We investigate the electron-phonon coupling in CH3NH3PbX3 lead halide perovskites through the observation of Landau levels and high-order excitons at weak magnetic fields, where the cyclotron energy is significantly smaller than the longitudinal optical phonon energy. The reduced masses of the carriers and the exciton binding energies obtained from these data are clearly influenced by polaron formation. We analyze the field-dependent polaronic and excitonic properties, and show that they can be quantitatively reproduced by the Frohlich large polaron model.
Two-dimensional (2D) perovskites with general formula $APbX_4$ are attracting increasing interest as solution processable, white-light emissive materials. Recent studies have shown that their broadband emission is related to the formation of intra-gap color centers; however, the nature and dynamics of the emissive species have remained elusive. Here we show that the broadband photoluminescence of the 2D perovskites $(EDBE)PbCl_4$ and $(EDBE)PbBr_4$ stems from the localization of small polarons within the lattice distortion field. Using a combination of spectroscopic techniques and first-princi…
Halide perovskites show unusual thermalisation kinetics for above bandgap photo-excitation. We explain this as a consequence of excess energy being deposited into discrete large polaron states. The cross-over between low-fluence and high-fluence `phonon bottleneck' cooling is due to a Mott transition where the polarons overlap ($n \ge 10^{18}/\mathrm{cm}^3$) and the phonon sub-populations are shared. We calculate the initial rate of cooling (thermalisation) from the scattering time in the Fröhlich polaron model to be 78 meVps$^{-1}$ for $\mathrm{CH}_3\mathrm{NH}_3\mathrm{PbI}_3$. This rapid in…
In this comment to [S. Lenjer, O. F. Schirmer, H. Hesse, and Th. W. Kool, Phys. Rev. B {\bf 66}, 165106 (2002)] we discuss the electronic structure of oxygen vacancies in perovskites. First principles computations are in favour of rather deep levels in these vacancies, and Lenjer et al suggest that the electrons' interaction energy is negative, but data on electroconductivity are against.
In halide perovskites, electrons (holes) exist as electronic (hole) polarons, excitons, free and trapped electrons (holes). Six kinds of collisions could lead to annihilation of electron and hole, three of them involve polaron(s). In the annihilation channel of each collision process, there is a certain probability to form a dying pair which the average distance between electron and hole is smaller than a critical distance. The annihilation probability per unit time of a collision process is a product of the formation probability of the dying pair in the annihilation channel and the annihilati…
Lead halide perovskite semiconductors are soft, polar, materials. The strong driving force for polaron formation (the dielectric electron-phonon coupling) is balanced by the light band effective-masses, leading to a strongly-interacting large-polaron. A first-principles prediction of mobility would help understand the fundamental mobility limits. Theories of mobility need to consider the polaron (rather than free-carrier) state due to the strong interactions. In this material we expect that at room temperature polar-optical phonon mode scattering will dominate, and so limit mobility. We calcul…
Chalcogenide perovskites have received considerable interest in photovoltaic research community owing to their stability (thermal and aqueous), non-toxicity and lead free composition. However, to date a theoretical study mainly focusing on the excitonic and polaronic properties are not explored rigorously, due to its huge computational demand. Herein, we capture the excitonic and polaronic effects in a series of chalcogenide perovskites ABS$_3$ where A=Ba, Ca, Sr, and B=Hf, Sn by employing state-of-the art hybrid density functional theory and many body perturbative approaches viz. GW and BSE. …
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 …
For the intrinsic carriers of MAPbBr$_{3}$, the temperature $T$ dependent mobility $μ(T)$ of behaves like $μ\propto T^{-1/2}$ in piezoelectric tetragonal phase, $μ\propto T^{-1.4}$ in non-piezoelectric cubic phase. But for the photo-generated carriers in other halide perovskites ABX$_{3}$, $μ\propto T^{-3/2}$ behavior is typical. Due to the strong interaction of carrier with longitudinal optical phonon, in ABX$_{3}$ the carriers mainly exist as optical polarons. The softness of ABX$_{3}$ renders it without inversion center in tetragonal phase, which allows piezoelectric effect at low carrier c…
