Orbital-Driven Rashba Effect in a Binary Honeycomb Monolayer AgTe

Maximilian Ünzelmann, Hendrik Bentmann, Philipp Eck, Tilman Kißlinger, Begmuhammet Geldiyev, Janek Rieger, Simon Moser, Raphael C. Vidal, Katharina Kißner, Lutz Hammer, M. Alexander Schneider, Thomas Fauster, Giorgio Sangiovanni, Domenico Di Sante, and Friedrich Reinert

Phys. Rev. Lett. 124, 176401 – Published 29 April 2020

Abstract

The Rashba effect is fundamental to the physics of two-dimensional electron systems and underlies a variety of spintronic phenomena. It has been proposed that the formation of Rashba-type spin splittings originates microscopically from the existence of orbital angular momentum (OAM) in the Bloch wave functions. Here, we present detailed experimental evidence for this OAM-based origin of the Rashba effect by angle-resolved photoemission (ARPES) and two-photon photoemission experiments for a monolayer AgTe on Ag(111). Using quantitative low-energy electron diffraction analysis, we determine the structural parameters and the stacking of the honeycomb overlayer with picometer precision. Based on an orbital-symmetry analysis in ARPES and supported by first-principles calculations, we unequivocally relate the presence and absence of Rashba-type spin splittings in different bands of AgTe to the existence of OAM.

Received 27 November 2019
Accepted 25 March 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.176401

Physics Subject Headings (PhySH)

Electronic structure Rashba coupling

2-dimensional systems

Angle-resolved photoemission spectroscopy First-principles calculations Low-energy electron diffraction Two-photon photoelectron spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Maximilian Ünzelmann¹, Hendrik Bentmann^1,*, Philipp Eck², Tilman Kißlinger³, Begmuhammet Geldiyev³, Janek Rieger³, Simon Moser⁴, Raphael C. Vidal ¹, Katharina Kißner¹, Lutz Hammer ³, M. Alexander Schneider³, Thomas Fauster ³, Giorgio Sangiovanni ², Domenico Di Sante ², and Friedrich Reinert¹

¹Experimentelle Physik VII and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany
²Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, 97074 Würzburg, Germany
³Lehrstuhl für Festkörperphysik, Universität Erlangen-Nürnberg, Staudtstraße 7, D-91058 Erlangen, Germany
⁴Experimentelle Physik IV and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany

^*Hendrik.Bentmann@physik.uni-wuerzburg.de

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Vol. 124, Iss. 17 — 1 May 2020

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Images

Figure 1
(a) LEED image of the AgTe honeycomb lattice on Ag(111) forming a $(\sqrt{3} \times \sqrt{3}) - R 30 °$ -Te superstructure. (b) Corresponding large-scale STM image (tunneling parameters $U_{b} = 80 mV$ and $I_{t} = 1.0 nA$ ) showing a defect density below 1%. (c) Comparison of selected LEED-I-V spectra (red) and best-fit curves (blue). The single-beam $R$ factors of the shown spectra are close to the overall fit quality of $R = 0.15$ . (d) Atomically resolved STM image ( $U_{b} = 100 mV$ and $I_{t} = 1.0 nA$ ) of the AgTe honeycomb lattice together with the simulated STM image as obtained by our DFT calculations. The bright protrusions are clearly the slightly outward buckled Te atoms. (e) Top view of the surface structure showing the hcp-like stacking of the outermost surface layer as determined from LEED-I-V. (f) Side view with geometrical parameters as obtained from the LEED-I-V analysis (green) and DFT (red), respectively.
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Figure 2
Band structure of an AgTe monolayer on Ag(111). (a) Angle-resolved photoemission ( $h ν = 21.21 eV$ , He $I_{α}$ ) and two-photon photoemission ( $h ν = 1.55 + 4.65 eV$ ) datasets measured along $\bar{Γ} \bar{K}$ and $\bar{Γ} \bar{M}$ , respectively. Two holelike bands, $α$ and $β$ , are observed in the occupied regime below $E_{F}$ , and one electronlike band, $γ$ , is found above $E_{F}$ . The band $β$ shows a sizable Rashba-type spin splitting into the branches $β_{\pm}$ , as also visible in the EDC at a $k_{∥}$ marked by the dashed line. (b) DFT band structure calculation for $AgTe / Ag (111)$ . The size of the dots indicates the localization of the states in the AgTe monolayer. (c) Top panel: Spin-orbit splitting of $α$ , $β$ , and $γ$ in dependence of $k_{∥}$ as extracted from the DFT calculation in (b). Bottom panel: Measured spin-orbit splitting of $β$ as determined from the data in (a). Lines in the top and bottom panels are linear or cubic fits to the data points as labeled.
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Figure 3
Orbital composition of the band structure. Constant energy cuts (CECs) of the measured band structure taken at $E - E_{F} = - 950$ (a) and $- 1300 meV$ (b) with $s$ -polarized light at $h ν = 65 eV$ . (c) Sketch of tangential $p_{t}$ and radial $p_{r}$ in-plane orbital configurations. Colored (gray) orbitals indicate an enhanced (suppressed) ARPES intensity in a CEC for $s$ - and $p$ -polarized light, as expected from dipole-selection rules (see the text for details). (d) CEC at $- 1300 meV$ obtained with $p$ -polarized light at $h ν = 25 eV$ . The plane of light incidence for all measurements is the $x z$ plane as indicated by the arrow in (a), enabling intensity asymmetries along $\pm k_{x}$ . (e) Orbital-polarization parameter $λ (k_{∥})$ as extracted from ARPES data measured with $s$ -polarized light (see the text for details). (f) DFT calculation of the AgTe band structure projected onto tangential and radial Te $p$ orbitals.
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Figure 4
OAM in the band structure of AgTe [48]. (a),(b) Calculated $⟨ L_{y} ⟩ OAM$ -projected bands in AgTe as obtained with and without including SOC. The green (orange) color code refers to positive (negative) $⟨ L_{y} ⟩ OAM$ . (c) Linear dichroism $I (k_{x}, k_{y}) - I (- k_{x}, k_{y})$ obtained from the CEC in Fig. 3. (d) Calculated $⟨ L_{y} ⟩ OAM$ on a CEC at an energy indicated in (b).
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