SpinâOrbit Interactions Greatly Accelerate Nonradiative Dynamics in

Subscriber access provided by Kaohsiung Medical University

Letter

Spin-orbit Interactions Greatly Accelerate Nonradiative Dynamics in Lead Halide Perovskites Wei Li, Liujiang Zhou, Oleg V. Prezhdo, and Alexey V. Akimov ACS Energy Lett., Just Accepted Manuscript • DOI: 10.1021/acsenergylett.8b01226 • Publication Date (Web): 16 Aug 2018 Downloaded from http://pubs.acs.org on August 16, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

Spin-orbit Interactions Greatly Accelerate Nonradiative Dynamics in Lead Halide Perovskites Wei Li,1 Liujiang Zhou,2 Oleg V. Prezhdo,3* Alexey V. Akimov4* 1 College of Science, Hunan Agricultural University, Changsha 410128, P. R. China 2 Los Alamos National Laboratory,

Los Alamos, New Mexico 87545, United States

3 Department of Chemistry, University of Southern California, Los Angeles, CA 90089, United States 4 Department of Chemistry, University at Buffalo, The State University of New York, Buffalo, NY 14260-3000 *Corresponding author. Email: [email protected] (O.V.P.) [email protected] (A.V.A.)

1 ACS Paragon Plus Environment

ACS Energy Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract

In this work, we study the role of spin-orbit coupling (SOC) in nonradiative relaxation of hot electrons and holes in methylammonium lead perovskite, MAPbI3. For this purpose, we have developed the nonadiabatic molecular dynamics method with 2-component spinor wavefunctions that are solutions of the relativistic Kohn-Sham (KS) equations. We find that SOC enhances contributions of Pb(px) and Pb(py) orbitals to the conduction and valence bands. As a result, the KS orbitals become more sensitive to nuclear motions, leading to the increased nonadiabatic couplings. Consequently, SOC greatly speeds up the electron and hole relaxation, making the computed relaxation timescales consistent with available experiments. We suggest that the fast hot carrier relaxation facilitated by the SOC allows rapid transition into the long-lived triplet state that extends charge-carrier lifetime and helps achieving high-efficiency perovskite solar cells.


Page 2 of 26

Page 3 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

Photovoltaic (PV) materials enable efficient conversion of solar energy to electricity, offer to reduce the world’s consumption on fossil fuels, and make the clean and sustainable energy production an everyday reality. Considerable efforts have been devoted to develop new generations of solar cells.1–3 In particular, perovskite materials has gained a lot of attention from scientific community lately.4–19 Among them, methylammonium lead halide perovskites, MAPbX3 (X = Cl, Br, I) has been under increasing studies in the past few years.20–24 Perovskite materials have a tunable band gap, long carrier diffusion length, high carrier mobilities, and are inexpensive to manufacture. Many investigations were carried out for perovskite materials from the experimental and theoretical viewpoints.2,25–31 Most theoretical works studied properties including the role of defects32, mechanisms of ionic migration6, dynamic disorder33, optical and electronic structure properties or the original and doped systems.34 A number of theoretical investigations of nonadiabatic molecular dynamics (NA-MD) have been undertaken35–38 using non-relativistic density functional theory (DFT) calculation. At the same time, the relativistic effects are expected to play an important role in such systems, since they contain heavy elements such as lead or iodine.30,31,39–41 The giant spin-orbit coupling (SOC) that notably influences the band structure of perovskite materials and has been reported in previous work.42 This effect leads to the band gap reduction in such systems by as much as 1 eV, generates non-degenerate spin states42, long-lived triplet states31, and room-temperature Rashba splitting effect.41 However, the influence of SO interactions on charge transfer (CT) and energy transfer (ET) dynamics remain largely unexplored to date. An understanding of this effect could provide further insights into the prominent performance of perovskite-based solar cells.



In this work, we aim to fill the indicated void in our knowledge of nonadiabatic dynamics in presence of SO interactions. In particular, we focus on the role of SOC in hot carrier relaxation dynamics in tetragonal phase MAPbI3 (Figure 1). To assess the role of the SOC, we have extended the earlier NA-MD procedure43,44 to 2-component spinor orbitals that are solutions of the relativistic Kohn-Sham (KS) equations. We compare the relaxation rates for electrons and holes as calculated using the fewest switches surface hopping (FSSH)45 method with the KS orbitals computed with and without SOC. Our results indicate that, consistent with previous reports, SOC reduces the band gap by ~1 eV by affecting the Pb-p contribution in the conduction band (CB) and valence band (VB) orbitals. The increase of the px and py projections relative to pz of Pb leads to variation of the nonadiabatic coupling (NAC). As a result, the SOC enhances the electron and hole relaxation rates within the CB and VB, respectively (“cooling”) because of the enlarged NACs and stronger coupling to low frequency phonon modes. The timescales computed when the SOC effects are accounted for are observed to be in a better agreement with the experimentally-derived timescales2. The accelerated dynamics in the mixed-spin states (relativistic wavefunctions) suggests a fast population of the superposition states that have a non-negligible triplet states contribution by decay of the initially prepared hot electrons. We hypothesize that the subsequent decoherence of generated superposition of singlet and triplet configurations results in a formation of a notable fraction of triplet electrons, whose recombination with the holes of singlet spin symmetry is notably inhibited. We suggest this mechanism as a possible rationalization of the remarkable solar energy conversion of lead halide perovskites. Our work indicates


Page 4 of 26

Page 5 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

that SOC effects cannot be neglected, if accurate modeling of the hot carrier relaxation in MAPbI3-based materials is to be performed.

