Atomic and Electronic Structure of Ultrathin Bi(111) Films Grown on ${\mathrm{Bi}}_2{\mathrm{Te}}_3(111)$ Substrates: Evidence for a Strain-Induced Topological Phase Transition

We studied the atomic and electronic structures of ultrathin Bi(111) films grown on ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ by means of angle-resolved photoemission, first-principles calculations, and low-energy electron diffraction. These Bi films were found to be strained due to the influence of the substrate. Accordingly, the band structure is affected and Bi undergoes a topological phase transition; it is shown that the $Z_2$ topological invariant in three dimensions switches from $+1$ (trivial) to $-1$ (nontrivial or topological). This was clearly confirmed from the change in the surface-state dispersion near the Fermi level. Our discovery offers a method to produce novel topological systems from simple materials.

Figure 1

(a) Raw ARPES band dispersion image of a 7 BL Bi(111) ultrathin film formed on ${\mathrm{Bi}}_2{\mathrm{Te}}_3(111)$. (b) Momentum distribution curve at 10 meV below the Fermi level [red horizontal solid line in (a)]. (c) Second derivative with respect to energy of (a). (d) Band dispersion of a 6.8 BL ultrathin Bi(111) film formed on $\mathrm{Si}(111)\mathrm{\text{−}}(7\times 7)$. (e) Surface Brillouin zone of Bi(111). The bright color represents high intensity.

Figure 2

(a) Experimental $I\mathrm{\text{−}}V$ spectra of LEED spots at 80 K for the 6 BL Bi(111) ultrathin film formed on ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and the calculated spectra of the optimized model shown in (b). The $I\mathrm{\text{−}}V$ curve for the Bi(111) ultrathin film formed on $\mathrm{Si}(111)\mathrm{\text{−}}(7\times 7)$ is shown for the $\{1,0\}$ spot. The inset shows the LEED pattern at 100 eV. (b) Cross-sectional view of the optimized model of the 6 BL Bi(111) film on ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. The Debye temperature for each layer is also shown.

Figure 3

(a) Experimentally measured raw ARPES image along the $\overline{\Gamma }\mathrm{\text{−}}\overline{M}$ direction of the 5 BL ultrathin Bi(111) film on ${\mathrm{Bi}}_2{\mathrm{Te}}_3$, and its second derivative with respect to energy (b), to highlight the spectral features. (c) The calculated weighed spectral function (WSF) for a 5 BL strained Bi(111) ultrathin film, which is the band dispersion weighed by the magnitude of the wave function localization at the topmost Bi bilayer. (d) Experimentally measured raw ARPES image along the $\overline{\Gamma }\mathrm{\text{−}}\overline{M}$ direction of the 6 BL Bi(111) film on ${\mathrm{Bi}}_2{\mathrm{Te}}_3$, and its second derivative with respect to energy (e). [(f) and (g)] The WSF for a 6 BL strained Bi(111) film. In (f), the optimized structure in the calculation is used, whereas in (g) the experimentally obtained lattice parameters are used. The arrows show the slight energy change. (h) The WSF for a 7 BL strained Bi(111) film. (i) The band dispersion for the 7 BL strained Bi(111) film together with the bulk band projection. The size of the circles represents the magnitude of the surface localization of the wave function. SS and QWS represent surface and quantum-well states, respectively.

Figure 4

(a) Bulk Brillouin zone of Bi. [(b)–(e)] Bulk band structure of Bi with different in-plane lattice constants of (b) 4.38 Å, (c) 4.54 Å, (d) 4.65 Å, and (e) 4.70 Å. The total parity at the $\Gamma$ and $T$, $X$, and $L$ points is shown at the horizontal axis. (f) Surface-state band dispersion by the transfer-matrix tight-binding model for the in-plane lattice constants of 4.54 and 4.38 Å.