One-dimensional spin texture of Bi(441): Quantum spin Hall properties without a topological insulator

The high index (441) surface of bismuth has been studied using scanning tunneling microscopy (STM), angle resolved photoemission spectroscopy (APRES), and spin-resolved ARPES. The surface is strongly corrugated, exposing a regular array of (110)-like terraces. Two surface localized states are observed, both of which are linearly dispersing in one in-plane direction ($k_x$), and dispersionless in the orthogonal in-plane direction ($k_y$), and both of which have a Dirac-like crossing at $k_x=0$. Spin ARPES reveals a strong in-plane polarization, consistent with Rashba-like spin-orbit coupling. One state has a strong out-of-plane spin component, which matches with the miscut angle, suggesting its possible origin as an edge state. The electronic structure of Bi(441) has significant similarities with topological insulator surface states and is expected to support one-dimensional quantum spin Hall-like coupled spin-charge transport properties with inhibited backscattering, without requiring a topological insulator bulk.

Figure 1

(a) Truncated bulk model of the surface, showing the $1\times 1$ (upper half) and the missing row (lower half) reconstruction. The $1\times 1$ unit cell is superimposed in green. (b) STM image (bias voltage = 0.091 V, tunneling current = 90 pA), similarly scaled with the same unit cell overlaid. (c) Side view of the $2\times 2$ truncated bulk model and the measured STM height profile. (d) Fermi surface map performed with photon energy $h\nu =70$ eV, showing the $1\times 1$ SBZ and the $\overline{\Gamma }$ points. Bright colors (light blue, white, yellow) indicate high intensity and dark colors (black, dark red) indicate low intensity. (e) Tight binding calculated constant energy surface indicating where the projected bulk states are close enough to the measured Fermi surface for a weak intensity contribution to be expected [using the parameters of Liu and Allen (Ref. [18])].

Figure 2

(a)–(d) ARPES measurements performed at $k_y=0 {\AA }^{-1}$ and photon energies 18, 22, 26, and 32 eV, respectively. (e) Schematic depicting the presence of “inner” (white) and “outer” (black) Dirac-like states.

Figure 3

(a) Fermi surface collected with photon energy 19 eV. Yellow horizontal lines indicate where the slices shown in (b), (c), and (d) have been extracted ($k_y=+0.33, k_y=0$, and $k_y=-0.33 {\AA }^{-1}$, respectively).

Figure 4

(a) ARPES measurement performed at $h\nu =9$ eV showing where two spin resolved MDCs (SR-MDC1 and SR-MDC2) were collected (green dashed lines). (b) and (c) The raw spin polarizations collected at the Fermi level and at $E_b=0.2$ eV, respectively, showing the in-plane (blue-red) and out-of-plane (gray) spin components. The red axis indicates corrected polarization, found by subtracting a nonpolarized background and correcting for the Sherman function of $17\%$. (d) ARPES measurement with the reconstructed spin vectors superposed. (e) In-plane (blue-red) and out-of-plane (gray) spin components from SR-MDCs atop an ARPES measurement at $h\nu =26$ eV, where the contribution of the outer state is stronger. In both cases $k_y=0$. (f) Similarly scaled polarization curves for the four SR-MDCs numbered in (a)–(c) and (e). (g) Schematic representation of the measured spin vectors and the positions at which they are measured.