Figure 1. Schematic representation of the electron and hole relaxation process in perovskite materials (left). The optimized ground state structure of tetragonal perovskite MAPbI3 (right).

The essentials of the FSSH algorithm and its implementation within the neglect of back-reaction (NBRA) approximation have been presented in details elsewhere.43,44 Here, we reiterate the key constructs, for completeness and then focus only on the elements of the methodology that change in the spin-orbital case. First, the overall time-dependent wavefunction of the system is represented as spin-adiabatic basis: ∑ Φ .

(1)



Here, the spin-adiabatic basis states, Φ

√!

Page 6 of 26

| … |, are represented by

Slater determinants composed of spin-orbitals, of N electrons, parametrically dependent on nuclear trajectories, . The spin-orbitals, , are the eigenvalues of the

KS equations with the Hamiltonian that includes the SOC terms, as computed with the Quantum Espresso (QE)46 electronic structure code:

ℎ + ℎ

! .

(2)

Within the non-collinear magnetism framework, the orbitals, , are represented in a %

form of 2-component spinors, which naturally mix alpha-, " $ , and beta, " , components

"$ &

+

% " '

(

"$

%) , +

"

1, … , -.

(3)

The evolution of the time-dependent amplitudes, , of the above-defined basis states is determined by solving the time-dependent Schrodinger equation (TD-SE) : +ℏ

/01 23

456 .

(4)

Here 456 is the vibronic Hamiltonian matrix: 456 478 − +ℏ:; . The vibronic

?78 Hamiltonian is composed of the electronic Hamiltonian, 478,; ⟨= │4 │=; ⟩, and

scalar (time-derivative) nonadiabatic couplings (NAC), :; A= B

2

23

B=; C. The NACs are

computed using the finite difference Hammes-Schiffer and Tully (HST) scheme47: :; D + F ≡ E dt

HI1 3JIK 3LdtMNHI1 3L 3JIK 3M Edt

.

(5)


Page 7 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

As has been suggested earlier,43,44 this formula can be reduced to the analogous expression only involving the 1-electron KS spin-orbitals. The procedure to compute the overlaps of the crystal orbitals expressed in terms of the plane waves has been elaborated earlier. The distinctive element of the present approach is that such computations must be performed with the 2-component spinors. Such calculations can be regarded as computing the dot product of the 2×1 Hilbert space vectors: H J; ′M "$

";$ ′ % ) " ( % "; ′

%

%

H"$ J";$ ′M + A" B"; ′C. (6)

The geometry optimization and electronic structure calculations has been carried out with the VASP code48,49. The lattice constant of the tetragonal MAPbI3 simulation cell was kept fixed at its experimental value of a=b=8.8 Å and c=12.68 Å50 during the geometry optimization. After the optimization of the geometry at 0 K, the system is thermalized to 300 K for a 2 ps NVT-MD that utilizes velocity rescaling to maintain constant temperature. This is followed by a 3 ps NVE-MD to obtain the nuclear trajectories. A nuclear integration time step of 1 fs is utilized. Calculations of projected densities of states (pDOS) and NACs are carried out at the ab initio level, using Quantum Espresso (QE) program.46 SOC effect is introduced by performing the non-collinear calculation using fully relativistic pseudopotentials. Bare DFT functional, PBE, and plane wave basis are used for all calculations. SOC effects are not included in VASP calculations since it doesn’t affect the structural parameters.51,52 The generated MD trajectories are utilized to compute NACs for all pairs of orbitals spanning several eV energy window around the fundamental band gap. The present workflow employing the SOC-enabled NA-MD is implemented in the PYXAID2 program.53 The implementation relies on the modular library for nonadiabatic and quantum dynamics simulations, 7 ACS Paragon Plus Environment


Libra.54 The latter implements the routines for surface hopping, statistics analysis, functions for reading and parsing the output of Quantum Espresso calculations. Further details of the employed methodologies and algorithms can be found in SI.

Figure 2. Projected density of states (pDOS) and charge density for selected KS orbitals involved in electron and hole relaxation without (top) and with (bottom) SOC based on the optimized ground state structure. The calculations are performed with QE code using a 9×9×9 k-points grid. Zero energy of the energy scale is set to the Fermi energy of the system. VBM-11 locates at ~1 eV below the VBM. SOC enhance the coupling of inplane px and py orbitals with out-of-plane pz orbital of Pb atoms, leading to significant overlap of the three components, see Figure S1.

