Metal-insulator transition and tunable Dirac-cone surface state in the topological insulator ${\mathrm{TlBi}}_{1-x}{\mathrm{Sb}}_x{\mathrm{Te}}_2$ studied by angle-resolved photoemission

We report a systematic angle-resolved photoemission spectroscopy on topological insulator (TI) ${\mathrm{TlBi}}_{1-x}{\mathrm{Sb}}_x{\mathrm{Te}}_2$ which is bulk insulating at $0.5\lesssim x\lesssim 0.9$ and undergoes a metal-insulator-metal transition with the Sb content $x$. We found that this transition is characterized by a systematic hole doping with increasing $x$, which results in the Fermi-level crossings of the bulk conduction and valence bands at $x\sim 0$ and $x\sim 1$, respectively. The Dirac point of the topological surface state is gradually isolated from the valence-band edge, accompanied by a sign reversal of Dirac carriers. We also found that the Dirac velocity is the largest among known solid-solution TI systems. The ${\mathrm{TlBi}}_{1-x}{\mathrm{Sb}}_x{\mathrm{Te}}_2$ system thus provides an excellent platform for Dirac-cone engineering and device applications of TIs.

Figure 1

(a) Crystal structure of TBST. (b) Bulk BZ (black lines) and corresponding (111) surface BZ (blue lines). (c) Temperature dependence of electrical resistivity ${\rho }_{xx}$ for various $x$. (d) Plot of VB ARPES intensity of TBST at $x=0.6$ as a function of wave vector ($k_x$) and binding energy ($E_{\mathrm{B}}$) measured along the $\overline{\mathrm{\Gamma }}\overline{M}$ cut with the $\mathrm{He}-\mathrm{I}\alpha$ line at 30 K. Black dashed curve is a guide for the eyes to trace the topmost VB. White rectangle corresponds to the $k$ region where the surface state is observed. (e) Near-$E_{\mathrm{F}}$ ARPES intensity at $x=0.6$ measured along the $\overline{\mathrm{\Gamma }}\overline{M}$ cut with the Xe-I and $\mathrm{He}-\mathrm{I}\alpha$ lines. SS, DP, and VB denote the surface state, the Dirac point, and the valence band, respectively. (f) ARPES-intensity contour plots as a function of 2D wave vector at various $E_{\mathrm{B}}$'s. (g) ARPES-intensity mapping at $E_{\mathrm{F}}$ covering the entire first BZ.

Figure 2

(a) Comparison of near-$E_{\mathrm{F}}$ ARPES intensity along the $\overline{\mathrm{\Gamma }}\overline{K}$ cut for various $x$ measured with the Xe-I photons at $T=30$ K. White dashed curves are a guide for the eyes to trace the Dirac-cone band. CB denotes the bulk conduction band, while arrows for $x=0.7$ and 1.0 indicate the location of Fermi wave vector ($k_{\mathrm{F}}$). (b) MDCs at selected $E_{\mathrm{B}}$'s for (top) $x=0.4$ and (bottom) $x=1.0$. Arrows indicate the peak position of the MDCs. (c) Composition dependence of the Dirac-cone band dispersion relative to the DP of TBST, compared with those of BSTS for $(x,y)=(0.25,1.15)$ (gray squares) [13] and ${\mathrm{Pb}\left({\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x\right)}_2{\mathrm{Te}}_4$ (PBST; $x=0.4$) (gray circles) [31]. Energy position of the chemical potential $\mu$ for each composition is indicated by horizontal dashed lines.

Figure 3

(a) ARPES-intensity map at $E_{\mathrm{B}}=0.15$ eV around $\overline{\mathrm{\Gamma }}$ for $x=0.6$ measured with the He-I photons. (b) Near-$E_{\mathrm{F}}$ ARPES intensity measured along cuts A–C shown in (a), which highlights the determination of the VB top. White dashed lines connect the local maxima of the VB for each cut. For cut B, the EDC at $k_y=0.0{\AA }^{-1}$ is shown by the red curve. The intersection of two black solid lines on the EDC, which represent the leading edge and the background, corresponds to the location of the VB top (blue arrow) [13, 24]. (c) Composition dependence of the ARPES intensity for cuts crossing the VB top, highlighting the systematic hole doping into the VB. White dashed lines for $x=0.6$ and 0.7 are linear extrapolation of the VB-intensity edges. White arrows indicate the VB top.

Figure 4

(a) Plot of three characteristic energies, i.e., the conduction-band (CB) bottom (green), the VB top (blue), and the DP energy (red) as a function of $x$. The bulk-insulating/metallic region determined from the resistivity measurements is indicated at the top, while the surface insulating/metallic region suggested from the present ARPES experiment is shown at the bottom. (b) Schematic band diagram of TBST determined from the present ARPES result. Dashed line corresponds to the chemical potential.