One-Dimensional Edge States with Giant Spin Splitting in a Bismuth Thin Film

To realize a one-dimensional (1D) system with strong spin-orbit coupling is a big challenge in modern physics, since the electrons in such a system are predicted to exhibit exotic properties unexpected from the 2D or 3D counterparts, while it was difficult to realize genuine physical properties inherent to the 1D system. We demonstrate the first experimental result that directly determines the purely 1D band structure by performing spin-resolved angle-resolved photoemission spectroscopy of Bi islands on a silicon surface that contains a metallic 1D edge structure with unexpectedly large Rashba-type spin-orbit coupling suggestive of the nontopological nature. We have also found a sizable out-of-plane spin polarization of the 1D edge state, consistent with our first-principles band calculations. Our result provides a new platform to realize exotic quantum phenomena at the 1D edge of the strong spin-orbit-coupling systems.

Figure 1

(a) FS mapping of Bi thin film ($d=15\mathrm{BL}$) at $T=30\mathrm{K}$ where the ARPES intensity integrated within $\pm 5\mathrm{meV}$ with respect to $E_F$ is plotted as a function of the 2D wave vector and folded with the $C_3$ symmetry. (b), (c) Band structure of a Bi thin film in the wide energy range along the $\overline{\mathrm{\Gamma }}\text{−}\overline{K}$ and $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ high-symmetry lines, respectively. The band dispersions were obtained by plotting the second derivatives of ARPES intensity as a function of wave vector and binding energy, to visualize more clearly the dispersive band with a relatively weak spectral weight. To better trace the weak signal around the $\overline{M}$ and $\overline{K}$ points, an enhanced color-scale image is shown in the inset. Arrows in the inset indicate the faint structure.

Figure 2

(a) ARPES intensity plot at $E_F$ around the $\overline{\mathrm{\Gamma }}\text{−}\overline{K}$ cut for a Bi thin film ($d=15\mathrm{BL}$) at $T=30\mathrm{K}$. (b), (c) Band dispersion near $E_F$ along cuts 1–2 and 3–6 [see (a)], respectively, obtained by taking the second derivatives of EDCs. Red dashed curve in (b) is a guide for the eye to trace the near-$E_F$ band. (d) EDCs for cuts 5 and 6.

Figure 3

(a) AFM image of a Bi thin film ($d=15\mathrm{BL}$) at $T=300\mathrm{K}$. (b) Front (top) and top (bottom) views of the artificially constructed model crystal structure used to calculate the energy band structure of the edge state. Area enclosed by gray and red solid lines in bottom panel show the unit cell. Crystal structure in the unit cell contains 1 BL Bi ribbon on 3 BL Bi where hydrogen atoms (small circles in top panel) terminate one side of the edge in Bi ribbon (Supplemental Material [29]). (c) The Brillouin zone (red line) of the model crystal structure [shown in (b)] compared to the hexagonal surface Brillouin zone (black line). (d) Calculated band dispersion along the high-symmetry line ($\overline{\mathrm{\Gamma }}\text{−}\overline{Y}$ or $\overline{\mathrm{\Gamma }}\text{−}\overline{K}$) for the model crystal shown in (b) and ordinary Bi thin film ($d=10\mathrm{BL}$), respectively. (e) Comparison of the second derivative of ARPES intensity near $E_F$ around the $\overline{\mathrm{Y}}$ point with the calculated band dispersion for the edge state [same as the left panel of (d)]. Calculated bands were shifted upward as a whole by 45 meV to take into account the finite hole doping effect of Bi thin film. (f) Spin-resolved EDCs for the in-plane and out-of-plane spin components at the $k$ point indicated by the dashed line in (e), together with the corresponding energy dependence of the spin polarization. (g) Experimental band dispersion for cuts 3–5 extracted from the peak position of the EDCs in Fig. 2, compared with the numerical simulation for a simple 1D Rashba splitting (dashed black curve). Rashba parameter ${\alpha }_{\mathrm{R}}$ is estimated to be 0.80 eV Å from the deduced band parameters of $\mathrm{\Delta }{k}_R=0.17{\AA }^{-1}$, $\mathrm{\Delta }{E}_R=68\mathrm{meV}$ [defined in (g)], and effective mass $m^{*}=1.62m_0$.