Using the optimized (zero-temperature) geometry, we compute the projected densities of states (pDOS) with and without SOC included (Figure 2). We specifically resolve the s- and p-contributions of Pb and I atoms. Pb-d orbital is not presented since it is extremely deep position.55 The band gap of ~1.59 eV is obtained at the Gamma-point when SOC is excluded. The inclusion of SOC decreases the gap by ~1 eV, down to approximately 0.56 eV, in agreement with previous investigations performed at a similar level of theory.42 The band gap reduction is mainly achieved by shifting in CB edge. It has been well established that the bare DFT provides the fortuitous band gap compared 8 ACS Paragon Plus Environment

Page 8 of 26

Page 9 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

with experimental value due to error cancellation between bare DFT and neglect of SOC effect.42 De Angelis et al. have reported the value of 1.67 eV obtained at a more advanced level of the theory - using the GW/SOC approach.52 The GW correction is not required in our simulation since we are not modeling the transition across the band gap and also such implementations are time-demanding for NAC computations which require thousands of electronic structure calculations. The computed pDOS shows an asymmetric distribution, such that the VBs are denser than CBs. Small DOS region favors slower carrier relaxation.56 The pDOS shows that the VBM consists of antibonding hybrids of Pb-6s state and I-5p state, whereas the CBM is composed mostly of Pb-6p state. SOC notably increases the contributions of px and py states of Pb atom to the VB and CB states, see Figure S1. This is further evidenced by the analysis of charge density plots for a number of selected KS orbitals (Figure 2, right panels): without SOC the pz orbital of Pb atoms hybridize with px and py orbitals to a smaller extent. The orbital hybridization is substantially enhanced by SOC. The mechanism of hybridization enhancement involves the inversion symmetry-breaking (ISB) field along the z direction induced by SOC allows the hopping between the px (or py) with pz orbitals, causing the significant mixing of the three states.57 The modulation of electronic structure by SOC is expected to affect the NACs, since the latter scale inversely with the corresponding energy gaps.58 To assess this effect, we have computed the average magnitudes of NACs of the two types. In doing this, we have utilized the identical nuclear trajectories as well as the identical electronic structure simulation protocols, other than the inclusion of SOC. A comparison of the 2D maps,



Page 10 of 26

showing NACs between all pairs of states within the spaces of KS orbitals considered in our calculations is presented in Figure 3. The averaged NACs are computed as: ⟨ PQ 456,; ⟩ ℏ/S ∑TN 3UV J:; J.

(7)

Here, T = 3000 is the number of MD steps, 456,; is a matrix element of the vibronic

Hamiltonian defined after Eq. 4, :; is an instantaneous NAC matrix element, ℏ -

Planck’s constant (ℏ 1 in atomic units used here), and ⟨⟩ denotes the time averaging.

The rate of electronic transition depends on the NAC elements (dij). Larger dij corresponds to the faster electronic transition between state i and j. In both types of calculations, the largest NACs are positioned at the first sub-diagonal, suggesting that the energetically close states are the ones that couple to each other most strongly. The couplings gradually decrease, as the states are energetically separated, indicating that the dominant non-radiative relaxation process involve the consecutive population transfer mechanisms. The numerical data are summarized in Table S1. The inclusion of SOC has two main effects. First, it increases the average magnitudes of NACs. This can be explained by the nature of the 2-component functions: because they represent superpositions of electrons/holes in alpha and beta states, it is reasonable to expect that these orbitals have lesser repulsion than the spatial components of samespin orbitals. Such an “extended” size of the resulting SOC-based orbitals is clear from Figue2. Because of the increased spatial overlap of different orbitals, the time-overlaps, Eq. 6, and the NACs, Eq. 5, increase. Second effect concerns the qualitative changes of the NAC structure. As Figure 3b shows, there is a substantial degree of coupling of states within either CB or VB. Unlike in the case without SOC enabled, the states do not have


Page 11 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

to be energetically close to experience notable NAC between them. This effect can be explained by the “mixing” of the spin-diabatic orbitals by the 4 operator. In the context

of perturbation theory, the 4 Hamiltonian couples several spin-diabatic (eigenfunctions

of spin-free Hamiltonian) states in a single spin-adiabatic superposition,

2

∑; ; ; . The NACs in the spin-adiabatic basis, :; A B 23 B; C are then

expressed as linear combinations of the corresponding NACs between spin-diabatic 2

states, :; A B B; C. As Figure 3a suggests, the latter are coupled locally – 23 each state is coupled only with a few energetically-close states. However, since :; is a

linear combinations of multiple :; , more energetically-distant states become notably coupled.

Figure 3. Visualization of the averaged nonadiabatic couplings (NAC) between states in orbital indices for without (a) and with (b) SOC cases, unit in meV. SOC significantly affects the NAC magnitude of CB and higher VB states since they have considerable contributions from Pb-6p states.

