Research ArticleMATERIALS SCIENCE

Large polarons in lead halide perovskites

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Science Advances  11 Aug 2017:
Vol. 3, no. 8, e1701217
DOI: 10.1126/sciadv.1701217
  • Fig. 1 TR-OKE transients from a CH3NH3PbBr3 crystal.

    (A) OKE transients from CH3NH3PbBr3 as a function of pump energy (1.85 to 2.30 eV). As it moves from nonresonant to preresonant condition, contribution from low-frequency motions coupled to electronic excitation is enhanced. As it reaches the carrier injection regime, additional subpicosecond dynamics manifest itself. (B) Fourier component of each OKE transient. The inset is the crystalline structure of CH3NH3PbBr3. Black ticks at the top show calculated frequencies of normal modes, and sticks represent projections of the displacement vector on the normal modes upon large polaron formation (see fig. S4). FFT, fast Fourier transform.

  • Fig. 2 TR-OKE transients from a CsPbBr3 crystal.

    (A) OKE transients from CsPbBr3 as a function of pump energy (1.83 to 2.43 eV). At the preresonant regime, low-frequency modes that are coupled to band-edge excitation are enhanced. At the carrier injection regime, additional subpicosecond dynamics, as well as long-lived polarization, manifest itself. (B) Fourier spectra of selected transients in nonresonant regime (1.83 and 2.00 eV), preresonant regime (2.21 and 2.25 eV), and carrier injection regime (2.43 eV). The inset is the crystalline structure of CsPbBr3. Black ticks at the top show calculated frequencies of normal modes, and sticks represent projections of the displacement vector on the normal modes upon large polaron formation (see fig. S5).

  • Fig. 3 Comparison of transient reflectance and TR-OKE with above-gap excitation.

    (A) Pseudocolor (Δα) representation of transient absorbance spectra of a CH3NH3PbBr3 single crystal retrieved from transient reflectance (ΔR/R) pumped by 2.92 eV at 100 μW. (B) Dynamics of screening extracted from transient reflectance probed at 2.31 eV for CH3NH3PbBr3 (blue) and at 2.38 eV for CsPbBr3 (red) as a function of pump-probe delay. The lines are monoexponential fits convoluted with a Gaussian function, which describes the cross-correlation between pump and probe pulse [full width at half maximum (FWHM), 100 fs]. (C) The structural dynamics triggered by photo-carrier injection as a function of pump-probe delay observed by TR-OKE with across-gap excitation. CH3NH3PbBr3 (blue) and at 2.38 eV for CsPbBr3 (red) as a function of the pump-probe delay. The lines are double-exponential fits convoluted with a Gaussian function, which describes cross-correlation between the pump and probe pulse (FWHM, 70 fs).

  • Fig. 4 Hybrid DFT calculations.

    (A) Relaxed structures of CH3NH3PbBr3 with positive and negative charge injection. Changes in Pb-Br-Pb bending and Pb-Br length are shown. (B to E) Potential energy surfaces for relaxation of the CH3NH3PbBr3 (B and C) and CsPbBr3 (D and E) unit cell (four formula units) upon positive (B and D; red curve) and negative (C and E; blue curve) charge injection. The neutral state energy (black) along the distortion coordinate is also shown.

  • Fig. 5 Estimation of polaron size from first principle.

    (A) Distribution of Pb-Br distances (Å; top) of the positive polaron state for a pseudocubic 2 × 2 × 8 CsPbBr3 model made by 32 formula units. (B) Distribution of the excess positive charge (red isosurface) following the pattern of Pb-Br distances. The figure has been centered at the maximum of hole localization.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/8/e1701217/DC1

    fig. S1. Optical images of single-crystalline CH3NH3PbBr3 and CsPbBr3.

    fig. S2. The spectra of pump pulses in the TR-OKE measurement.

    fig. S3. A schematic diagram of TR-OKE measurement and polarization-dependent OKE traces on the CH3NH3PbBr3 crystal.

    fig. S4. Calculated IR spectrum and the coefficients of the displacement vector associated with a positve charge injection in CsPbBr3 projected to the normal modes.

    fig. S5. Calculated IR spectrum and the coefficients of the displacement vector associated with a positive charge injection in CH3NH3PbBr3 projected to the normal modes.

    fig. S6. Details in transient reflectance measurements.

    fig. S7. Hybrid DFT calculations of the relaxed structures of CH3NH3PbI3.

    fig. S8. Potential energy surface for the neutral and positive charged 2 × 2 × 8 cubic CsPbBr3 supercells.

    fig. S9. Pseudocubic 2 × 2 × 8 CsPbBr3 model with elongated (shortened) Pb-Br bonds in the left (right) halves of the supercell.

    fig. S10. Localization of the positive charge as a function of the octahedral tilting in 2 × 2 × 8 cubic CsPbBr3 supercells.

    fig. S11. Hybrid DFT calculations of stabilization energy of CH3NH3PbBr3 and CsPbBr3 with and without cations.

    fig. S12. Calculated dielectric functions of CsPbBr3 and MAPbBr3.

    table S1. Lattice constants for MAPbBr3 and CsPbBr3 single crystals.

    table S2. The list of input parameters for the polaron calculations.

    table S3. The list of the results of polaron calculations under the Feynman-Ōsaka model.

  • Supplementary Materials

    This PDF file includes:

    • fig. S1. Optical images of single-crystalline CH3NH3PbBr3 and CsPbBr3.
    • fig. S2. The spectra of pump pulses in the TR-OKE measurement.
    • fig. S3. A schematic diagram of TR-OKE measurement and polarization-dependent OKE traces on the CH3NH3PbBr3 crystal.
    • fig. S4. Calculated IR spectrum and the coefficients of the displacement vector associated with a positive charge injection in CsPbBr3 projected to the normal modes.
    • fig. S5. Calculated IR spectrum and the coefficients of the displacement vector associated with a positive charge injection in CH3NH3PbBr3 projected to the normal modes.
    • fig. S6. Details in transient reflectance measurements.
    • fig. S7. Hybrid DFT calculations of the relaxed structures of CH3NH3PbI3.
    • fig. S8. Potential energy surface for the neutral and positive charged 2 × 2 × 8 cubic CsPbBr3 supercells.
    • fig. S9. Pseudocubic 2 × 2 × 8 CsPbBr3 model with elongated (shortened) Pb-Br bonds in the left (right) halves of the supercell.
    • fig. S10. Localization of the positive charge as a function of the octahedral tilting in 2 × 2 × 8 cubic CsPbBr3 supercells.
    • fig. S11. Hybrid DFT calculations of stabilization energy of CH3NH3PbBr3 and CsPbBr3 with and without cations.
    • fig. S12. Calculated dielectric functions of CsPbBr3 and MAPbBr3.
    • table S1. Lattice constants for MAPbBr3 and CsPbBr3 single crystals.
    • table S2. The list of input parameters for the polaron calculations.
    • table S3. The list of the results of polaron calculations under the Feynman-Ōsaka model.

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