Photoemission of Bi$_2$Se$_3$ with Circularly Polarized Light: Probe of Spin Polarization or Means for Spin Manipulation?

Topological insulators are characterized by Dirac cone surface states with electron spins aligned in the surface plane and perpendicular to their momenta. Recent theoretical and experimental work implied that this specific spin texture should enable control of photoelectron spins by circularly polarized light. However, these reports questioned the so far accepted interpretation of spin-resolved photoelectron spectroscopy. We solve this puzzle and show that vacuum ultraviolet photons (50-70 eV) with linear or circular polarization probe indeed the initial state spin texture of Bi$_2$Se$_3$ while circularly polarized 6 eV low energy photons flip the electron spins out of plane and reverse their spin polarization. Our photoemission calculations, considering the interplay between the varying probing depth, dipole selection rules and spin-dependent scattering effects involving initial and final states explain these findings, and reveal proper conditions for light-induced spin manipulation. This paves the way for future applications of topological insulators in opto-spintronic devices.

Since the discovery of three-dimensional topological insulators (TI's), the spin properties of their surface states have been of central importance to the field [1]. Spin-resolved angleresolved photoemission spectroscopy (SR-ARPES) has become the most powerful and the sole tool in systematically revealing the spin polarization of the topological surface states (TSS's) in energy and momentum space. Understanding and utilization of the spin properties of TI materials are believed to be the key of measuring the topological invariances hidden in the bulk electronic wave functions [2], realizing exotic magnetic-spin physics such as the axion electrodynamics [3,4] or the magnetic monopole [5], as well as future spin-based low power transistors and devices. While extensive SR-ARPES studies on various TI compounds have successfully identified and confirmed the helical spin texture of the TSS's [6][7][8][9][10], much remains to be addressed regarding the critical response of the measured spin properties to the incident light and its polarizations (electric or magnetic fields).
In spite of the considerable success of SR-ARPES, it has been recently challenged by other experimental [11,12] and theoretical [13,20] proposals regarding both the efficiency and the reliability of the SR-ARPES measurements in studying the spin properties of TI surfaces. Part of these proposals involve the interpretation of the circular dichroism in the angular distribution (CDAD) of ARPES as the spin polarization of TSS's [11][12][13], which, if correct, can significantly improve the efficiency of spin detection. The CDAD effect has also been predicted as an indirect measure of the intrinsic momentum-space orbital angular momentum texture of the TSS's [14,15]. These interpretations are, however, unrealistic for several reasons and one is the dominance of final-state effects in CDAD from TI's which changes sign several times with photon energy [16]. Because of this dominance of final-state effects in an ARPES-based method, the influence of the photoemission process and the significance of conclusions drawn from SR-ARPES of TI's, so far conducted using linearly polarized light, are under question.
On the other hand, in the presence of strong spin-orbit coupling, such predicted orbital texture would likely be better coupled to and thus easier controlled by electric fields which can be utilized in coherent spin rotation [17], spin-orbit qubits [18], as well as photonpolarization driven spin current devices based on the spin-orbit coupled electrons on TI surfaces [19]. In this context, a recent theoretical work [20] has also raised concerns regarding the reliability of SR-ARPES in properly revealing the spin polarization of TSS's, in particular concerning the response of the measured spin properties to the polarization of the 3 incident light. Assuming strong spin-flip or spin-rotation effects during the photoemission process, it has been proposed that the spin texture of the photoelectrons (i.e., of the final states) is completely different from that of the TSS's in the initial state when linearly or circularly polarized light is used under specific experimental conditions and sample geometries, depending on the angle between light polarization and initial state spins [20]. Consequently, the measured spin texture of the photoelectrons should completely "lose memory" of the initial state spin texture and instead rotate depending on the chosen polarization of the incident light. However, it is important to note that the previously existing SR-ARPES data have been interpreted under the assumption that electron spins emitted from TI surfaces are conserved in the photoemission process. Following the first theoretical work [20], a recent SR-ARPES experiment using laser light of 6 eV photon energy [21] has reported spinresolved data strongly supporting the spin-rotation final-state scenario, and it was concluded that this scenario essentially dominates the spin polarization of photoelectrons emitted from TI's [21,22]. While such final-state effects are of high interest for the purpose of spin manipulation in opto-spintronics applications, these theoretical and experimental studies do on the other hand also strongly challenge the reliability and robustness of SR-ARPES in studying the spin properties of TI surfaces. Considering the fact that SR-ARPES is presently the only available tool for such a purpose, it is critically important to systematically study the impact of such final-state effects in SR-ARPES measurements under different experimental conditions. Namely, under which conditions the proposed final state effects are merely a weak perturbation on the initial spin texture and when they become enhanced or even dominate as proposed recently [20][21][22].
In the present work, we utilize the TSS of the prototype TI Bi 2 Se 3 as a platform to systematically investigate the recently proposed basis of manipulating the spin orientation of photoelectrons emitted from the surface of TI's by the polarization of the incident photons [20]. By using different experimental conditions and sample geometries, we investigate the reliability of SR-ARPES in studying the initial state spin texture of TSS's with linearly and circularly-polarized photons. We demonstrate the existence of two limiting cases where spin manipulation with light polarization is either a weak perturbation or strongly dominates the photoemission process. We further identify the underlying mechanism that triggers the spin polarization and support our experiments by comparing to results of one-step model photoemission calculations.

