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Local Berry curvature signatures in dichroic angle-resolved photoelectron spectroscopy from two-dimensional materials

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Science Advances  28 Feb 2020:
Vol. 6, no. 9, eaay2730
DOI: 10.1126/sciadv.aay2730
  • Fig. 1 Illustration of the Berry curvature and orbital angular momentum.

    The surfaces represent the valence and conduction band, while the coloring indicates the Berry curvature. The arrows illustrate the orbital angular momentum of the valence band.

  • Fig. 2 Setup and circular dichroism in graphene.

    (A) Sketch of the calculation setup: photoemission by left-hand circularly polarized light (LCP) or right-hand circularly polarized light (RCP), with polarization vector in the plane. (B) Band structure of graphene close to the Dirac point with zero (black line) and enhanced (blue line) SOC, respectively, obtained from density functional theory (DFT). The first Brillouin zone (BZ) of the system with honeycomb lattice is shown in the inset. The shaded boxes indicate the magnified regions shown in (C) to (F). (C and D) Total ARPES intensity Itot (k, εf) (normalized to its maximum value Imax) at εf = 47 eV, close to the K and Kˊ point, respectively. (E and F) Corresponding dichroic signal ICD (k, εf). The quasi-momentum is measured in atomic units (a.u.) (inverse Bohr). (G) Integrated signal [over the shaded regions in (B)] Itot and ICD as a function of the binding energy (circles, TDDFT results; lines, TB + PW model). The black arrow indicates the energy for which the angle-resolved intensities in (C) to (F) are shown. arb. u. (arbitrary units). (H) Integrated signal from spin-up electrons [analogous to (G)] for graphene with enhanced SOC.

  • Fig. 3 Berry curvature and circular dichroism in hBN.

    (A) Berry curvature Ωv(k) of the top valence band, comparing TDDFT and TB results. The angular momentum amounts to Lz = 0.1 at K and Lz = −0.1 at Kˊ. (B and C) Total ARPES intensity Itot(k, εf) at εf = 45.811 eV. (D and E) Corresponding circular dichroism. The color coding is analogous to Fig. 2. (F and G) The integrated signals as a function of the binding energy at K and Kˊ, respectively.

  • Fig. 4 Circular dichroism in BiH.

    (A) Lattice structure of hexagonal BiH. (B) Band structure of hydrogenated bismuthane (BiH; obtained from DFT), fully including SOC (black) and, for the purpose of comparison, without any SOC (blue lines). (C) Integrated dichroic signal as in Fig. 2 for spin-up (left panels) and spin-down (right panels) electrons at K (top panels) and Kˊ (bottom panels), respectively.

  • Fig. 5 Circular dichroism and topological phase diagram for the Haldane model.

    Energy- and valley-integrated circular dichroism SCD around the K (A) and Kˊ (B) valley, respectively, as a function of the phase ϕ and gap parameter M. (C) Asymmetry signal ΔSCD (see text): red color corresponds to ΔSCD = 1, blue corresponds to ΔSCD = −1, and white corresponds to ΔSCD = 0. The dashed lines represent the critical gap Mcrit(ϕ), for which M > Mcrit(ϕ) turns the system into a trivial insulator. The Chern numbers C are given for each phase. The parameters are analogous to graphene, with J′ = 0.1J.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/9/eaay2730/DC1

    Section S1. SOC effects in graphene and BiH

    Section S2. Orbital angular momentum and Berry curvature in multiband systems

    Section S3. Wave-packet picture

    Section S4. TB modeling of photoemission

    Section S5. Pseudospin picture

    Section S6. Orbital polarization for monolayer TMDCs

    Fig. S1. Spin as quantum number.

    Fig. S2. Orbital polarization and Berry curvature of BiH.

    Fig. S3. Angular momentum in hBN.

    Fig. S4. Topological properties of monolayer TMDCs.

  • Supplementary Materials

    This PDF file includes:

    • Section S1. SOC effects in graphene and BiH
    • Section S2. Orbital angular momentum and Berry curvature in multiband systems
    • Section S3. Wave-packet picture
    • Section S4. TB modeling of photoemission
    • Section S5. Pseudospin picture
    • Section S6. Orbital polarization for monolayer TMDCs
    • Fig. S1. Spin as quantum number.
    • Fig. S2. Orbital polarization and Berry curvature of BiH.
    • Fig. S3. Angular momentum in hBN.
    • Fig. S4. Topological properties of monolayer TMDCs.

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