Electronic and spin structure of the topological insulator Bi${}_2$Te${}_{2.4}$Se${}_{0.6}$

High-resolution spin- and angle-resolved photoemission spectroscopy measurements were performed on the three-dimensional topological insulator Bi${}_2$Te${}_{2.4}$Se${}_{0.6}$, which is characterized by enhanced thermoelectric properties. The Fermi level position is found to be located in the bulk energy gap independent of temperature and it is stable over a long time. Spin textures in the Dirac-cone state at energies above and below the Dirac point as well as in the Rashba-type valence band surface state are observed in agreement with theoretical prediction. The calculations of the surface electronic structure demonstrate that the fractional stoichiometry induced disorder within the Te/Se sublattice does not influence the Dirac-cone state dispersion. In spite of relatively high resistivity, temperature dependence of conductivity shows a weak metallic behavior that could explain the effective thermoelectric properties of the Bi${}_2$Te${}_{2.4}$Se${}_{0.6}$ compound with the in-plane Seebeck coefficient reaching $-330$ $\mu$V/K at room temperature.

Figure 1

Schematic drawing of the geometry of the experiment. Variation of $k_{\parallel }$ takes place by tilting the sample in the plane perpendicular to the plane of polarization of the incident light. Linear $p$ and circularly polarized photons are used. The measured in-plane orientation of spin is parallel to the plane of the incident light polarization.

Figure 2

Atomic structure of Bi${}_2$Te${}_3$ (a), Bi${}_2$Te${}_2$Se (b), and Bi${}_2$Te${}_{2.4}$Se${}_{0.6}$ with different distribution of Se atoms in the Te/Se sublattice: (c) homogeneous distribution; (d) distribution of Se atoms in the central layer of QL.

Figure 3

ARPES spectra along the $\overline{\mathrm{K}}\text{−}\overline{\Gamma }\text{−}\overline{\mathrm{K}}$ line acquired at 52-eV photon energy for freshly cleaved surface at (a) cryogenic (18 K) and (b) room temperatures, and (c) for the aged surface.

Figure 4

ARPES spectra measured at room temperature with different photon energies: (a) 57 eV and (b) 47 eV using synchrotron radiation and (c) at 21.2 eV using the discharge He lamp.

Figure 5

(a) Band spectra of 6 QL slabs of Bi${}_2$Te${}_3$, Bi${}_2$Te${}_2$Se, and Bi${}_2$Te${}_{2.4}$Se${}_{0.6}$ with different Se disordering in the latter system; zero energy corresponds to the top of the bulk valence band. (b) ARPES measurement at 52-eV photon energy on Bi${}_2$Te${}_{2.4}$Se${}_{0.6}$ with overlaid surface band structure obtained from DFT calculations.

Figure 6

ARPES (a) and DFT (b) spectra of the occupied electronic states of Bi${}_2$Te${}_{2.4}$Se${}_{0.6}$ along $\overline{\mathrm{K}}\text{−}\overline{\Gamma }\text{−}\overline{\mathrm{K}}$; in panel (b) circles represent weights of the states, localized in the outermost QL, multiplied by value of in-plane spin components (red and blue colors denote positive and negative values of spin, respectively).

Figure 7

Circular dichroism of the topological surface states of Bi${}_2$Te${}_{2.4}$Se${}_{0.6}$ measured along the $\overline{\mathrm{K}}\text{−}\overline{\Gamma }\text{−}\overline{\mathrm{K}}$ direction of the SBZ. Angle-resolved photoemission intensity ($E-k_{\parallel }$) measured for (a) clockwise (right) and (b) counterclockwise (left) circular polarization of the incident light. (c) MDCs extracted at different binding energies for opposite circular polarizations and (d) the corresponding dichroism dispersion.

Figure 8

Spin-resolved EDCs measured at 52-eV photon energy at room temperature in the $\overline{\mathrm{K}}\text{−}\overline{\Gamma }\text{−}\overline{\mathrm{K}}$ direction of the SBZ (a) the Dirac-cone topological surface state and (b) the region including the Rashba-type surface state located near the lower edge of the surface-projected valence band gap. Panel (c) summarizes the spin structure of the Dirac and Rashba-type states.

Figure 9

Temperature dependence of the magnetoresistance MR ($\Delta$$R/R$) (a), Hall resistance (b), and electrical conductivity and Hall concentration (c).