Widespread spin polarization effects in photoemission from topological insulators

High-resolution spin- and angle-resolved photoemission spectroscopy (spin-ARPES) was performed on the three-dimensional topological insulator Bi${}_2$Se${}_3$ using a recently developed high-efficiency spectrometer. The topological surface state's helical spin structure is observed, in agreement with theoretical prediction. Spin textures of both chiralities, at energies above and below the Dirac point, are observed, and the spin structure is found to persist at room temperature. The measurements reveal additional unexpected spin polarization effects, which also originate from the spin-orbit interaction, but are well differentiated from topological physics by contrasting momentum and photon energy and polarization dependencies. These observations demonstrate significant deviations of photoelectron and quasiparticle spin polarizations. Our findings illustrate the inherent complexity of spin-resolved ARPES and demonstrate key considerations for interpreting experimental results.

Figure 1

(a) Cartoon depictions of the defining spin-polarized characteristics of the topological insulator surface states, in real and momentum space. (b) Diagram illustrating the sample and experiment geometry in the spin-resolved measurements. Photoelectrons are collected along the vector ${\mathbf{k}}_{\mathbf{e}}$ that is a fixed 45${}^{\circ }$ from the incident photon direction, both of which are fixed in the horizontal $xz$ plane. Spectra are taken along $\Gamma$M ($\Gamma$K) by rotating the sample about the $y$ axis ($x$ axis). (c) spin-ARPES intensity map of Bi${}_2$Se${}_3$ as a function of binding energy and momentum along the $\Gamma$M direction, taken with hv = 36 eV at 20 K. The inset depicts the theoretical band structure, with the projection of the bulk bands in gray, and the TSS in blue (red) according to its spin-up (-down) polarization, quantized along the perpendicular ${\widehat{\mathbf{k}}}_y$ direction. (d) spin-ARPES-derived Fermi surface. The theoretical spin polarization orientation of the TSS at E${}_F$ is depicted by the white arrows. The inset depicts the surface Brillouin zone and the TSS (orange ring) and BCB (gray circle) contributions to the Fermi surface.

Figure 2

(a) Spin-integrated EDCs as a function of momentum along $k_x$ ($\Gamma$M) of Bi${}_2$Se${}_3$. UDC peaks are marked by blue (spin-up) and red (spin-down) arrows according to the predicted $P_y$. Other peaks are related to bulk bands. (b) Spin-resolved EDCs corresponding to the red EDC in (a), with the spin quantization axis along the out-of-plane $\widehat{\mathbf{z}}$ direction (upper), and the in-plane $\widehat{\mathbf{y}}$ direction (lower). The EDC location is depicted by the vertical green line in the TSS cartoon inset, and the green circle in the Fig. 1d inset. The corresponding spin polarization curves are shown in the bottom panel. Open black circles are the raw $P_y$, while the solid gray circles correspond to the effective polarization once a constant background (dash-dot line in upper panel) is removed. Inset shows closeup of spin-resolved Fermi level with Fermi edge fits.

Figure 3

(a) Spin-resolved EDCs along $k_x$ ($\Gamma$M). Approximate locations are shown by vertical green lines in left insets and corresponding green circle and dots in the Fig. 1d inset. Spin polarization curves for the two extreme $k$-space locations at $\pm k_x$ and at $\Gamma$ are shown in the lower panel. (b) Same as for (a), except along $k_y$ ($\Gamma$K). (c) Same as for (a), except at room temperature. All other panels are at 20 K.

Figure 4

(a) Spin-resolved EDCs of the Bi 5$d$ core levels. (b) Polarization (integrated across width of peak) of the 5$d^{5/2}$ core level, as a function of incident photon energy.

Figure 5

Spin-resolved EDCs of VB peak, taken along $k_x$ ($\Gamma$M), similar to Fig. 2b. Spin is measured along $\widehat{\mathbf{y}}$. The upper (lower) EDC is taken with $p$-polarized ($s$-polarized) light with $\widehat{\mathbf{\epsilon }}$ within the $xz$ plane ($yz$ plane). The reported $P_y$ values for each are integrated through the full energy range shown.

Figure 6

(a) Spin-integrated EDCs as a function of momentum along $k_x$ ($\Gamma$M) with hv = 70 eV. Peaks related to the TSS are marked by blue (spin-up) and red (spin-down) arrows according to their polarization along $\widehat{\mathbf{y}}$. Other features are related to the bulk bands. (b) Same as (a), except along $k_y$ ($\Gamma$K). Peaks related to the TSS are marked by purple arrows, and are not expected to be polarized along $\widehat{\mathbf{y}}$. (c) Spin-resolved EDCs along $k_x$ ($\Gamma$M). Spin is measured along $\widehat{\mathbf{y}}$. Approximate locations are shown by vertical green lines in left inset and the center and outer dots in the Fig. 1d inset. The corresponding spin polarization curves are shown in the lower panel. (d) Same as (c), except along $k_y$ ($\Gamma$K).