Nondegenerate Metallic States on Bi(114): A One-Dimensional Topological Metal

The (114) surface of the semimetal Bi is found to support a quasi-one-dimensional, metallic surface state. As required by symmetry, the state is degenerate along the $\overline{\Gamma }-\overline{Y}$ line of the surface Brillouin zone with a highest binding energy of $\approx 150\mathrm{meV}$. In the $\overline{\Gamma }-\overline{X}$ direction the degeneracy is lifted by the strong spin-orbit splitting in Bi, as directly shown by spin-resolved photoemission. This results in a Fermi contour consisting of two closely separated, parallel lines of opposite spin direction. It is argued that similar states on related insulators would give rise to a one-dimensional quantum spin Hall effect.

Figure 1

(a) Truncated bulk structure of the Bi(114) surface. The pseudocovalent bonds of the bulk bismuth double layer structure are indicated as solid lines, for the sake of clarity only some are shown. (b–d) STM images (sample bias 54 mV, $-150\mathrm{mV}$ and $-40\mathrm{mV}$, respectively). The zoomed image (d) is from the region marked with the yellow rectangle in (c). The unit cell in (d) is also indicated in the atomic model of the ($1\times 2$) surface shown in top and side views in (e). Panel (e) also shows the projected STM topography along the $x$ direction.

Figure 2

(a) Photoemission intensity at the Fermi energy (taken at a photon energy of $h\nu =70\mathrm{eV}$), revealing the existence of a quasi-one-dimensional Fermi line, passing through the origin. Also indicated is the surface Brillouin zone (SBZ) for the truncated bulk surface. (b) Energy vs $k$ cut through the data set of (a) along the red (medium grey) line in (a). (c) Cut along the blue (dark grey) line in (a) taken at $h\nu =20\mathrm{eV}$. (d) Projected band structure along several high-symmetry directions in the truncated bulk SBZ. (e) Projection of the bulk Fermi surface on the (114) truncated bulk face. Regions marked in black represent states within 40 meV of the Fermi energy. Grey regions are the Fermi surface segments translated by the reciprocal lattice of the ($1\times 2$) reconstruction. The projections have been calculated using the tight-binding parameters of Liu and Allen [27].

Figure 3

(a) Black open markers: spin-integrated photoemission intensity for an azimuthal angle scan through the surface Fermi line, taken at a polar off-normal emission angle of 35°. Two Gaussian components [red (medium grey) and blue (dark grey)] are fitted to the data to represent the two spin-split components. The black line is the result of the fit. (b) Sketch of the scan geometry. (c) Measured (markers) and fitted (lines) spin polarization data along the scan, split up into three mutually perpendicular components: $x$, $y$, and out of the surface plane ($z$). (d) The directions of the experimentally determined spin polarization vectors relative to the surface plane.

Figure 4

(a) Surface Fermi contour of Bi(114) resulting from this work. The arrows mark the main spin direction in the plane of the surface. (b) Qualitative sketch of the surface state dispersion in the $x$ direction on top of the projected bulk band structure for the truncated bulk surface along $\overline{\Gamma }-\overline{X}$ [dark green (dark grey) area] and along $\overline{Y}-\overline{C}$ [light green (light grey) area].