Lead-halide perovskite (LHP) semiconductors are emergent optoelectronic materials with outstanding transport properties which are not yet fully understood. We find signatures of large polaron formation in the electronic structure of the inorganic LHP CsPbBr$_3$ by means of angle-resolved photoelectron spectroscopy. The experimental valence band dispersion shows a hole effective mass $0.26\pm0.02\,\,m_e$, 50% heavier than the bare mass $m_0 =0.17 m_e$ predicted by density functional theory. Calculations of electron-phonon coupling indicate that phonon dressing of the carriers mainly occurs via …
Polarons in Lead-Halide Perovskites: What the Structural Evidence Does and Does Not Establish
YUHS-KRIBB Medical Convergence Research Institute, College of Medicine, Yonsei University（延世大学医学院尤赫-韩国生命科学研究院）；Pohang Accelerator Laboratory, POSTECH（浦项科技大学波汉加速器实验室）；Department of Physics, University of Seoul（首尔大学物理系）；Global Institute of Future Technology, Shanghai Jiao Tong University（上海交通大学未来技术学院）
The microscopic origin of slow carrier cooling in lead-halide perovskites remains debated, and has direct implications for applications. Slow carrier cooling has been attributed to either polaron formation or a hot-phonon bottleneck effect at high excited carrier densities (> 10$^{18}$ cm$^{-3}$). These effects cannot be unambiguously disentangled from optical experiments alone. However, they can be distinguished by direct observations of ultrafast lattice dynamics, as these effects are expected to create qualitatively distinct fingerprints. To this end, we employ femtosecond electron diffract…
The formation of Frohlich polaron in metal halide perovskites, arising from the charge carrierlongitudinal optical (LO) phonon coupling, has been proposed to explain their exceptional properties, but the effective identification of polaron in these materials is still a challenge task. Herein, we theoretically present the infrared optical absorption of Frohlich polaron based on Huang-Rhys model. We find that multiphonon overtones are appeared as the energy of incident photon matches the multiple LO phonons, wherein the average phonon numbers of a polaron can be directly evaluated by the order o…
In recent years, metal halide perovskites have generated tremendous interest for optoelectronic applications and their underlying fundamental properties. Due to the large electron-phonon coupling characteristic of soft lattices, self-trapping phenomena are expected to dominate hybrid perovskite photoexcitation dynamics. Yet, while the photogeneration of small polarons was proven in low dimensional perovskites, the nature of polaron excitations in technologically relevant 3D perovskites, and their influence on charge carrier transport, remain elusive. In this study, we used a combination of fir…
The formation of polarons due to the interaction between charge carriers and the crystal lattice has been proposed to have wide-ranging effects on charge carrier dynamics in lead--halide perovskites (LHPs). The hypothesis underlying many of those proposals is that charge carriers are "protected" from scattering by their incorporation into polarons. We test that hypothesis by deriving expressions for the rates of scattering of polarons by polar-optical and acoustic phonons, and ionised impurities, which we compute for electrons in the LHPs MAPbI$_{3}$ , MAPbBr$_{3}$ and CsPbI$_{3}$. We then use…
Hybrid organic-inorganic halide perovskites have shown remarkable optoelectronic properties (1-3), believed to originate from correlated motion of charge carriers and the polar lattice forming large polarons (4-7). Few experimental techniques are capable of probing these correlations directly, requiring simultaneous sub-meV energy and femtosecond temporal resolution after absorption of a photon (8). Here we use transient multi-THz spectroscopy, sensitive to the internal motions of charges within the polaron, to temporally and energetically resolve the coherent coupling of charges to longitudin…
Temperature dependent optical conductivity spectra of a La0.7Ca0.3MnO3 (LCMO) sample were measured. In the metallic regime at very low temperatures, they clearly showed two types of absorption features, i.e., a sharp Drude peak and a broad mid-infrared absorption band, which could be explained as coherent and incoherent bands of a large lattice polaron. This elementary excitation in LCMO was found to be in a strong coupling regime and to have interactions with the spin degree of freedom.
