near the Fermi energy with a bulk insulating property. However, this is barely achieved in most of the discovered topological insulators. It was found recently that ${\mathrm{TlBiSe}}_2$ features an in-gap Dirac point, where the upper and lower parts of the Dirac-cone surface state are both utilized. Nevertheless, investigations of the surface transport properties of this material are limited due to the lack of bulk insulating characteristics. Here, we present a realization of the bulk insulating property by tuning the composition of ${\mathrm{Tl}}_{1-x}{\mathrm{Bi}}_{1+x}{\mathrm{Se}}_{2-\delta }$ without introducing guest atoms. This result promises to shed light on exotic topological phenomena on the surface.

Figure 1

Schematic energy band structures for (a) ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and (b) ${\mathrm{TlBiSe}}_2$, where shaded areas denote bulk continuum states including the bulk conduction band (BCB) and bulk valence band (BVB) with a surface Dirac cone. The BCB is located at the $E_{\mathrm{F}}$ in both grown samples, which leads to the large bulk conduction. These features have been obtained in previous works [6, 9, 11].

Figure 2

(a) Constant energy contour maps at several $E_{\mathrm{B}}$ from $E_{\mathrm{F}}$ to 600 meV in 50 meV step for TBS with $x=0.064$. Selected constant energy contours at (b) $E_{\mathrm{F}}$, (c) below the DP ($E_{\mathrm{B}}=450$ meV), and (d) at $E_{\mathrm{B}}=600$ meV. Intensity maxima obtained from the momentum distribution curves (MDCs) are denoted with open circles in (b) and (c). The colored arrows indicate the spin orientations determined by SARPES measurement (see below). (e) Spin-resolved EDCs along $\overline{K}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{K}$ at the emission angles ($\theta$) from $-1.8^{\circ }$ to $+1.8^{\circ }$ in $0.9^{\circ }$ step, which correspond approximately to the $k$ positions denoted with closed circles in (b). Spin-up and spin-down spectra are plotted with closed upright (filled) and inverted (open) triangles. (f) Experimental spin polarizations taken after subtraction of a constant background as a function of $E_{\mathrm{B}}$ for $\theta =-1.8^{\circ }$ and $+1.8^{\circ }$. Maximum (minimum) polarization of $32\%$ is denoted with the dashed line. Red and blue circles show the data taken with linear polarization, and black ones denote those taken with circular polarization [30]. (g) Schematic picture of the spin-helical surface Dirac cone with reversed spin helicity at the Dirac point (DP).

Figure 3

Estimated chemical compositions by EPMA analysis. (a) Result of chemical composition analysis for $\alpha =0$. (b) Evaluated $x$ values vs $\alpha$ values. (c) Result of chemical composition analysis for an excess Tl sample $\left(\alpha =0.6\right)$.

Figure 4

(a)–(d) Measured band dispersions for $x=0.064\text{–}0.015$ TBSs along the $\overline{M}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ direction. (e) Surface-state dispersions for different $x$ plotted with respect to the DP energy. The colored solid line indicate the $E_{\mathrm{F}}$ for each TBS. (f) The energy distribution curve for TBS with $x=0.032$ at the central $k$ position with a numerical fitting result (solid line).

Figure 5

(a) Se $3d$ core level with spin-orbit splitting for TBS with different $x$. The samples with $x=0.064$, 0.032, and 0.025 are denoted with black, red, and blue open circles and thin solid lines, respectively. (b) Comparison of the $x$ dependence with respect to the sample with $x=0.064$ for bulk core levels and the surface DP energy shown in Fig. 4. The energy shifts for the Tl $5d$, Bi $5d$, and Se $3d$ core levels are denoted with red, green, and blue colored circles and solid lines, respectively. (c) Schematic picture of $E_{\mathrm{F}}$ positions with the bulk states for the samples with $x=0.064$ (black solid line) and 0.025 (red solid line). (d) Schematics of the surface band bending for the sample with $x=0.025$, and the energy structures at the surface and in the buried bulk, which are confirmed by surface-sensitive ARPES and bulk-sensitive HAXPES measurements. $E_C \left(E_V\right)$ is the bulk conduction-band bottom (valence-band top).

Figure 6

Temperature dependence of longitudinal resistivity $\left({\rho }_{xx}\right)$ for $x=0.025$. The inset shows the observed temperature dependence of the Hall coefficient $\left(R_{\mathrm{H}}\right)$ with numerical fitting results assuming the Arrhenius low (solid line).