Hierarchical spin-orbital polarization of a giant Rashba system

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Science Advances  25 Sep 2015:
Vol. 1, no. 8, e1500495
DOI: 10.1126/sciadv.1500495
  • Fig. 1 Surface electronic structure of BiTeI.

    (A) ARPES measurements of the Fermi surface and near-EF band dispersions measured ( = 52 eV, p-polarization) from the Te-terminated surface of BiTeI. (B) A lack of inversion symmetry of the bulk crystal structure together with strong spin-orbit coupling mediates a large Rashba-like spin splitting. Additionally, the polar nature of the Te-terminated surface induces a strong downward band bending, causing a ladder of Rashba-split subband states to emerge in the near-surface quantum well. (C) These are clearly resolved in measurements of the dispersion along Γ–M. The conventional spin texture associated with such Rashba splitting is shown schematically by colored arrows, with the spin expected to lie predominantly in the surface plane.

  • Fig. 2 Disentangling intertwined atomic and orbital characters.

    (A) Fermi level momentum distribution curve (EF ±15 meV) measured along Γ–M as a function of probing photon energy using p-polarized light. No dispersion is observed, indicating 2D states consistent with our assignment of quantum well subbands, whereas strong matrix element variations give rise to pronounced intensity modulations. (B) Extracted spectral weight of the outermost band (kF ≈ −0.2 Å−1) as a function of binding energy, revealing characteristic intensity enhancement due to resonant photoemission at the Bi O-edge. (C and D) Corresponding dispersions (along Γ–M) measured on-resonance ( = 28 eV) and off-resonance ( = 30 eV), respectively, with p-polarized (left) and s-polarized (center) light. The difference in spectral weight between these dispersions (right) indicates a band and element-dependent orbital polarization.

  • Fig. 3 py-projected spectral weight distribution.

    (A) Experimental geometry for our measurements and (B to D) resulting CESs measured using s-polarized light to probe the py orbital character at 200 meV above, exactly at, and at 100 meV below the Dirac point (ED) formed by the crossing of the two spin-split branches of the lowest subband. On-resonance measurements ( = 28 eV) with the scattering plane aligned to (B) Γ–M and (C) Γ–K, and (D) off-resonance ( = 30 eV, scattering plane along Γ–K) measurements show pronounced angular variations in spectral weight, characteristic of strongly momentum-dependent orbital textures.

  • Fig. 4 Mapping the angle-dependent orbital wave functions.

    (A) Angular distribution of the Bi py-projected spectral weight distribution measured on-resonance around the inner band of CESs (see, for example, Fig. 3B), each normalized to its average value. Above (below) the Dirac point, ED, this is peaked at an azimuthal angle of α = π/2 (0 and π) indicative of a tangential (radial) in-plane orbital alignment. (B) The smooth evolution between these two configurations is captured by the relative spectral weight ADF, λ(ω) = [Iα=π/2(ω) − Iα=0,π(ω)]/[Iα=π/2(ω) + Iα=0,π(ω)], which crosses zero at the Dirac point within our experimental error. (C) This behavior is fully captured by the momentum-dependent Bi py:px in-plane orbital polarization, ζ(ω, k), extracted from our density functional theory (DFT) calculations. (D) The in-plane orbital polarization is reversed for the Te-projected component, with radial alignment above the Dirac point and tangential alignment below ED, as also captured by the opposite ADF measured off-resonance (hν = 30 eV; see Fig. 3C, summarized in B).

  • Fig. 5 Hierarchy of atomic, spin, and orbital coupling in BiTeI.

    (A) Schematic representation of disparate in-plane orbital textures uncovered for the inner and outer “spin-split” branches of a model Rashba system. (B to D) Corresponding spin textures calculated from DFT for Bi (B) px, (C) py, and (D) pz projections of CESs 200 meV above the Dirac point. The in-plane spin texture is shown by arrows, and the out-of-plane by the background color, both in units of ℏ/2. (E) Schematic of the in-plane spin textures coupled to the net in-plane and out-of-plane orbital textures. (F) Circular dichroism measurements performed on-resonance (hν = 28 eV, CES at ED + 200 meV), revealing a significant sixfold modulation for the outer band indicative of pronounced out-of-plane spin canting.

Supplementary Materials

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. Photon energy–dependent ARPES.
    • Fig. S2. Calculated surface electronic structure of BiTeI.
    • Fig. S3. Coupled Te spin-orbital texture.
    • References (39, 40)

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