The energy decay of the “hot” electrons and holes computed with and without consideration of SOC interactions in NA-MD are presented in Figure 4. In general, electron and hole energy relaxes much faster with SOC than without it. Particularly, 11 ACS Paragon Plus Environment


when SOC is not included, we do not observe apparent decay of electron energies within the 2.5 ps timescale of our simulation. The relaxation of highly-energetic holes occurs on the order of 2 ps, and is only weakly dependent on their initial energy. The accelerated relaxation of holes in contrast to that of electrons may be attributed to their higher densities of states, as is suggested by the pDOS (Figure 2). Once the SOC is included, both electrons and holes undergo fast relaxation, on a 200-300 fs timescales, in agreement with photoluminescence experiments2,59 which suggest ~400 fs hole relaxation timescales. Interestingly, the inclusion of SOC accelerates the relaxation of both holes and electrons, making both processes less sensitive to densities of states. The observed acceleration is a direct consequence of the increased NACs in the treatment that incorporates SO interactions. It worth mentioning that nonradiative electron-hole recombination across the band gap takes place on the hundreds of nanoseconds timescale60,61 and is not considered in this work.


Page 12 of 26

Page 13 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

Figure 4. Time evolution of the population-weighted electron (a,b) and hole (c,d) energy decay starting from different initial states without (a,c) and with (b,d) SOC. The population-weighted electron and hole energies exhibits much slower decay without SOC. Hole relaxation is faster than electron relaxation, because VB states are denser than electron states. Hole relaxation from VBM-9, ~1 eV below VBM, shows relaxation time of 178 fs with SOC, agree with the experimental 400 fs relaxation time starting from similar initial state.

The phonon modes are computed via Fourier Transform (FT) of the autocorrelation functions of fluctuation of energy difference between pair of states, according to the optical response function formalism of Mukamel.62 The computed influence spectra illustrate the phonon modes that drive particular pairs of transitions. As Figure 5 suggests, the inclusion of SOC can notably change the spectra. Note that since the two types of spectra (with and without SOC) are obtained from the identical nuclear trajectories, the difference in the influence spectra originates from the change of the electronic structure, not due to possible changes of nuclear dynamics. In particular, the inclusion of the SOC Hamiltonian makes the 1-electron orbitals (spin-adiabatic) to be linear combinations of spin-diabatic orbitals, which are eigenfunctions of a spin-free Hamiltonian. This mixing of the spin-diabatic states translates not only into NACs, as discussed above, but also into the influence spectra (Figure 5). In earlier work reporting simulation of electron-hole recombination in MAPbI3,60 the low frequency below 100 cm1

arising from Pb-I stretching and I-Pb-I bending was found to dominate the FT spectrum:

charge recombination couples little to the vibration of organic cation. In the present work, we observe a similar relationship both for electron and hole intraband relaxation. In general, the electronic transition between adjacent states couple more strongly to the vibration of inorganic cage for electron and hole relaxation with SOC, an indication of



the larger NAC.

Overall, the low frequency modes dominate the FT spectrum for

electron and hole relaxation process.

Figure 5. Spectral density between pair states without (a,c) and with (b,d) SOC for electron (a,b) and hole (c,d) relaxation in perovskite MAPbI3.

So far, we have demonstrated that Pb and I-induced SOC in MAPI3 accelerates a transition between different 2-component spinors of the system. It is interesting to know how this helps generating long-lived charge carriers, which are important for improved power conversion efficiencies in perovskite solar cells (Figure 6). First, the photon absorption generates an excitation by primarily promoting an electron of one spin symmetry (no changing the spin character of the system). The photoexcited electron can 14 ACS Paragon Plus Environment

Page 14 of 26

Page 15 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

now either recombine with the hole (spin-allowed) or can evolve in the manifold of the spin-adiabatic (mixed spin states) leading to a new wavefunction with distinct overall spin symmetry (“coherent evolution”). This wavefunction can be represented by a coherent superposition of singlet and triplet configurations. This process contains both adiabatic and nonadiabatic components, but it is only possible in the presence of SO coupling (SOC-enabled). The evolved superposition can decohere, which can be regarded as generation of a mixture of different spin-symmetry excitations (singlet and triplet electron/hole pairs). The singlet electron/hole (e/h) pair can experience a fast recombination, since it is spin-allowed. At the same time, the triplet e/h pair remains long-lived since its recombination is spin-forbidden. As it follows from the proposed mechanism, the fast coherent evolution of the spinadiabatic states enabled by the SO interactions is important in two aspects. First, it reduces the chances of electron-hole recombination, since it opens another “reaction” channel. Second, SOC enables evolution of mixed-spin states, which eventually enables generation of triplet configurations. As a result, these factors may improve the photocurrent density generated in perovskite-based materials. Indeed, recent experiment showed that the replacement of Pb with Sn in perovskite could reduce SOC, decreasing the singlet-to-triplet conversion efficiency and lowering the photocurrent density.31 Thus, we conclude that the fast coherent evolution of the mixed-spin state charge carriers is essential for improved performance of PV materials via enabling generation of the longlived triplet states.



Figure 6. Schematic of the mechanism of SOC-enabled generation of long-lived charge carriers. Blue and red arrows represent electrons of particular spin. Red-and-black arrows represent holes in orbitals of corresponding spin symmetry.