An ab initio LMTO approach and semi-empirical quantum chemical INDO method have been used for supercell calculations of basic point defects - F-type centers and hole polarons bound to cation vacancy - in partly covalent perovskite KNbO3. We predict the existence of both one-site and two-site (molecular) polarons with close absorption energies (~ 1 eV). The relevant experimental data are discussed and interpreted.
We investigate photoluminescence (PL) transitions of MAPbX$_{3}$ (X = I, Br and Cl) organic-inorganic hybrid perovskite single crystals under magnetic fields of up to 60 T. In these materials, sharp free-exciton transition peaks emerge at a low temperature (4.2 K). Under strong magnetic fields, the free-exciton PL transitions of three different halogens show dramatic differences. The free-exciton transitions of the MAPbCl$_{3}$ crystal undergo negative energy shifts, while those of the MAPbBr$_{3}$ crystal show normal diamagnetic shifts. To obtain the variation from Cl to Br, we attempt to mea…
Charge transport is crucial to the performance of hybrid halide perovskite solar cells. A theoretical model based on large polarons is proposed to elucidate charge transport properties in the perovskites. Critical new physical insights are incorporated into the model, including the recognitions that acoustic phonons as opposed to optical phonons are responsible for the scattering of the polarons; these acoustic phonons are fully excited due to the "softness" of the perovskites, and the temperature-dependent dielectric function underlies the temperature dependence of charge carrier mobility. Th…
While polarons --- charges bound to a lattice deformation induced by electron-phonon coupling --- are primary photoexcitations at room temperature in bulk metal-halide hybrid organic-inorganic perovskites (HOIP), excitons --- Coulomb-bound el\-ectron-hole pairs --- are the stable quasi-particles in their two-dimensional (2D) analogues. Here we address the fundamental question: are polaronic effects consequential for excitons in 2D-HIOPs? Based on our recent work, we argue that polaronic effects are manifested intrinsically in the exciton spectral structure, which is comprised of multiple non-d…
Excitation localization involving dynamic nanoscale distortions is a central aspect of photocatalysis, quantum materials and molecular optoelectronics. Experimental characterization of such distortions requires techniques sensitive to the formation of point-defect-like local structural rearrangements in real time. Here, we visualize excitation-induced strain fields in a prototypical member of the lead halide perovskites via femtosecond resolution diffuse x-ray scattering measurements. This enables momentum-resolved phonon spectroscopy of the locally-distorted structure and reveals radially-exp…
The long carrier lifetime and defect tolerance in metal halide perovskites (MHPs) are major contributors to the superb performance of MHP optoelectronic devices. Large polarons were reported to be responsible for the long carrier lifetime. Yet microscopic mechanisms of the large polaron formation including the so-called phonon melting, are still under debate. Here, time-of-flight (TOF) inelastic neutron scattering (INS) experiments and first-principles density-functional theory (DFT) calculations were employed to investigate the lattice vibrations (or phonon dynamics) in methylammonium lead io…
Exciton-polaritons offer a versatile platform for realization of all-optical integrated logic gates due to the strong effective optical nonlinearity resulting from the exciton-exciton interactions. In most of the current excitonic materials there exists a direct connection between the exciton robustness to thermal fluctuations and the strength of exciton-exciton interaction, making materials with highest levels of exciton nonlinearity applicable at cryogenic temperatures only. Here, we show that strong polaronic effects, characteristic for perovskite materials, allow to overcome this limitatio…
Single crystals of electron-doped SrMnO3 with a cubic perovskite structure have been systematically investigated as the most canonical (orbital-degenerate) double-exchange system, whose ground states have been still theoretically controversial. With only 1-2% electron doping by Ce substitution for Sr, a G-type antiferromagnetic metal with a tiny spin canting in a cubic lattice shows up as the ground state, where the Jahn-Teller polarons with heavy mass are likely to form. Further electron doping above 4%, however, replaces this isotropic metal with an insulator with tetragonal lattice distorti…
Polaron-mediated metal-insulator transition and proton conduction in hydrogenated nickelate perovskites
