Connection of a Topological Surface State with the Bulk Continuum in ${\mathrm{Sb}}_2{\mathrm{Te}}_3(0001)$

The surface state of a ${\mathbb{Z}}_2$ topological insulator connects with the conduction and valence band continua of the bulk, thereby bridging the band gap of the volume. We investigate this connection of the surface and bulk electronic structure for ${\mathrm{Sb}}_2{\mathrm{Te}}_3(0001)$ by photoemission experiments and calculations. Upon crossing the topmost valence band the topological surface state (TSS) maintains a coherent spectral signature, a two-dimensional character, and a linear dispersion relation. Surface-bulk coupling manifests itself in the spectra through (i) a characteristic kink in the TSS dispersion as it crosses the topmost valence band and (ii) the appearance of hybridization gaps between the TSS and bulk-derived surface resonance states at higher binding energies. The findings provide a natural explanation for the unexpectedly weak surface-bulk mixing indicated by recent transport experiments on ${\mathrm{Sb}}_2{\mathrm{Te}}_3$.

Figure 1

ARPES data sets for ${\mathrm{Sb}}_2{\mathrm{Te}}_3(0001)$ along the $\overline{\mathrm{\Gamma }K}$ direction measured at photon energies of (a) $h\nu =12\mathrm{eV}$, (b) $h\nu =10\mathrm{eV}$, and (c) $h\nu =8\mathrm{eV}$. The topological surface state (TSS), a surface state with Rashba-type spin splitting (RSS), and two bulk-derived valence band features, BVB and BVB2, are indicated. Photon-energy variation gives rise to strong changes in the relative spectral weights of the individual bands. The TSS maintains a coherent spectral signature and a linear dispersion upon crossing the topmost valence band feature, BVB.

Figure 2

Photon-energy dependent analysis of the electronic structure of ${\mathrm{Sb}}_2{\mathrm{Te}}_3(0001)$ near $E_F$. (a) Peak positions for the TSS obtained from EDC and MDC. The lack of a photon-energy dependence indicates a 2D character of the TSS in the considered energy interval. EDC at the $\overline{\mathrm{\Gamma }}$ point are shown in (b). Unlike for the surface state RSS, the energy position of the valence band BVB changes with photon energy indicating its bulk origin near the $\overline{\mathrm{\Gamma }}$ point.

Figure 3

Interaction of the TSS with other spectral features. Peak positions and linewidths for the TSS are plotted in (a) and (b), respectively. The data were obtained from MDC of the data set in Fig. 1. The group velocity of the TSS abruptly increases when crossing the band BVB at $-0.1\mathrm{eV}$. Grey bars in (b) serve as guides for the eye. (c) Displays a curvature plot [35] of a section of the data set in Fig. 1. It shows a complex band hybridization involving the TSS, the two bulk-derived features, BVB and BVB2, and the two branches of the Rashba-split state RSS.

Figure 4

Theoretical ARPES data sets for ${\mathrm{Sb}}_2{\mathrm{Te}}_3(0001)$ along $\overline{\mathrm{\Gamma }K}$ for a photon energy of 10 eV. The TSS and the bulk feature BVB are indicated. Their dispersions are emphasized by dashed lines serving as guides for the eye. (a) and (b) Data calculated for $s$- and $p$-polarized light, respectively.