Topological metal at the surface of an ultrathin ${\text{Bi}}_{1-x}{\text{Sb}}_x$ alloy film

We have studied the growth and electronic/transport properties of ultrathin ${\text{Bi}}_{1-x}{\text{Sb}}_x$ alloy films, which the bulk is reported to be a topological insulator for $0.07<x<0.22$. We found that single crystal epitaxial films as thin as $\sim 30\text{Å}$ could be grown on silicon for $0\le x<0.32$. The $Z_2$ topological number of the films was shown to be nontrivial from the surface Fermi surface. Moreover a crossover from an insulating to a metallic behavior was observed upon reducing the film thickness, revealing the clear detection of the topological-metal conductivity. Our results settle the controversial issues concerning the metallicity of ${\text{Bi}}_{1-x}{\text{Sb}}_x$ at low temperature and verify that the surface/volume ratio must be extensively enhanced to properly understand the nature of these surface states.

Figure 1

RHEED patterns of $29\text{Å}$ (7 BL) thick pure Bi (a), ${\text{Bi}}_{0.91}{\text{Sb}}_{0.09}$ (b), ${\text{Bi}}_{0.78}{\text{Sb}}_{0.22}$ (c), and $50\text{Å}$ (13 BL) thick ${\text{Bi}}_{0.68}{\text{Sb}}_{0.32}$ (d) ultrathin films. The electrons are incident along the $\left[11\overline{2}\right]$ direction and the energy is 15 keV.

Figure 2

(Color online) Core level photoemission spectra of $\text{Sb}4d$ and $\text{Bi}5d$ peaks for $43\text{Å}$ (11 BL) thick ${\text{Bi}}_{0.92}{\text{Sb}}_{0.08}$ (a) and $39\text{Å}$ (10 BL) thick ${\text{Bi}}_{0.84}{\text{Sb}}_{0.16}$ (b) ultrathin films measured at normal emission with $h\nu =80\text{eV}$.

Figure 3

(Color online) (a, b) Fermi surfaces of $43\text{Å}$ thick ${\text{Bi}}_{0.92}{\text{Sb}}_{0.08}$ (a) and $39\text{Å}$ thick ${\text{Bi}}_{0.84}{\text{Sb}}_{0.16}$ (b) ultrathin films. (c, d) $E-\theta$ band dispersions for the cuts shown in (a) and (b), respectively. (e, f) Energy distribution curves for the images shown in (c) and (d), respectively. The photon energy was $h\nu =29\text{eV}$.

Figure 4

(Color online) (a) Comparison of the peak width for the ARPES spectra near $\overline{\Gamma }$ and those shown in Figs. 3e, 3f. The arrows show the width of the peak. (b) Representative results of the fitting for the spectra shown in Figs. 3e, 3f. The red (dark) and green (light) curves show the states at higher and lower binding energies, respectively. (c) Schematic drawing of the band dispersion of Figs. 3c, 3d, 3e, 3f. (d) Schematic drawing of the Fermi surface shown in the surface Brillouin zone. The photon energy was $h\nu =29\text{eV}$.

Figure 5

(Color online) The temperature dependence of two-dimensional resistivity for $239\text{Å}$ thick pure Bi (purple open circles), $239\text{Å}$ thick ${\text{Bi}}_{0.9}{\text{Sb}}_{0.1}$ (blue filled diamonds), $98\text{Å}$ thick ${\text{Bi}}_{0.9}{\text{Sb}}_{0.1}$ (green filled squares), and $29\text{Å}$ thick ${\text{Bi}}_{0.9}{\text{Sb}}_{0.1}$ (orange filled circles) ultrathin films measured by in situ micro-four-point probe method. The pink solid lines are the least-square linear fits to Eq. (2) and the red solid lines show the linear extrapolation to $T=0$.