In summary, we have investigated the effect of SOC on the electron and hole relaxation in perovskite MAPbI3. Our results show that SOC enhances the contribution of the px and py orbitals of Pb atoms to the CB and VB states, leading to the larger NAC. SOC greatly speeds up the electron and hole relaxation, particularly, producing timescales in agreement with the available experimental data. Hole relaxation is faster than electron relaxation because VB states are denser than CB states. The difference in the relaxation rate can be explained by the increased NAC, which grows because the KS orbitals show stronger dependence on nuclear coordinates as a result of the enhanced contributions of the px and py orbitals of Pb. SOC does not change the nature of the phonon modes that couple to the charge carriers. Both electrons and holes couple primarily to low frequency phonon modes, involving vibrations of Pb and I atoms. Finally, we propose a mechanism 16 ACS Paragon Plus Environment

Page 16 of 26

Page 17 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

by which the SOC-accelerated NA dynamics in the manifold of spin-adiabatic states may favor generation of longer-lived charge carrier pairs to improve the PV characteristics of such materials.

Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: XXXX Description of the computation methods and algorithms, Pb(px), Pb(py), Pb(pz)resolved pDOS of perovskite MAPbI3, numerical values of averaged nonadiabatic couplings.

Acknowledgement A.V.A. acknowledges support of the University at Buffalo, SUNY (award number 57333). O.V.P. acknowledges support of the U.S. National Science Foundation (award CHE-1565704). L.Z acknowledges support of the U.S. Department of Energy through the LANL/LDRD Program and the Center for Non-Linear Studies for this work. The simulations were performed at the University of Southern California’s Center for HighPerformance Computing (hpcc.usc.edu).



References (1)

Huang, J.; Yuan, Y.; Shao, Y.; Yan, Y. Understanding the Physical Properties of Hybrid Perovskites for Photovoltaic Applications. Nat. Rev. Mater. 2017, 2, natrevmats201742.

(2)

Xing, G.; Mathews, N.; Sun, S.; Lim, S. S.; Lam, Y. M.; Gratzel, M.; Mhaisalkar, S.; Sum, T. C. Long-Range Balanced Electron- and Hole-Transport Lengths in Organic-Inorganic CH3NH3PbI3. Science 2013, 342, 344–347.

(3)

Quilettes, D. W. de; Vorpahl, S. M.; Stranks, S. D.; Nagaoka, H.; Eperon, G. E.; Ziffer, M. E.; Snaith, H. J.; Ginger, D. S. Impact of Microstructure on Local Carrier Lifetime in Perovskite Solar Cells. Science 2015, 348, 683–686.

(4)

Balakrishnan, S. K.; Kamat, P. V. Au–CsPbBr3 Hybrid Architecture: Anchoring Gold Nanoparticles on Cubic Perovskite Nanocrystals. ACS Energy Lett. 2017, 2, 88–93.

(5)

Azpiroz, J. M.; Mosconi, E.; Bisquert, J.; Angelis, F. D. Defect Migration in Methylammonium Lead Iodide and Its Role in Perovskite Solar Cell Operation. Energy Environ. Sci. 2015, 8, 2118–2127.

(6)

Mosconi, E.; De Angelis, F. Mobile Ions in Organohalide Perovskites: Interplay of Electronic Structure and Dynamics. ACS Energy Lett. 2016, 1, 182–188.

(7)

Rajagopal, A.; Liang, P.-W.; Chueh, C.-C.; Yang, Z.; Jen, A. K.-Y. Defect Passivation via a Graded Fullerene Heterojunction in Low-Bandgap Pb–Sn Binary Perovskite Photovoltaics. ACS Energy Lett. 2017, 2531–2539.

(8)

Brennan, M. C.; Draguta, S.; Kamat, P. V.; Kuno, M. Light-Induced Anion Phase Segregation in Mixed Halide Perovskites. ACS Energy Lett. 2018, 3, 204–213.


Page 18 of 26

Page 19 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

(9)

Leijtens, T.; Srimath Kandada, A. R.; Eperon, G. E.; Grancini, G.; D’Innocenzo, V.; Ball, J. M.; Stranks, S. D.; Snaith, H. J.; Petrozza, A. Modulating the Electron– Hole Interaction in a Hybrid Lead Halide Perovskite with an Electric Field. J. Am. Chem. Soc. 2015, 137, 15451–15459.

