Spin-polarized saddle points in the topological surface states of elemental bismuth revealed by pump-probe spin- and angle-resolved photoemission spectroscopy (2024)

Authorization Required

×

×

• 

  Figure 1

  (a)Crystal structure of Bi in the (111) orientation. (b)Brillouin zone for bulk and (111) surface. (c)Schematic band structure along the $\overline{\mathrm{\Gamma }}$ - $\overline{\mathrm{M}}$ direction on the Bi(111) surface. Blue and red lines show the surface bands (SS1 and SS2) with in-plane spin polarization in opposite directions. (d)–(g) All possible relationships between surface and bulk bands around $\overline{\mathrm{M}}$ corresponding to different bulk topologies. [31].

  Reuse & Permissions

• 

  Figure 2

  Band structures of Bi revealed by pump-probe ARPES. (a)Fermi surface map. (b), (c)Band dispersion along $\overline{\mathrm{\Gamma }}$ - $\overline{\mathrm{M}}$ measured without and with pump. (d)Energy contour maps on the unoccupied side from 0.10 to 0.25eV. (e), (f) Band dispersions crossing the saddle point along $k_x$ and $k_y$ [momentum cuts e and f marked in (d)]. (g) Three-dimensionally plotted ARPES intensities along $k_x,k_y$, and energy. (h) Schematic of spin-polarized saddle points with a hexagonal structure. Magenta arrows in (c), (e), (f), and (g) indicate the saddle point.

  Reuse & Permissions

• 

  Figure 3

  Spin texture of surface states in Bi revealed by pump-probe spin-ARPES. (a), (b)Spin polarization and spin-polarized band along $\overline{\mathrm{\Gamma }}$ - $\overline{\mathrm{M}}$, respectively. Red and blue represent up and down spin in the $Y$ direction for two surface bands (SS1 and SS2). The painted areas in (a)represent errors (see more details in the Supplemental Material [55]). (c)High-resolution map of spin polarization around $\overline{\mathrm{M}}$ within the black frame in (b). (d)Spin-resolved EDCs at $k^{\prime }\mathrm{s}$ marked by arrows in (c). Energy positions of surface bands are pointed by red and blue arrows. Black curves are the addition of the up- and down-spin spectra. (e) Surface bands determined from spin-resolved EDCs. Fitting curves to the data (solid and dotted lines) are overlayed.

  Reuse & Permissions

• 

  Figure 4

  Bulk bands and their relationship with surface bands. (a)Pump-probe ARPES map around $\overline{\mathrm{M}}$. Here, the original spectra are symmetrized across $\overline{\mathrm{M}}$ to remove the matrix element effect. They are also divided by the Fermi-Dirac distribution function at the electron temperature (250K) estimated from the spectral edge broadening due to the pumping. (b)MDCs of (a). Thick black lines represent energies of two surface bands. Intensities of BCB and BVB are each painted green and orange. (c)Bulk bands (color bars) obtained from (b)and surface bands (dashed lines) determined in Fig.3 are superimposed. (d)Schematic band structure and characteristic energies obtained in our experiments.

  Reuse & Permissions

• 

  Figure 5

  (a)Comparison of characteristic energies in band structures obtained: bottoms of BCB at $\overline{\mathrm{\Gamma }}$ and $\overline{\mathrm{M}}$, energy of vHS, and energy gaps at $\overline{\mathrm{M}}$ between BCB and BVB (${\mathrm{\Delta }}_{\mathrm{B}}$) and between SS1 and SS2 (${\mathrm{\Delta }}_{\mathrm{S}}$). Bulk topology is also listed. $\alpha$ is a parameter of the modified Becke-Johnson potential used in our calculations. (b)First-principles band calculations of semi-infinite layer Bi(111) along $\overline{\mathrm{\Gamma }}$- $\overline{\mathrm{M}}$ for different $\alpha$ values. $\alpha$=1.0 corresponds to the original band, whereas the states with $\alpha$ less than 1.0 are assigned as trivial ($Z_2=0)$, and those with larger $\alpha \mathrm{s}$ are as nontrivial ($Z_2=1)$.

  Reuse & Permissions

×