RESULTS
We perform SR-ARPES measurements on Bi 2 Se 3 films with linear p-and circularly polarized light of opposite helicities (C+ and C-) incident at an angle of φ = 45 • with respect to the sample normal. Because it is theoretically expected that light-induced manipulation of photoelectron spins must depend on the angle between light polarization and initial state spin [20], we use two different sample geometries shown in Fig. 1(a) (geometry I) and  Figure 1 shows SR-ARPES results of the in-plane spin polarization of the TSS and bulk valence band states of Bi 2 Se 3 measured using sample geometry I with different photon energies and light polarizations. In order to investigate the predicted spin-rotation finalstate effect [20], we first reverse the helicity of the circular light polarization to search for photon energies where the circular dichroism in ARPES changes its sign. We find for Bi 2 Se 3 pronounced sign changes in the CDAD signal between 50 and 70 eV. We note that these are different from the ones reported for Bi 2 Te 3 [16]. Specifically, the color representation of The reason is hexagonal warping [24] near the Fermi surface [see Fig. 2(i) (top)] which is rather small in Bi 2 Se 3 as compared to Bi 2 Te 3 [8].
Moreover, for linearly polarized light, the angle between linear light polarization and spin should lead to a change of the spin in the final state [20]. This results in a complex in-plane spin texture where the circulation of photoelectron spins around the Fermi surface appears similar to the one followed by a magnetic field in an idealized quadrupole [20,21]. Light polarization and in-plane spins are parallel in geometry II and perpendicular in geometry I but Fig. 2(f1) shows that the in-plane spin polarization has not changed compared to Fig.   1(d4), demonstrating that it is indeed independent of the sample geometry and follows the expected [7] initial state helical texture of surface-state electron spins.
This deviates from recent reports of nearly 100% spin polarization from TSS's in Bi 2 Se 3 [9,10]. We do not observe large nonzero spin polarization values at the Dirac point [10] or k-independent spin polarizations contributing to the specific spin texture of TSS's in the photoelectron distribution [10]. Considering the multiple orbital origin of the Bi 2 Se 3 surface states and their multiple contribution to the net spin polarization, a magnitude of ∼50%, as reported here, is consistent with first-principles calculations of Bi 2 Se 3 [25]. We do note that in Fig. 1 the measured spin polarization magnitude of the lower Dirac cone at photon energies of 50 eV and 60 eV appears considerably reduced as compared to that at 70 eV.
This can be understood based on the superposition of photoemission from the TSS and the bulk valence band, as the bulk bands in Bi 2 Se 3 are essentially unpolarized. Hence, at photon energies (effectively k ⊥ values) where the contribution of the bulk valence band is weak (such as 70 eV), we find that the spin polarization measured from the lower Dirac cone accordingly increases up to the expected value [25]. However, we find a completely different situation when using circularly polarized light at 6 eV photon energy, in agreement with recent findings [21]. Our laser SR-ARPES results

DISCUSSION
To resolve this issue and further explore the origin of these two contrasting experimental findings, we have performed one-step photoemission calculations including spin-dependent transition matrix elements between initial and final states. Figure 4 We also do note that in Fig. 4(a)  The fact that in Bi 2 Se 3 free-electron final states are not accessible at photon energies of the order of 50-70 eV becomes clear from, e.g., the reversal of the CDAD effect in ARPES (see Fig. 1), which involves transitions from p-type initial states to d-type final states [16,23]. To reach spin-degenerate free-electron final states in a reasonable approximation, much higher photon energies are required. Figure 4(b) shows calculations in normal incidence for such a condition (300 eV), where we find the result that the out-of-plane spin polarization reverses completely with the circular polarization, as theoretically predicted [20]. It is surprising that an experiment at 6 eV appears to confirm a theory that invokes free-electron final states. Therefore, we also performed calculations at 6 eV for comparison (please see Supplemental Material for details [23]). Our 6 eV calculations reveal that positive and negative circularly polarized photons reverse ∼25-30% out-of-plane spin polarization, in qualitative agreement with the calculation in Fig. 4 The above results show that we have to distinguish between three different spectral ranges, and this is also related to different inelastic mean free paths. The existence of lightinduced spin polarization control depends not only strongly on the final states, as discussed above, but additionally on the probing depth of the photoelectrons, which is considered in our theoretical model. The TSS of Bi 2 Se 3 extends several layers deep into the bulk (∼ 2-3 nm) and therefore appears for a wide range of probing depths. Indeed, enhanced bulk sensitivity at 6 eV photon energy (i. e., ∼ 1 eV kinetic energy) is provided by an order of magnitude larger probing depth than at 50-70 eV [26], and similarly at photon energies in the x-ray range. Specifically, our detailed analysis of the initial state identifies the low binding energy states in Bi 2 Se 3 as mainly arising from different p-orbitals of Bi (6p 3 ) and

(b) and the experiments in
Se (4p 4 ). This results in a layer-dependent spin-orbital texture with a large out-of-plane p z orbital character within the first quintuple layer (∼ 1 nm), and a significant in-plane p x,y contribution deeper below the surface. As a consequence, entanglement between orbital and spin-degrees of freedom due to strong spin-orbit coupling is present in our calculations when deeper lying layers are taken into account, as reported also in recent independent calculations [27]. In combination with dipole selection rules for different final states, this causes the light-  [29,30]. Initial and final states are obtained for a semi-infinite half-space using the low-energy electron diffraction method [31].