(10) Ghosh, D.; Walsh Atkins, P.; Islam, M. S.; Walker, A. B.; Eames, C. Good Vibrations: Locking of Octahedral Tilting in Mixed-Cation Iodide Perovskites for Solar Cells. ACS Energy Lett. 2017, 2, 2424–2429. (11) Yoon, S. J.; Draguta, S.; Manser, J. S.; Sharia, O.; Schneider, W. F.; Kuno, M.; Kamat, P. V. Tracking Iodide and Bromide Ion Segregation in Mixed Halide Lead Perovskites during Photoirradiation. ACS Energy Lett. 2016, 1, 290–296. (12) Eames, C.; Sanchez-Molina, I.; Kosco, J.; Islam, M. S.; Aristidou, N.; Haque, S. A.; Bu, X. Fast Oxygen Diffusion and Iodide Defects Mediate Oxygen-Induced Degradation of Perovskite Solar Cells. Nat. Commun. 2017, 8, 15218. (13) Chakraborty, S.; Xie, W.; Mathews, N.; Sherburne, M.; Ahuja, R.; Asta, M.; Mhaisalkar, S. G. Rational Design: A High-Throughput Computational Screening and Experimental Validation Methodology for Lead-Free and Emergent Hybrid Perovskites. ACS Energy Lett. 2017, 2, 837–845. (14) Zheng, X.; Chen, H.; Li, Q.; Yang, Y.; Wei, Z.; Bai, Y.; Qiu, Y.; Zhou, D.; Wong, K. S.; Yang, S. Boron Doping of Multiwalled Carbon Nanotubes Significantly Enhances Hole Extraction in Carbon-Based Perovskite Solar Cells. Nano Lett. 2017, 17, 2496–2505. (15) Whalley, L. D.; Crespo-Otero, R.; Walsh, A. H-Center and V-Center Defects in Hybrid Halide Perovskites. ACS Energy Lett. 2017, 2, 2713–2714.



(16) Hutter, E. M.; Gélvez-Rueda, M. C.; Osherov, A.; Bulović, V.; Grozema, F. C.; Stranks, S. D.; Savenije, T. J. Direct-Indirect Character of the Bandgap in Methylammonium Lead Iodide Perovskite. Nat. Mater. 2017, 16, 115–120. (17) Savory, C. N.; Walsh, A.; Scanlon, D. O. Can Pb-Free Halide Double Perovskites Support High-Efficiency Solar Cells? ACS Energy Lett. 2016, 1, 949–955. (18) Price, M. B.; Butkus, J.; Jellicoe, T. C.; Sadhanala, A.; Briane, A.; Halpert, J. E.; Broch, K.; Hodgkiss, J. M.; Friend, R. H.; Deschler, F. Hot-Carrier Cooling and Photoinduced Refractive Index Changes in Organic–Inorganic Lead Halide Perovskites. Nat. Commun. 2015, 6, ncomms9420. (19) Meggiolaro, D.; Mosconi, E.; De Angelis, F. Mechanism of Reversible Trap Passivation by Molecular Oxygen in Lead-Halide Perovskites. ACS Energy Lett. 2017, 2, 2794–2798. (20) Zohar, A.; Levine, I.; Gupta, S.; Davidson, O.; Azulay, D.; Millo, O.; Balberg, I.; Hodes, G.; Cahen, D. What Is the Mechanism of MAPbI3 p-Doping by I2? Insights from Optoelectronic Properties. ACS Energy Lett. 2017, 2, 2408–2414. (21) Zhang, Z.-Y.; Wang, H.-Y.; Zhang, Y.-X.; Hao, Y.-W.; Sun, C.; Zhang, Y.; Gao, B.-R.; Chen, Q.-D.; Sun, H.-B. The Role of Trap-Assisted Recombination in Luminescent Properties of Organometal Halide CH3NH3PbBr3 Perovskite Films and Quantum Dots. Sci. Rep. 2016, 6, 27286. (22) Zuo, L.; Chen, Q.; De Marco, N.; Hsieh, Y.-T.; Chen, H.; Sun, P.; Chang, S.-Y.; Zhao, H.; Dong, S.; Yang, Y. Tailoring the Interfacial Chemical Interaction for High-Efficiency Perovskite Solar Cells. Nano Lett. 2017, 17, 269–275.


Page 20 of 26

Page 21 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

(23) Sheikh, A. D.; Munir, R.; Haque, M. A.; Bera, A.; Hu, W.; Shaikh, P.; Amassian, A.; Wu, T. Effects of High Temperature and Thermal Cycling on the Performance of Perovskite Solar Cells: Acceleration of Charge Recombination and Deterioration of Charge Extraction. ACS Appl. Mater. Interfaces 2017, 9, 35018– 35029. (24) Kong, L.; Liu, G.; Gong, J.; Hu, Q.; Schaller, R. D.; Dera, P.; Zhang, D.; Liu, Z.; Yang, W.; Zhu, K.; et al. Simultaneous Band-Gap Narrowing and Carrier-Lifetime Prolongation of Organic–Inorganic Trihalide Perovskites. Proc. Natl. Acad. Sci. 2016, 113, 8910–8915. (25) Ju, M.-G.; Dai, J.; Ma, L.; Zeng, X. C. Lead-Free Mixed Tin and Germanium Perovskites for Photovoltaic Application. J. Am. Chem. Soc. 2017, 139, 8038–8043. (26) Ambrosio, F.; Wiktor, J.; Angelis, F. D.; Pasquarello, A. Origin of Low ElectronHole Recombination Rate in Metal Halide Perovskites. Energy Environ. Sci. 2018, 11, 101-105. (27) Filip, M. R.; Eperon, G. E.; Snaith, H. J.; Giustino, F. Steric Engineering of MetalHalide Perovskites with Tunable Optical Band Gaps. Nat. Commun. 2014, 5, ncomms6757. (28) Yang, Y.; Ostrowski, D. P.; France, R. M.; Zhu, K.; van de Lagemaat, J.; Luther, J. M.; Beard, M. C. Observation of a Hot-Phonon Bottleneck in Lead-Iodide Perovskites. Nat. Photonics 2016, 10, 53–59. (29) Ihly, R.; Dowgiallo, A.-M.; Yang, M.; Schulz, P.; Stanton, N. J.; Reid, O. G.; Ferguson, A. J.; Zhu, K.; Berry, J. J.; Blackburn, J. L. Efficient Charge Extraction and Slow Recombination in Organic–Inorganic Perovskites Capped with