School of Physics and Astronomy, Beijing Normal University（北京师范大学物理学院）；Key Laboratory of Multiscale Spin Physics (Beijing Normal University), Ministry of Education（教育部多尺度自旋物理重点实验室（北京师范大学））；College of Physics, Hebei Normal University（河北师范大学物理学院）；Hebei Advanced Thin Films Laboratory（河北省先进薄膜实验室）
We investigate the formation of self-trapped holes (STH) in three prototypical perovskites (SrTiO3, BaTiO3, PbTiO3) using a combination of density functional theory (DFT) calculations with local potentials and hybrid functionals. First we construct a local correction potential for polaronic configurations in SrTiO3 that is applied via the DFT+U method and matches the forces from hybrid calculations. We then use the DFT+U potential to search the configuration space and locate the lowest energy STH configuration. It is demonstrated that both the DFT+U potential and the hybrid functional yield a …
Systems supporting exciton-polaritons represent solid-state optical platforms with a strong built-in optical nonlinearity provided by exciton-exciton interactions. In conventional semiconductors with hydrogen-like excitons the nonlinearity rate demonstrates the inverse scaling with the binding energy. This makes excitons stable at room temperatures weakly interacting, which obviously limits the possibilities of practical applications of the corresponding materials for nonlinear photonics. We demonstrate experimentally and theoretically, that these limitations can be substantially softened in h…
We study the ultrafast phonon response of mixed-valence perovskite Cs$_2$Au$_2$I$_6$ using pump-probe spectroscopy under high-pressure in a diamond anvil cell. We observed a remarkable softening and broadening of the Au - I stretching phonon mode with both applied pressure and photoexcitation. Using a double-pump scheme we measured a lifetime of the charge transfer excitation into single valence Au$^{2+}$ of less than 4 ps, which is an indication of the local character of the Au$^{2+}$ excitation. Furthermore, the strong similarity between the pressure and fluence dependence of the phonon soft…
Hybrid organic-inorganic semiconductors feature complex lattice dynamics due to the ionic character of the crystal and the softness arising from non-covalent bonds between molecular moieties and the inorganic network. Here we establish that such dynamic structural complexity in a prototypical two-dimensional lead iodide perovskite gives rise to the coexistence of diverse excitonic resonances, each with a distinct degree of polaronic character. By means of high-resolution resonant impulsive stimulated Raman spectroscopy, we identify vibrational wavepacket dynamics that evolve along different co…
Transition metal oxides such as \ce{BiVO4} are promising materials as photoelectrodes in solar-to-fuel conversion applications. However, their performance is limited by the low carrier mobility (especially electron mobility) due to the formation of small polarons. Recent experimental studies show improved carrier mobility and conductivity by atomic dopings. We studied the small polaron hopping mobility in pristine and doped \ce{BiVO4} by combining Landau-Zener theory and kinetic Monte Carlo (kMC) simulation fully from first-principles, and investigated the effect of dopant-polaron interactions…
Owing to both electronic and dielectric confinement effects, two-dimensional organic-inorganic hybrid perovskites sustain strongly bound excitons at room temperature. Here, we demonstrate that there are non-negligible contributions to the excitonic correlations that are specific to the lattice structure and its polar fluctuations, both of which are controlled via the chemical nature of the organic counter-cation. We present a phenomenological, yet quantitative framework to simulate excitonic absorption lineshapes in single-layer organic-inorganic hybrid perovskites, based on the two-dimensiona…
Understanding the appearance of commensurate and incommensurate modulations in perovskite antiferroelectrics (AFEs) is of great importance for material design and engineering. The dielectric and elastic properties of the AFE domain boundaries are lack of investigation. In this work, a novel Landau theory is proposed to understand the transformation of AFE commensurate and incommensurate phases, by considering the coupling between the oxygen octahedral tilt mode and the polar mode. The derived relationship between the modulation periodicity and temperature is in good agreement with the experime…
