Figure 1

A single massless topological spin-Dirac cone on the surface of ${\mathrm{Bi}}_{2-x}{\mathrm{Mn}}_x{\mathrm{Te}}_3$: (a) Schematic of the (111) surface Brillouin zone with the four time-reversal-invariant momenta ($\overline{\Gamma }$, $3\times \overline{M}$) marked by blue circles. A single Fermi surface enclosing $\overline{\Gamma }$ that arises from a Dirac cone is the signature of the most basic topological insulator. Red arrows denote the direction of spin [6] around the Fermi surface of a Dirac cone. (b) Calculated band structure along the $\overline{K}-\overline{\Gamma }-\overline{M}$ cut of the ${\mathrm{Bi}}_2{\mathrm{Te}}_3(111)$ BZ. Bulk band projections are represented by the shaded areas. The band structure results with SOC are presented in blue and that without SOC in green. The magnitude of the bulk indirect gap is typically underestimated by ab initio calculations. No pure surface band is observed within the bulk band gap without SOC (black lines). One pure gapless surface band crossing $E_F$ is observed when SOC is included (red lines). The inset shows an enlargement of the low energy region (shaded box) near $\overline{\Gamma }$. (c) ARPES second derivative image of the bulk valence bands of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ along $\overline{\Gamma }-\overline{M}$. (d) ARPES intensity map of the gapless surface state bands imaged 1 h after cleavage. The blue dotted lines are guides to the eye. The spin directions are marked based on calculations. (e) Energy distribution curves of the data shown in (d). (f) Constant energy ARPES intensity map collected at $E_F$ using $h\nu =35\mathrm{eV}$. Yellow dotted lines are guides to the eye.Reuse & Permissions

Figure 2

Observation of insulating bulklike states in stoichiometric ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ supporting a six-peak electronic structure: (a) bulk rhombohedral Brillouin zone of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. According to local-density approximation band structure calculations [24, 25], six valence band maxima are located at the $\mathbf{b}$ points that are related to one another by 60° rotations about $\widehat{z}$. The red lines show the momentum space trajectories of the ARPES scans taken using $h\nu =31$, 35, and 38 eV. The inset shows a schematic of the indirect bulk band gap. (b) Calculated valence band structure along cut 2 superimposed on the second derivative image of a corresponding ARPES cut. The calculated band energies have been shifted downwards to match the data. (c)–(e) show ARPES intensity maps along the $h\nu =31$, 35, and 38 eV trajectories, respectively, obtained 1 h after sample cleavage. The in-plane momentum components of the $\mathbf{b}$ and $\mathbf{d}$ points are marked by black arrows, and the energy of the valence band maximum relative to $E_F$ ($\delta$) is marked by a double-headed arrow. Yellow arrows denote the direction of the spin of Dirac-cone surface states. (f)–(h) show the energy distribution curves corresponding to images (c)–(e), respectively.Reuse & Permissions

Figure 3

Slow dynamics of the surface Dirac-cone dispersion in ${\mathrm{Bi}}_{2-x}{\mathrm{Mn}}_x{\mathrm{Te}}_3$: (a) the crystal structure of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ viewed parallel to the quintuple layers. The Te(1) $5p$ orbitals that form the interquintuple layer van der Waals bonds are shown in yellow. (b) Schematic of the band bending of the bulk VBM near the cleaved surface. (c) ARPES spectra of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ along the $\overline{\Gamma }\mathrm{\text{−}}\overline{M}$ direction taken with $h\nu =30\mathrm{eV}$ (c) 8, (d) 20, and (e) 40 min after cleavage in UHV. Analogous ARPES spectra for ${\mathrm{Bi}}_{1.95}{\mathrm{Mn}}_{0.05}{\mathrm{Te}}_3$ (f) 15 min, (g) 4 h, and (h) 9 h after cleavage, showing a slower relaxation rate. Red lines are guides to the eye. (i) The energy distribution curves of ${\mathrm{Bi}}_{1.95}{\mathrm{Mn}}_{0.05}{\mathrm{Te}}_3$ at $\overline{\Gamma }$ at various times after cleavage.Reuse & Permissions

Figure 4

Evidence for a topologically nontrivial band structure in ${\mathrm{Sb}}_2{\mathrm{Te}}_3$: (a) calculated band structure along the $\overline{K}\mathrm{\text{−}}\overline{\Gamma }\mathrm{\text{−}}\overline{M}$ cut of the ${\mathrm{Sb}}_2{\mathrm{Te}}_3(111)$ BZ. Bulk band projections are represented by the shaded areas. The bulk (surface) band structure results with SOC are presented in blue (red lines) and that without SOC in green (black lines). (b) Schematic of the single surface spin-Dirac cone in ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ based on calculations. (c) Enlargement of low energy region [shaded box in (a)] near $\overline{\Gamma }$. (d) Second derivative image of the bulk valence bands along $\overline{\Gamma }\mathrm{\text{−}}\overline{M}$ and (e) $\overline{\Gamma }\mathrm{\text{−}}\overline{K}$ at $k_z=-0.77$ $\Gamma \mathrm{\text{−}}Z$. Corresponding bulk band calculations are superimposed.Reuse & Permissions