Semiconducting Single-Walled Carbon Nanotubes. Energy Environ. Sci. 2016, 9, 1439–1449. (30) Liu, Y.-Q.; Cui, H.-L.; Wei, D. Effects of Spin–Orbit Coupling on Nonequilibrium Quantum Transport Properties of Hybrid Halide Perovskites. J. Phys. Chem. C 2018, 122, 4150-4155.. (31) Zhang, J.; Wu, T.; Duan, J.; Ahmadi, M.; Jiang, F.; Zhou, Y.; Hu, B. Exploring Spin-Orbital Coupling Effects on Photovoltaic Actions in Sn and Pb Based Perovskite Solar Cells. Nano Energy 2017, 38, 297–303. (32) Yin, W.-J.; Shi, T.; Yan, Y. Unusual Defect Physics in CH3NH3PbI3 Perovskite Solar Cell Absorber. Appl. Phys. Lett. 2014, 104, 063903. (33) Shimamura, K.; Hakamata, T.; Shimojo, F.; Kalia, R. K.; Nakano, A.; Vashishta, P. Rotation Mechanism of Methylammonium Molecules in Organometal Halide Perovskite in Cubic Phase: An Ab Initio Molecular Dynamics Study. J. Chem. Phys. 2016, 145, 224503. (34) Feng, J.; Xiao, B. Crystal Structures, Optical Properties, and Effective Mass Tensors of CH3NH3PbX3 (X = I and Br) Phases Predicted from HSE06. J. Phys. Chem. Lett. 2014, 5, 1278–1282. (35) Madjet, M. E.-A.; Akimov, A. V.; El-Mellouhi, F.; Berdiyorov, G. R.; Ashhab, S.; Tabet, N.; Kais, S. Enhancing the Carrier Thermalization Time in Organometallic Perovskites by Halide Mixing. Phys. Chem. Chem. Phys. 2016, 18, 5219–5231. (36) Madjet, M. E.-A.; Berdiyorov, G. R.; El-Mellouhi, F.; Alharbi, F. H.; Akimov, A. V.; Kais, S. Cation Effect on Hot Carrier Cooling in Halide Perovskite Materials. J. Phys. Chem. Lett. 2017, 8, 4439–4445.


Page 22 of 26

Page 23 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

(37) Jankowska, J.; Long, R.; Prezhdo, O. V. Quantum Dynamics of Photogenerated Charge Carriers in Hybrid Perovskites: Dopants, Grain Boundaries, Electric Order, and Other Realistic Aspects. ACS Energy Lett. 2017, 2, 1588–1597. (38) Long, R.; Fang, W.; Prezhdo, O. V. Moderate Humidity Delays Electron–Hole Recombination in Hybrid Organic–Inorganic Perovskites: Time-Domain Ab Initio Simulations Rationalize Experiments. J. Phys. Chem. Lett. 2016, 7, 3215–3222. (39) Zhu, T.; Huhn, W. P.; Wessler, G. C.; Shin, D.; Saparov, B.; Mitzi, D. B.; Blum, V. I2–II–IV–VI4 (I = Cu, Ag; II = Sr, Ba; IV = Ge, Sn; VI = S, Se): Chalcogenides for Thin-Film Photovoltaics. Chem. Mater. 2017, 29, 7868–7879. (40) Han, Y.; Vogel, D. J.; Inerbaev, T. M.; May, P. S.; Berry, M. T.; Kilin, D. S. Photoinduced Dynamics to Photoluminescence in Ln3+ (Ln = Ce, Pr) Doped βNaYF4 Nanocrystals Computed in Basis of Non-Collinear Spin DFT with SpinOrbit Coupling. Mol. Phys. 2018, 116, 697–707. (41) Zheng, F.; Tan, L. Z.; Liu, S.; Rappe, A. M. Rashba Spin–Orbit Coupling Enhanced Carrier Lifetime in CH3NH3PbI3. Nano Lett. 2015, 15, 7794–7800. (42) Even, J.; Pedesseau, L.; Jancu, J.-M.; Katan, C. Importance of Spin–Orbit Coupling in Hybrid Organic/Inorganic Perovskites for Photovoltaic Applications. J. Phys. Chem. Lett. 2013, 4, 2999–3005. (43) Akimov, A. V.; Prezhdo, O. V. The PYXAID Program for Non-Adiabatic Molecular Dynamics in Condensed Matter Systems. J. Chem. Theory Comput. 2013, 9, 4959–4972.



