Intra- and interband electron scattering in a hybrid topological insulator: Bismuth bilayer on ${\mathrm{Bi}}_2{\mathrm{Se}}_3$

The band structure and intra- and interband scattering processes of the electrons at the surface of a bismuth bilayer on ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ have been experimentally investigated by low-temperature Fourier-transform scanning tunneling spectroscopy. The observed complex quasiparticle interference patterns are compared to a simulation based on the spin-dependent joint density of states approach using the surface-localized spectral function calculated from first principles as the only input. Thereby, the origin of the quasiparticle interferences can be traced back to intraband scattering in the bismuth-bilayer valence band and ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ conduction band and to interband scattering between the two-dimensional topological state and the bismuth-bilayer valence band. The investigation reveals that the bilayer band gap, which is predicted to host one-dimensional topological states at the edges of the bilayer, is pushed several hundred meV above the Fermi level. This result is rationalized by an electron transfer from the bilayer to ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ which also leads to a two-dimensional electron state in the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ conduction band with a strong Rashba spin splitting, coexisting with the topological state and bilayer valence band.

Figure 1

Constant-current STM image of the Bi BL. (a) Bi BL grown at full coverage on ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ ($V=1\mathrm{V}$, $I=20\mathrm{pA}$). (Inset) Atomically resolved STM image taken on a flat area of the BL ($V=-100\mathrm{mV}$, $I=5\mathrm{nA}$). (b) Bi BL islands grown by deposition of 60% BL ($V=1\mathrm{V}$, $I=20\mathrm{pA}$). (c) Height profile taken along the line in (b).

Figure 2

(a) Constant-current STM image of an area of the closed BL without vacancy islands and Bi excess islands ($V=-50\mathrm{mV}$, $I=3\mathrm{nA}$; scale bar from 0 to 80 pm). The crystallographic directions as derived from the atomic resolution in the inset of Fig. 1 are indicated. (b)–(i) STS images of the same sample area as in (a) measured at the indicated sample biases ($I=3\mathrm{nA}$). The color range covers the following ranges of conductances: (b) $0.09$ to $0.13\mathrm{nS}$, (c) $0.09$ to $0.17\mathrm{nS}$, (d) $0.17$ to $0.29\mathrm{nS}$, (e) $0.23$ to $0.4\mathrm{nS}$, (f) $0.4$ to $0.7\mathrm{nS}$, (g) $1.2$ to $2\mathrm{nS}$, (h) $0.46$ to $1.8\mathrm{nS}$, (i) $0.23$ to $0.79\mathrm{nS}$. (j)–(q) FT-STS images resulting from Fourier transformation of (b)–(i) and image processing as described in the text.

Figure 3

(a) DFT calculation of the bands along $\overline{\Gamma }\text{−}\overline{M}$. The size of a symbol is proportional to the localization of the state at the surface of the BL. The colors indicate the origin of the four principal bands dominating the surface layer: light blue, ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ conduction band (CB); dark blue, ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ valence band (VB); green, Bi BL VB; red: topological state (TS). The gray symbols indicate bulk states or states from the opposite surface of the slab without Bi BL. (b) Three-dimensional surface-localized spectral function modeled by 3D interpolation of the DFT-calculated bands of (a) and a similar DFT calculation of the bands along two other directions in the SBZ ($\overline{\Gamma }-\overline{K}$, $\overline{\Gamma }-\overline{B}$). (c) (Right) Constant-energy contours (CECs) through the surface-localized spectral function of (b) at the energies indicated by the vertical axis in electron volts. (Top left) CEC at $E=0.4\mathrm{eV}$ containing the orientations of the electron spin in each band. (Bottom left) DFT calculation of the bands along $\overline{\Gamma }\text{−}\overline{K}$ (dots, the data at positive $k$ is mirror symmetric to the shown data at negative $k$) superimposed on the band dispersion as measured by ARPES along the same direction (red). (Bottom center) CECs measured by ARPES at energies in electron volts given by the vertical axis. (d) Comparison between calculated spin-dependent JDOS and measured FT-STS at $E=0.4\mathrm{eV}$ ($I=3\mathrm{nA}$). $k_x$ is along $\overline{\Gamma }\text{−}\overline{K}$ and $k_y$ along $\overline{\Gamma }\text{−}\overline{M}$ in (b)–(d).

Figure 4

Comparison between calculated CECs (a)–(e), resultant JDOS (f)–(j), and measured FT-STS (k)–(o) at the indicated energies. The arrows in the CECs represent scattering vectors $\mathbf{q}$, and the arrows or crosses of the same color indicate the resulting features present or absent, respectively, in the JDOS or FT-STS images.

Figure 5

(a) Comparison of the dispersion of the scattering vectors from FT-STS (dots) and JDOS simulation (lines) along $\overline{\Gamma }-\overline{M}$ corresponding to the following $\mathbf{q}$ as indicated: Bi BL intraband scattering (green), ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ CB intraband scattering (light blue), interband scattering between Bi BL and ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ VB (gray), and between Bi BL and TS (pink and orange). The dotted pink and orange lines are the corresponding interband scattering channels of the TS into the second branch of the Bi BL band of equal spin helicity, which are forbidden by spin conservation. Dark blue line, scattering alongside the hexagonal part of the Bi BL CEC [see arrow of same color in Figs. 4 and 4]; gray dotted lines, ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ CB intraband scattering vectors. The red line indicates the dispersion of the TS intraband scattering which is observed neither in the JDOS nor in the FT-STS images. (b) DFT-calculated band structure including the observed scattering vectors $\mathbf{q}$ as arrows with the same colors as the corresponding dispersions in (a).