Many transition metal oxides (TMOs) are Mott insulators due to strong Coulomb repulsion between electrons, and exhibit metal-insulator transitions (MITs) whose mechanisms are not always fully understood. Unlike most TMOs, minute doping in CaMnO3 induces a metallic state without any structural transformations. This material is thus an ideal platform to explore band formation through the MIT. Here, we use angle-resolved photoemission spectroscopy to visualize how electrons delocalize and couple to phonons in CaMnO3. We show the development of a Fermi surface where mobile electrons coexist with h…
The behavior of hot carriers in metal-halide perovskites (MHPs) present a valuable foundation for understanding the details of carrier-phonon coupling in the materials as well as the prospective development of highly efficient hot carrier and carrier multiplication solar cells. Whilst the carrier population dynamics during cooling have been intensely studied, the evolution of the hot carrier properties, namely the hot carrier mobility, remain largely unexplored. To address this, we introduce a novel ultrafast visible pump - infrared push - terahertz probe spectroscopy (PPP-THz) to monitor the …
The coherence of collective modes, such as phonons, and their modulation of the electronic states are long sought in complex systems, which is a cross-cutting issue in photovoltaics and quantum electronics. In photovoltaic cells and lasers based on metal halide perovskites, the presence of polaronic coupling, i.e., photocarriers dressed by the macroscopic motion of charged lattice, assisted by terahertz (THz) longitudinal optical (LO) phonons, has been intensely studied yet still debated. This may be key for explaining the remarkable properties of the perovskite materials, e.g., defect toleran…
How unconventional oxidation state Au$^{2+}$ is stabilized in halide perovskite Cs$_4$Au$_3$Cl$_{12}$: a first-principles study of its polaron crystal nature
We report on the exciton formation and relaxation dynamics following photocarrier injection in a single-layer two-dimensional lead-iodide perovskite. We probe the time evolution of four distinct exciton resonances by means of time-resolved photoluminescence and transient absorption spectroscopies, and find that at 5\,K a subset of excitons form on a $\lesssim$ 1-ps timescale, and that these relax subsequently to lower-energy excitons on $\sim$ 5--10\,ps with a marked temperature dependence over $<$ 100\,K. We implement a mode projection analysis that determines the relative contribution of all…
A system of strongly-interacting electron-lattice polarons can exhibit charge and orbital order at sufficiently high polaron concentrations. In this study, the structure of short-range polaron correlations in the layered colossal magnetoresistive perovskite manganite, La1.2Sr1.8Mn2O7, has been determined by a crystallographic analysis of broad satellite maxima observed in diffuse X-ray and neutron scattering data. The resulting q=(0.3,0,1) modulation is a longitudinal octahedral-stretch mode, consistent with an incommensurate Jahn-Teller-coupled charge-density-wave fluctuations, that implies a…
The list of possible commensurate phases obtained from the parent tetragonal phase of Ruddlesden-Popper systems, A$_{n+1}$B$_n$C$_{3n+1}$ for general $n$ due to a single phase transition involving the reorienting of octahedra of C (oxygen) ions is reexamined using a Landau expansion. This expansion allows for the nonlinearity of the octahedral rotations and the rotation-strain coupling. It is found that most structures allowed by symmetry are inconsistent with the constraint of rigid octahedra which dictates the form of the quartic terms in the Landau free energy. For A$_2$BC$_4$ our analysis …
The parity-preserving $U(1)\times U(1)$ massless QED$_3$ is proposed as a pristine graphene-like planar quantum electrodynamics model. The spectrum content, the degrees of freedom, spin, masses and charges of the quasiparticles (electron-polaron, hole-polaron, photon and Néel quasiparticles) which emerge from the model are discussed. The four-fold broken degeneracy of the Landau levels, similar as the one experimentally observed in pristine graphene submitted to high applied external magnetic fields, is obtained. Furthermore, the model exhibits zero-energy Landau level indicating a kind of ano…
Electron-boson interaction is fundamental to a thorough understanding of various exotic properties emerging in many-body physics. In photoemission spectroscopy, photoelectron emission due to photon absorption would trigger diverse collective excitations in solids, including the emergence of phonons, magnons, electron-hole pairs, and plasmons, which naturally provides a reliable pathway to study electron-boson couplings. While fingerprints of electron-phonon/-magnon interactions in this state-of-the-art technique have been well investigated, much less is known about electron-plasmon coupling, a…
