Spin polarization of photoelectrons emitted from spin-orbit coupled surface states of Pb/Ge(111)

Microscopy, 2024, 73(5), 439–445 DOI: https://doi.org/10.1093/jmicro/dfae021 Advance Access Publication Date: 25 April 2024 Article Spin polarization of photoelectrons emitted from spin-orbit coupled surface states of Pb/Ge(111) Koichiro Yaji 1,* , Kenta Kuroda 2,3 , Shunsuke Tsuda 1 and Fumio Komori 1 1 Center for Basic Research on Materials, National Institute for Materials Science, 3-13 Sakura, Tsukuba, Ibaraki 305-0003, Japan Graduate School of Advanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8526, Japan 3 International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM2 ), Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8526, Japan 2 To whom correspondence should be addressed. E-mail: Abstract We report that the spin vector of photoelectrons emitted from an atomic layer Pb grown on a germanium substrate [Pb/Ge(111)] can be controlled using an electric field of light. The spin polarization of photoelectrons excited by a linearly polarized light is precisely investigated by spin- and angle-resolved photoemission spectroscopy. The spin polarization of the photoelectrons observed in the mirror plane reverses between p- and s-polarized lights. Considering the dipole transition selection rule, the surface state of Pb/Ge(111) is represented by a linear combination of symmetric and asymmetric orbital components coupled with spins in mutually opposite directions. The spin direction of the photoelectrons is different from that of the initial state when the electric field vector of linearly polarized light deviates from p- or s-polarization conditions. The quantum interference in the photoexcitation process can determine the direction of the spin vector of photoelectrons. Key words: spin polarization, surface state, spin-orbit coupling, quantum interference, spin- and angle-resolved photoemission spectroscopy, Pb/Ge(111) Introduction Spintronics utilizing both charge and spin has been intensively studied because of the potential for high-speed and energysaving devices. It is essential to control the spin direction to apply electron spin in devices, typically achieved through external magnetic fields, electric fields, lights and heat. On the other hand, electrons exhibit wave-like characteristics, allowing them to undergo superposition and interference. According to quantum mechanics, the superposition of spinup and spin-down states can yield an arbitrarily oriented spin state. Spin control using coherent spin has been proposed and demonstrated in qubits so far [1,2], and their practical applications are anticipated in future quantum computing and quantum communication [3]. In a general consequence of the spin-orbit coupled systems, such as topological insulators and Rashba spin-split systems, the spin and momentum of the surface states are strongly coupled to each other, and the surface state exhibits helical spin texture, the so-called spin-momentum locking (Fig. 1a). In more detail, the direction of the spin vector depends on the symmetry of the orbital wavefunctions due to the spin-orbit coupling [4–9]. In particular, the symmetric and asymmetric parts of the wavefunction are coupled to spins pointing to mutually opposite directions when the system has mirror symmetry (Fig. 1b) [10]. This has been demonstrated experimentally and theoretically in Bi(111) and Bi2 Se3 (111), in which the spin polarizations of photoelectrons emitted from the surface states by p- and s-polarized lights have reversed each other [8–12]. Meanwhile, the spin direction of the photoelectron differs from the initial states when the excitation light has deviated from the p- and s-polarization conditions [10,12]. A lead atomic layer grown on a germanium (111) substrate [Pb/Ge(111)] is a prototypical example of a metallic surface state on a semiconductor substrate with a large Rashba spin splitting [13]. The surface structure of Pb/Ge(111) is well established, where one Pb atom is located at the H3 site and three Pb atoms at the off-center bridge position between the T1√and T √4 sites (Fig. 2a) [14–17]. The surface periodicity is ( 3 × 3) R30∘ . The (11) plane is a mirror ̄ ̄ plane√parallel √ to the ΓK axis of the surface Brillouin zone of the ( 3 × 3) R30∘ periodicity. The band structures along the Γ̄ M̄ and Γ̄ K̄ directions have been investigated by angleresolved photoemission spectroscopy (ARPES), and several surface states have been reported [18]. Besides, the spin polarization of the metallic surface state in Γ̄ M̄ is confirmed by both spin- and angle-resolved photoemission spectroscopy (SARPES) and theoretical calculations [13]. However, the spin ̄ direction has not been investigated. The polarization in the Γ̄ K√ √ Γ̄ K̄ direction of the ( 3 × 3) R30∘ periodicity is parallel to the mirror plane of the crystal. Thus, the spin-split electronic states in the Γ̄ K̄ direction are suitable for the demonstration of the quantum interference in the photoexcitation process based on the mirror symmetry. Received 22 January 2024; Revised 15 April 2024; Editorial Decision 19 April 2024; Accepted 22 April 2024 © The Author(s) 2024. Published by Oxford University Press on behalf of The Japanese Society of Microscopy. This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial License (https://creativecommons.org/ licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact for reprints and translation rights for reprints. All other permissions can be obtained through our RightsLink service via the Permissions link on the article page on our site–for further information please contact . * 440 K. Yaji et al. Photoelectron spin emitted from Pb/Ge(111) Results and discussion In the present study, we report on the spin polarization of photoelectrons emitted from the surface states o Pb/Ge(111) excited by a linearly polarized light investigated by SARPES. The spin polarization of the photoelectrons in the Γ̄ K̄ mirror plane reverses between the p- and s-polarized lights. Furthermore, the spin direction of the photoelectron is modulated from that of the initial state when the electric field vector of the linearly polarized light deviates from the p- or s-polarization conditions. The changes in the spin polarization of photoelectrons are attributed to the quantum interference in the photoexcitation process. We demonstrate that the spin direction of photoelectrons can be controlled by orbital-selective photoexcitation from strongly spinorbit coupled surface states with polarized lights. The present concept is applicable to spin-polarized electron sources. Methods Experiments were conducted in an ultra-high vacuum environment with a base pressure of <1 × 10−8 Pa. The clean surface of the Ge(111) substrate was prepared by repeated cycles of A (...truncated)