Carrier Lifetimes and Polaronic Mass Enhancement in the Hybrid Halide Perovskite ${\mathrm{CH}}_{3}{\mathrm{NH}}_{3}{\mathrm{PbI}}_{3}$ from Multiphonon Fr\"ohlich Coupling

Carrier Lifetimes and Polaronic Mass Enhancement in the Hybrid Halide Perovskite ${CH}_{3} {NH}_{3} {PbI}_{3}$ from Multiphonon Fröhlich Coupling

Martin Schlipf, Samuel Poncé, and Feliciano Giustino

Phys. Rev. Lett. 121, 086402 – Published 23 August 2018

Abstract

We elucidate the nature of the electron-phonon interaction in the archetypal hybrid perovskite ${CH}_{3} {NH}_{3} {PbI}_{3}$ using ab initio many-body calculations and an exactly solvable model. We demonstrate that electrons and holes near the band edges primarily interact with three distinct groups of longitudinal-optical vibrations, in order of importance: the stretching of the Pb—I bond, the bending of the Pb—I—Pb bonds, and the libration of the organic cations. These polar phonons induce ultrafast intraband carrier relaxation over timescales of 6–30 fs and yield polaron effective masses 28% heavier than the bare band masses. These findings allow us to rationalize previous experimental observations and provide a key to understanding carrier dynamics in halide perovskites.

Received 12 February 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.086402

Physics Subject Headings (PhySH)

Electron-phonon coupling Electronic structure First-principles calculations Optical phonons Phonons Semiconductors

Perovskites

Density functional theory Many-body techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Martin Schlipf¹, Samuel Poncé¹, and Feliciano Giustino^1,2,*

¹Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
²Department of Materials Science and Engineering, Cornell University, Ithaca, New York 14853, USA

^*feliciano.giustino@materials.ox.ac.uk

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Vol. 121, Iss. 8 — 24 August 2018

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Figure 1
(a) Quasiparticle broadening in ${CH}_{3} {NH}_{3} {PbI}_{3}$ from EPIs near the band edges at 1 K. The carrier energy for wave vectors along various high-symmetry directions is referred to the band edge, and the bands are indicated schematically. epw calculations are shown as filled black symbols; red symbols indicate the contribution of all phonons with energy $≲ 2 meV$ ; the lines are calculated with Eq. (2) using Rayleigh-Schrödinger (teal, dashed line) or Brillouin-Wigner (green, solid line) perturbation theory. (b) Smallest relaxation rates (left-hand axis) and largest lifetime (right-hand axis) for holes with energy above (purple diamond and line) or below (brown circle and line) the maximum energy of polar phonons ${\hat{ϵ}}_{LO} \sim 22 meV$ . Filled symbols are epw calculations, lines are from the multiphonon model. The data for electrons are practically indistinguishable from the holes and are not shown. The open symbols are the relaxation rates measured by Ref. [10] (triangle) and Ref. [22] (square). (c) Mass enhancement parameter for holes (data for electrons are practically indistinguishable). epw calculations are shown as filled symbols. The lines are from Rayleigh-Schrödinger (teal, dashed line) or Brillouin-Wigner (green, solid line) perturbation theory. The colored bars indicate the contributions of the three groups of LO modes shown in Fig. 2, using the same color code.
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Figure 2
(a) Density of electron-phonon coupling strength associated with polar phonons in ${CH}_{3} {NH}_{3} {PbI}_{3}$ , $g^{2} (ℏ ω)$ , as defined in the Supplemental Material [30]. The yellow, blue, and red regions correspond to bending, stretching, and libration-translation modes, respectively. The vertical arrows indicate the energies and couplings of the compact, three-phonon model used in the analysis. (b)–(d) Schematic ball-and-stick representations of the three groups of vibrations appearing in (a). The Pb and I atoms are at the centers and at the corners of the octahedra, respectively, C is in gray, and N is in blue. The H atoms are not shown for clarity.
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Figure 3
Calculated spectral function of ${CH}_{3} {NH}_{3} {PbI}_{3}$ including EPIs at 1 and 300 K near the edges of conduction ( $c$ ) and valence ( $v$ ) band. The dashed blue lines are the band structures without EPI. The black lines are obtained by renormalizing the band according to the mass enhancement in Fig. 1. To facilitate the rendering, the quasiparticle spectral function is calculated after convoluting the self-energy in Eq. (2) with a 5 meV Gaussian. The energy of the electron-phonon band replicas could be improved by using the cumulant expansion [69, 70, 75, 76, 77, 78], but the qualitative picture would not change.
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Physical Review Letters

Carrier Lifetimes and Polaronic Mass Enhancement in the Hybrid Halide Perovskite CH3NH3PbI3 from Multiphonon Fröhlich Coupling

Martin Schlipf, Samuel Poncé, and Feliciano Giustino

Phys. Rev. Lett. 121, 086402 – Published 23 August 2018

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Carrier Lifetimes and Polaronic Mass Enhancement in the Hybrid Halide Perovskite ${CH}_{3} {NH}_{3} {PbI}_{3}$ from Multiphonon Fröhlich Coupling