Manipulation of Topological States and the Bulk Band Gap Using Natural Heterostructures of a Topological Insulator

We have performed angle-resolved photoemission spectroscopy on $(\mathrm{PbSe}{)}_5({\mathrm{Bi}}_2{\mathrm{Se}}_3{)}_{3m}$, which forms a natural multilayer heterostructure consisting of a topological insulator and an ordinary insulator. For $m=2$, we observed a gapped Dirac-cone state within the bulk band gap, suggesting that the topological interface states are effectively encapsulated by block layers; furthermore, it was found that the quantum confinement effect of the band dispersions of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ layers enhances the effective bulk band gap to 0.5 eV, the largest ever observed in topological insulators. For $m=1$, the Dirac-like state is completely gone, suggesting the disappearance of the band inversion in the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ unit. These results demonstrate that utilization of naturally occurring heterostructures is a new promising strategy for manipulating the topological states and realizing exotic quantum phenomena.

Figure 1

(a) Schematic illustration of the building blocks of $[(\mathrm{PbSe}{)}_5{]}_n[({\mathrm{Bi}}_2{\mathrm{Se}}_3{)}_3{]}_m$ homologous series. (b) Comparison of the valence-band ARPES intensities of $(\mathrm{PbSe}{)}_5({\mathrm{Bi}}_2{\mathrm{Se}}_3{)}_{3m}$ for $m=1$, 2, and $\infty$, plotted as a function of $E_B$ and wave vector measured along the $k_y$ axis (the $\overline{\Gamma }\overline{K}$ cut) at $T=30\mathrm{K}$ with $h\nu =60\mathrm{eV}$. (c) Normal-emission photoemission spectra in a wide energy region for $m=1$ and 2 measured with $h\nu =80\mathrm{eV}$ at $T=30\mathrm{K}$. The right-hand inset shows a magnified view around the $\mathrm{Pb}\mathrm{\text{−}}5d$ core levels. Schematic illustration of the cleaved surface and the photoemission process for $m=1$ and 2 is also displayed in the left-hand inset.

Figure 2

(a),(b) Comparison of near-$E_F$ ARPES intensity (a) and corresponding energy dispersion curves (b). Dashed curves in (b) are a guide to the eyes.

Figure 3

(a) Second-derivative ARPES intensities near the $\overline{\Gamma }$ point for $m=2$ plotted as a function of $k_y$ and $E_B$ measured at $h\nu =36$ (left) and 60 eV (center), compared to that for $m=\infty$ (right, measured with $h\nu =60\mathrm{eV}$) which is shifted downward by 0.35 eV to take into account the doping difference. Gray (green) arrows and dashed lines depict a conservative estimate of the bulk band gap of 0.5 eV, judged from the energy difference between the edges of the bands B and E. Notice that band E is likely of the surface origin and, hence, the true bulk band gap may well be larger than 0.5 eV. The band dispersions expected for $m=\infty$ above $E_F$ are also illustrated. (b) Direct comparison of the band dispersions obtained from the peak positions in the energy distribution curves for $m=2$ and $\infty$; the dispersions for $m=\infty$ are shifted downward to account for the doping difference. (c) ARPES intensity mapping at $E_F$ for $m=2$ plotted as a function of 2D wave vector. The intensity is obtained by integrating the spectral intensity within $\pm 10\mathrm{meV}$ of $E_{\mathrm{F}}$. The Fermi vector of each pocket is plotted by dots.

Figure 4

(a) ARPES intensity mappings for $m=1$, 2, and $\infty$ as a function of 2D wave vector at various $E_B$’s. (b) Schematic 3D plots of the near-$E_F$ band dispersions showing the energy positions at which the 2D intensity mappings in (a) are displayed.

Figure 5

Schematic band diagrams and illustrations of the heterostructures for various $m$. Dark (red) area in heterostructures depicts the topological interface (surface) states. $m_c$ is the characteristic thickness where the hybridization gap between two topological interface states starts to open. The interface-to-volume ratio is also shown schematically at the bottom.