Single Dirac Cone Topological Surface State and Unusual Thermoelectric Property of Compounds from a New Topological Insulator Family

Angle resolved photoemission spectroscopy study on ${\mathrm{TlBiTe}}_2$ and ${\mathrm{TlBiSe}}_2$ from a thallium-based ternary chalcogenides family revealed a single surface Dirac cone at the center of the Brillouin zone for both compounds. For ${\mathrm{TlBiSe}}_2$, the large bulk gap ($\sim 200\mathrm{meV}$) makes it a topological insulator with better mechanical properties than the previous binary 3D topological insualtor family. For ${\mathrm{TlBiTe}}_2$, the observed negative bulk gap indicates it as a semimetal, instead of a narrow-gap semiconductor as conventionally believed; this semimetality naturally explains its mysteriously small thermoelectric figure of merit comparing to other compounds in the family. Finally, the unique band structures of ${\mathrm{TlBiTe}}_2$ also suggest it as a candidate for topological superconductors.

Figure 1

(a) Crystal structure of ${\mathrm{TlBiTe}}_2$ with repeating Tl-Te-Bi-Te layers. (b),(c) Laue and x-ray diffraction characterizations show the high quality of the crystal. Inset in (c) shows a flat cleavage surface along (111) direction. (d) LEED pattern acquired after ARPES demonstrates clear diffraction spots without surface reconstruction. (e) Core level photoemission spectrum shows the $d$-shell electron peaks of all three compositional elements.

Figure 2

(a) 3D band structure of ${\mathrm{TlBiTe}}_2$, with the BCB, BVB, SSB, and the Dirac point indicated. (b) FS maps (symmetrized according to the crystal symmetry) for 21, 23, and 25 eV photons. (c) Dispersion along $M\mathrm{\text{−}}\Gamma \mathrm{\text{−}}K$ direction. Four regions defined by characteristic energy positions are labeled as I, II, III, and IV. (d) Constant energy plots of the band structure from different regions defined in (c), showing the BCB FS inside SSB (region I), SSB only (region II), BVB outside SSB (region III) and all BVB (region IV).

Figure 3

(a) Typical FS geometry in region III as defined in Fig. 2. (b) Broad $k$-space scan shows no additional features besides the FS pockets illustrated in (a). High symmetry points $\Gamma$, $M$, and $K$ are marked; the uneven intensity at different BZs results from the matrix element effect. (c) Comparison between the ab initio calculation (top panels) and experimental band structures (bottom panels), with the prominent BCB, BVB, and SSB features labeled.

Figure 4

(a) 3D illustration of the band structure of ${\mathrm{TlBiSe}}_2$ around $\Gamma$, with the BCB, BVB, SSB, and the Dirac point indicated. (b) Detailed band structure along $M\mathrm{\text{−}}\Gamma \mathrm{\text{−}}M$ and $K\mathrm{\text{−}}\Gamma \mathrm{\text{−}}K$ directions, with less anisotropy compared to Fig. 2c. The bottom of the BCB at $\Gamma$ is $\sim 100\mathrm{meV}$ below $E_F$ and the Dirac point residing on top of the BVB is $\sim 200\mathrm{meV}$ below the BCB bottom. The smearing of the distinct SSB below the Dirac point is due to the hybridization with the BVB. (c) Constant energy contours of the band structure at different binding energies. (d) Stacking constant energy plots shows the evolution of the band structure. Red dashed line traces the dispersion of the SSB from the Dirac point.

Figure 5

(a) Broad FS map of $n$-type ${\mathrm{TlBiSe}}_2$ shows a FS sheet without BCB pocket at $M$ point. (b) Comparison between the calculation (top panels) and measured band structure (bottom panels). Results along $\Gamma \mathrm{\text{−}}M\mathrm{\text{−}}\Gamma$ and $\Gamma \mathrm{\text{−}}K\mathrm{\text{−}}\Gamma$ directions are shown on the left and right rows, respectively. Prominent BCB, BVB, and SSB features are marked in both the calculated and measured band structures.