(44) Akimov, A. V.; Prezhdo, O. V. Advanced Capabilities of the PYXAID Program: Integration Schemes, Decoherence Effects, Multiexcitonic States, and Field-Matter Interaction. J. Chem. Theory Comput. 2014, 10, 789–804. (45) Tully, J. C. Molecular Dynamics with Electronic Transitions. J. Chem. Phys. 1990, 93, 1061–1071. (46) Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I.; et al. QUANTUM ESPRESSO: A Modular and Open-Source Software Project for Quantum Simulations of Materials. J. Phys. Condens. Matter 2009, 21, 395502. (47) Hammes ‐ Schiffer, S.; Tully, J. C. Proton Transfer in Solution: Molecular Dynamics with Quantum Transitions. J. Chem. Phys. 1994, 101, 4657–4667. (48) Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for Liquid Metals. Phys. Rev. B 1993, 47, 558–561. (49) Kresse, G.; Hafner, J. Ab Initio Molecular-Dynamics Simulation of the LiquidMetal–Amorphous-Semiconductor Transition in Germanium. Phys. Rev. B 1994, 49, 14251–14269. (50) Kawamura, Y.; Mashiyama, H.; Hasebe, K. Structural Study on Cubic–Tetragonal Transition of CH3NH3PbI3. J. Phys. Soc. Jpn. 2002, 71, 1694–1697. (51) Torres, A.; Rego, L. G. C. Surface Effects and Adsorption of Methoxy Anchors on Hybrid Lead Iodide Perovskites: Insights for Spiro-MeOTAD Attachment. J. Phys. Chem. C 2014, 118, 26947–26954. (52) Amat, A.; Mosconi, E.; Ronca, E.; Quarti, C.; Umari, P.; Nazeeruddin, M. K.; Grätzel, M.; De Angelis, F. Cation-Induced Band-Gap Tuning in Organohalide


Page 24 of 26

Page 25 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

Perovskites: Interplay of Spin–Orbit Coupling and Octahedra Tilting. Nano Lett. 2014, 14, 3608–3616. (53) Pyxaid2 Package; Quantum-Dynamics-Hub, 2018, https://github.com/QuantumDynamics-Hub/pyxaid2. (54) Akimov, A. V. Libra: An Open-Source “Methodology Discovery” Library for Quantum and Classical Dynamics Simulations. J. Comput. Chem. 2016, 37, 1626– 1649. (55) Zhou, L.; Neukirch, A. J.; Vogel, D. J.; Kilin, D. S.; Pedesseau, L.; Carignano, M. A.; Mohite, A. D.; Even, J.; Katan, C.; Tretiak, S. Density of States Broadening in CH3NH3PbI3 Hybrid Perovskites Understood from Ab Initio Molecular Dynamics Simulations. ACS Energy Lett. 2018, 787–793. (56) Kawai, H.; Giorgi, G.; Marini, A.; Yamashita, K. The Mechanism of Slow HotHole Cooling in Lead-Iodide Perovskite: First-Principles Calculation on Carrier Lifetime from Electron–Phonon Interaction. Nano Lett. 2015, 15, 3103–3108. (57) Kim, M.; Im, J.; Freeman, A. J.; Ihm, J.; Jin, H. Switchable S = 1/2 and J = 1/2 Rashba Bands in Ferroelectric Halide Perovskites. Proc. Natl. Acad. Sci. 2014, 111, 6900–6904. (58) Lin, Y.; Akimov, A. V. Dependence of Nonadiabatic Couplings with Kohn–Sham Orbitals on the Choice of Density Functional: Pure vs Hybrid. J. Phys. Chem. A 2016, 120, 9028–9041. (59) Hedley, G. J.; Quarti, C.; Harwell, J.; Prezhdo, O. V.; Beljonne, D.; Samuel, I. D. W.

Hot-Hole

Cooling

Controls

the

Initial

Ultrafast

Relaxation

Methylammonium Lead Iodide Perovskite. Sci. Rep. 2018, 8, 26207.


in


(60) Li, W.; Liu, J.; Bai, F.-Q.; Zhang, H.-X.; Prezhdo, O. V. Hole Trapping by Iodine Interstitial Defects Decreases Free Carrier Losses in Perovskite Solar Cells: A Time-Domain Ab Initio Study. ACS Energy Lett. 2017, 2, 1270–1278. (61) Chen, T.; Chen, W.-L.; Foley, B. J.; Lee, J.; Ruff, J. P. C.; Ko, J. Y. P.; Brown, C. M.; Harriger, L. W.; Zhang, D.; Park, C.; et al. Origin of Long Lifetime of BandEdge Charge Carriers in Organic–Inorganic Lead Iodide Perovskites. Proc. Natl. Acad. Sci. 2017, 114, 7519–7524. (62) Mukamel, S. Principles of Nonlinear Optical Spectroscopy; Oxford University Press: New York, 1995.


Page 26 of 26

SpinâOrbit Interactions Greatly Accelerate Nonradiative Dynamics in

Recommend Documents

SpinâOrbit Interactions Greatly Accelerate Nonradiative Dynamics in