Spectroscopic evidence of a topological quantum phase transition in ultrathin ${\text{Bi}}_2{\text{Se}}_3$ films

We have measured the band dispersion of ultrathin ${\text{Bi}}_2{\text{Se}}_3$ films formed on a silicon substrate using angle-resolved photoemission spectroscopy. An energy gap opening in the topological surface-state bands of the three-dimensional topological insulator ${\text{Bi}}_2{\text{Se}}_3$ is observed due to the hybridization of the top and bottom surfaces. The drastic change in the shape of the band structure and the reversal of the size of the energy gap between 2 and 3 quintuple layer (QL) films indicate that the parity of the conduction and valence bands are exchanged by finite-size effects. The analyses based on an effective four-band model also support the occurrence of a quantum topological phase transition, thus, implying that 2 QL films are trivial while the 3 QL films are in the quantum spin Hall state.

Figure 1

(Color online) (a) Schematic of the topological quantum phase transition in 2D from the QSH state $\left(d>d_c\right)$ to the trivial insulator $\left(d<d_c\right)$ by reducing the film thickness. At $d=d_c$, the band gap closes and the parity of the conduction and valence bands is exchanged. (b) Schematic of the surface-state linear band dispersion of the 3D topological insulator.

Figure 2

(Color online) (a) A RHEED pattern of a 10 QL $\left(95\text{Å}\right)$ thick ${\text{Bi}}_2{\text{Se}}_3$. The electrons are incident along the $\left[11\overline{2}\right]$ direction of the underlying Si substrate and the energy is 15 keV. (b) RHEED spot intensity of the (00) spot during ${\text{Bi}}_2{\text{Se}}_3$ growth showing clear oscillation and quintuple-layer by quintuple-layer growth.

Figure 3

(Color online) [(a)–(d)] $E-k$ band dispersion images for the 1 QL (a), 2 QL (b), 3 QL (c), and 8 QL (d) ultrathin ${\text{Bi}}_2{\text{Se}}_3$ films along the $\overline{\Gamma }\text{−}\overline{K}$ direction near the $\overline{\Gamma }$ point, respectively. [(e) and (f)] Raw ARPES data for the 2 QL (e) and 3 QL (f) films near the $\overline{\Gamma }$ point. The diamonds show the bulk (quantum well) states. (g) The gap size deduced from the ARPES spectra of (a)–(f) plotted as a function of film thickness. The photon energy was $h\nu =20\text{eV}$.

Figure 4

(Color online) The band dispersion image overlapped with the fitted curves using Eq. (1).