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Giant Rashba splitting in 2D organic-inorganic halide perovskites measured by transient spectroscopies

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Science Advances  28 Jul 2017:
Vol. 3, no. 7, e1700704
DOI: 10.1126/sciadv.1700704
  • Fig. 1 Introduction to Rashba splitting and the 2D layered hybrid perovskite PEPI.

    (A) Schematic electron dispersion relation of a regular CB that shows a doubly spin-degenerate parabolic band having a single minimum at k = 0. (B) Same as in (A) but subjected to Rashba splitting; two parabolic branches having opposite spin sense are formed. The Rashba energy (ER) and momentum offset (k0) are denoted. (C) Structure of PEPI having alternating organic (C6H5C2H4NH3+) and inorganic [PbI6]4− layers that form multiple quantum wells. (D) Absorption (Abs) and PL spectra of PEPI film at room temperature. a.u., arbitrary units.

  • Fig. 2 Absorption and EA spectra of PEPI film.

    (A) Absorption spectra of PEPI film at various temperatures. The 1s and 2s exciton (E1s and E2s, respectively) and an IB transition are assigned. OD, optical density. (B) EA spectra of PEPI measured at 45 K at various applied electric fields (the applied voltage, V). Various EA spectral features are assigned. (C) EA spectra close to the zero-crossing energy “c” measured at various field strengths; broadening of the FK oscillation is seen. “c” represents zero crossing energies, and “d” represents the high-energy FK oscillation that blueshifts with increasing field. (D) Field broadening of the EA features related to the FK oscillation; “a,” “b,” “c,” and “d” are assigned as zero-crossing energies and peak positions, respectively. The inset shows the peak values of EA versus V2 of bands b and d, which saturate at large V. (E) Energy differences δEac and δEbc plotted versus V2/3. (F) Energy levels of the excitons (E1s and E2s) and interband transition [E(IB)] are assigned with respect to the ground state (GS).

  • Fig. 3 Ultrafast PM spectroscopy of PEPI film excited at 3.1 eV.

    (A) PM spectrum at t = 0 ps; PA1, PA2, and PM are assigned. The solid line through the data points of PA1 shown in the inset is a fit using a theoretical model for the exciton transition into the continuum (see main text and the Supplementary Materials). (B) Decay dynamics of the PM band at 2.4 eV and PA1 at 0.36 eV up to 500 ps. The lines through the data points are fits using double exponential decay (A1e-t/t1 + A2et/t2 + C), where t1 = 11.9 and 11.8 ps, t2 = 103 and 108 ps, and C = 0.003 and 0.094 for the PA1 and PM bands, respectively. (C) Schematic energy diagram with Rashba splitting that explains the PA1 transition. The Rashba energy (ER) may be obtained from the one-quarter of energy difference (ΔE) between PA1 transition and the 1s exciton binding energy (Eb).

  • Fig. 4 DFT calculations on the 2D perovskite.

    (A) One layer of the Pb-I octahedra that describes the relaxed structure of the PEPI used in the DFT calculations. The Pb atom (gray sphere) is displaced from the octahedra center along the a + b direction, which breaks off the inversion symmetry, resulting in Rashba splitting caused by SOC. The unit cell vectors a and b lie in the x-y plane with an angle of 99.7° between them. (B) Schematic of the CB energy dispersion near the R point in the Brillouin zone, where k1(2) is directed along the a +(−) b direction. (C) Electronic band structure near the R point, which shows the Rashba splitting along a direction perpendicular to the symmetry-breaking direction; c1 and c2 represent the lower and upper Rashba bands, respectively. (D) DFT-calculated momentum matrix elements versus k near the band minimum (at k0 = 0.07 Å−1) away from the R point along the (1, −1) direction. Red and blue lines correspond to x and y component of the momentum matrix element between lowest CB c1 and itself, showing the vanishing transition between the exciton and lowest Rashba split CB at k = k0. The green curve is the z component of the momentum matrix element between the Rashba split bands c1 and c2, which is nonzero for all k. The y axis is dimensionless, with the computed momentum p presented in terms of its value in Rydberg units: p0 = 1.99 × 10−24 kg/(m·s).

  • Fig. 5 Steady-state PM spectroscopy of PEPI film excited at 2.8 eV.

    (A) PM spectrum of PEPI film compared to that of a silicon wafer measured at modulation frequency of 350 Hz and temperature of 45 K. The PA bands, PAFCA for PEPI and FCA for Si, are assigned. The solid lines through the data points are fits using the Drude model (PA, ~ω−2) for the Si wafer and eq. S4 for the PEPI (see the Supplementary Materials). (B) Schematic electron energy bands with Rashba splitting that explain the FCA in PEPI. The Rashba energy (ER) and momentum offset (k0 = Δq/2) are assigned.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/7/e1700704/DC1

    Supplementary Text

    Fitting the PA1 band at t = 0 ps shown in Fig. 3A

    Inter-Rashba optical transitions in 2D perovskites

    DFT calculations

    Fitting the PAFCA band shown in Fig. 5A

    fig. S1. Schematic structure of PEPI with alternating organic and inorganic layers, forming multiple quantum wells onto the substrate.

    fig. S2. The absorption spectrum of a PEPI film measured at temperatures ranging from 10 to 290 K, as denoted.

    fig. S3. The dependence of the EA signal on V2 at various energies below the IB edge at 2.55 eV, where V is the applied voltage.

    fig. S4. The transient PM band of PEPI film measured at t = 0 ps and 300 K and its fit using a linear combination of the absorption spectrum and its first and second derivatives.

    References (3438)

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Text
    • Fitting the PA1 band at t = 0 ps shown in Fig. 3A
    • Inter-Rashba optical transitions in 2D perovskites
    • DFT calculations
    • Fitting the PAFCA band shown in Fig. 5A
    • fig. S1. Schematic structure of PEPI with alternating organic and inorganic layers, forming multiple quantum wells onto the substrate.
    • fig. S2. The absorption spectrum of a PEPI film measured at temperatures ranging from 10 to 290 K, as denoted.
    • fig. S3. The dependence of the EA signal on V2 at various energies below the IB edge at 2.55 eV, where V is the applied voltage.
    • fig. S4. The transient PM band of PEPI film measured at t = 0 ps and 300 K and its fit using a linear combination of the absorption spectrum and its first and second derivatives.
    • References (34–38)

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