Ruddlesden-Popper (RP) phases of Ba$_{\textrm{n+1}}$Zr$_{\textrm{n}}$S$_{\textrm{3n+1}}$ (n=[1-3]) are evolved as new promising class of chalcogenide perovskites in the field of optoelectronics, especially in solar cells. However, detailed studies regarding its optical, excitonic, polaronic and transport properties are hitherto unknown. Here, we have explored the excitonic and polaronic effect in RP phases of Ba$_{\textrm{n+1}}$Zr$_{\textrm{n}}$S$_{\textrm{3n+1}}$ (n=[1-3]) using several first-principles based state-of-the-art methodologies under the framework of Many Body Perturbation Theory.…
The formation of large polarons has been proposed as reason for the high defect tolerance, low mobility, low charge carrier trapping and low nonradiative recombination rates of lead halide perovskites. Recently, direct evidence for large-polaron formation has been reported from a 50% effective mass enhancement in angle-resolved photoemission of CsPbBr3 over theory for the orthorhombic structure. We present in-depth band dispersion measurements of CsPbBr3 and GW calculations which lead to almost identical effective masses at the valence band maximum of 0.203+/-0.016 m0 in experiment and 0.226 m…
The hyperfine features and thermal stability of a muonium (Mu)-related paramagnetic center were investigated in the SrTiO$_3$ perovskite titanate via muon spin rotation spectroscopy. The hyperfine coupling tensor of the paramagnetic center was found to have prominent dipolar characteristics, indicating that the electron spin density is dominantly distributed on a Ti site to form a small polaron near an ionized Mu$^+$ donor. Based on a hydrogen-Mu analogy, interstitial hydrogen is also expected to form such a polaronic center in the dilute doping limit. The small activation energy of 30(3) meV …
We develop techniques to study the temperature dependent localization, thermalization, and the effects of phonon scattering on the excitons in halide perovskites from the analysis of the emission spectra. The excitonic Urbach edge, when inferred from the low energy tails of the temperature dependent luminescence spectra, is shown to be sensitive to the electron distribution and thermalization. A method to observe the Urbach focus is devised for halide perovskites where the temperature dependence of the excitonic gap is anomalous. The value of the zero-point bandgap renormalization is inferred …
Chalcogenide perovskites have emerged as non-toxic and stable photovoltaic materials, acting as an alternative to lead halide hybrid perovskites having similar optoelectronic properties. In the present work, we report the electronic and optical properties of chalcogenide perovskites AZrS$_3$ (A=Ca, Sr, Ba) by using the density functional theory (DFT) and many-body perturbation theory (MBPT viz. G$_0$W$_0$ and BSE). This study includes excitonic analysis for the aforementioned systems. The exciton binding energy (E$_\textrm{B}$) is found to be larger than that of the halide perovskites, as the …
The discovery of lead free all-inorganic alloyed double perovskites have revolutionized photovoltaic research, showing promising light emitting efficiency and its tunability. However, detailed studies regarding optical, exciton, polaron and transport properties remain unexplored. Here, we report a theoretical study on the variation of carrier-lattice interaction and optoelectronic properties of pristine as well as alloyed Cs$_2$AgInCl$_6$ double perovskites. We have employed many-body perturbation theory (G$_0$W$_0$@HSE06) and density functional perturbation theory (DFPT) to compute exciton bi…
The phenomenological theory for the polar instability giving rise to a two-dimensional electron gas at perovskite interfaces is hereby extended to include the coupling to perovskite tilts. A Landau theory for homogeneous tilts is first explored, setting the scene for the further, more realistic Landau-Ginzburg theory describing varying tilt amplitudes across a thin film. The theory is also generalized to account for the response to an applied electric field normal to the interface, which allows a finer control on phase transitions. The conventionally described physics of a single metal-insulat…
Recently discovered fine structure of the morphotropic phase boundaries in highly piezoelectric mixture compounds PZT, PMN-PT, and PZN-PT demonstrates the importance of highly non-linear interactions in these systems. We show that an adequate Landau-type description of the ferroelectric phase transitions in these compounds is achieved by the use of a twelfth-order expansion of the Landau potential in terms of the phenomenological order parameter. Group-theoretical and catastrophe-theory methods are used in constructing the appropriate Landau potential. A complete phase diagram is calculated in…
