Photoelectron Spin-Polarization Control in the Topological Insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$

We study the manipulation of the spin polarization of photoemitted electrons in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ by spin- and angle-resolved photoemission spectroscopy. General rules are established that enable controlling the photoelectron spin-polarization. We demonstrate the $\pm 100\%$ reversal of a single component of the measured spin-polarization vector upon the rotation of light polarization, as well as full three-dimensional manipulation by varying experimental configuration and photon energy. While a material-specific density-functional theory analysis is needed for the quantitative description, a minimal yet fully generalized two-atomic-layer model qualitatively accounts for the spin response based on the interplay of optical selection rules, photoelectron interference, and topological surface-state complex structure. It follows that photoelectron spin-polarization control is generically achievable in systems with a layer-dependent, entangled spin-orbital texture.

Figure 1

(a)–(c) In-plane spin texture as obtained separately for the $p_x$ (a), $p_y$ (b), and $p_z$ (c) orbital contributions to the topological surface state (TSS). Red and blue arrows indicate the light electric field ($\pi /\sigma$ polarization) that must be used to excite photoelectrons from each of the individual orbitals, according to the electric dipole selection rules.

Figure 2

(a) ARPES dispersion of TSS Dirac fermions measured along the $\overline{M}$-$\overline{\mathrm{\Gamma }}$-$\overline{M}$ direction with $\pi$ polarization. (b) Schematics of the experimental geometry, with $\pi$ (horizontal) and $\sigma$ (vertical) linear polarization also indicated. (c) The top panel shows spin-ARPES EDCs, with spin quantization axis along the $y$ direction, measured with $\pi$ polarization along the gray bar highlighted in (a) [27]; the corresponding $P_y$ spin polarization is shown in the lower panel (the TSS is located at 0.1 eV in these data taken at $k_x=0.07{\AA }^{-1}$). (d) Spin-ARPES data analogous to those in (c), now measured with $\sigma$ polarization.

Figure 3

(a),(b) Schematics of photoelectron interference effects in two configurations: (a) $\pi$-polarization incident in the $xz$ plane probes $p_x$ and $p_z$ orbitals with the same spin state (Fig. 1); (b) when incident in the $yz$ plane, $\pi$ polarization probes $p_y$ and $p_z$ orbitals with opposite spin states (Fig. 1). (c)–(e) Spin polarization curves at the $+k_x$ point as sketched in (e), measured for (a) or (b) configurations (red or blue curves). (f)–(h) Spin polarization curves at $\pm k_x$ as sketched in (h) for the (b) configuration, together with $k_x=\pm 0.04{\AA }^{-1}$ DFT calculated values [28] [for the red data in (c)–(e), DFT gives $\mathrm{P⃗}=(0,-1,0)$].

Figure 4

(a)–(c) Solid blue lines: calculated photon-energy dependence of the photoelectron spin-polarization-vector components, as obtained at the $-k_y$ point for $\pi$-polarized light incident in the $xz$ plane as shown in the sketch in (d). Solid red symbols are spin-ARPES data from this work; open red symbols are from Refs. [16, 17]; solid yellow symbols were measured on crystals from Golden’s group [31] and a 6-quintuple-layer film (22 eV data) by Tjernberg and collaborators [32].