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The series of compounds FexCr3-xSe4, with 0 less than or equal to x less than or equal to 3, has been prepared and various thermoelectric properties measured from 5 to 900 K.
In the simplest picture, a “self-trapped” polaron forms when an excess electron or hole deforms a crystal lattice, creating a potential well with bound states. Properties of self-trapped polarons in methylammonium lead iodide perovskite (MAPbI 3 ), which is widely used as solar cell absorber, are of great interest, and are a subject of ongoing investigations and debates concerning the existence of large polarons with the co-presence of metastable self-trapping. Herein, we employ a self-interaction-free density functional theory method to investigate the stability of small polarons in tetragonal MAPbI 3 phase. The electron small polaron is found to be unstable, while the hole small polaron is found to be metastable at realistic operation temperatures of solar cells. Further, the hole polaron is found to have a hole band close to the conduction band, which in conjunction with its metastability suggests that small polarons will have an appreciable effect on charge-carrier recombinations in MAPbI 3 . Further, in this study, we posit that the existence of the metastable polarons in addition to the large polarons may explain the experimentally observed non-monotonic temperature dependence of bimolecular charge-carrier recombination rate in tetragonal MAPbI 3 phase.
A key reaction underlying the charge transport in iron containing oxides, clays, micas is the Fe$^{2+}$-Fe$^{3+}$ exchange reaction between edge-sharing iron octahedra. These reactions facilitate conduction in these minerals by the thermally-activated hopping of small polarons across the lattice. Depending on the mineral and local charge state the small polaron can either encase an electron or hole. The probability for conduction of small polarons depends strongly on the height and adiabicity of the reaction barrier, with larger and more diabatic barriers yielding slow conduction associated with either weak coupling or a large prerequisite rearrangement of the lattice during charge transport. To model these reactions, a first principle electron transfer (ET) method was developed to model the small polaron hopping between the edge-sharing octahedra sites in hematite ($e^{-}$ polaron), goethite ($e^{-}$ polaron), and annite ($h^{+}$ polaron) bulk structures. The ET method is based on electronic structure methods (i.e., plane-wave Density Functional Theory) capable of performing calculations with periodic cells and large size systems efficiently while at the same time being accurate enough to be used in the estimation of the electron-transfer coupling matrix element, $V_{AB}$, and the electron transfer transmission factor, $\kappa_{el}$. Additionally, the calculations confirmed the existence of small polarons in all three minerals, and the reactions were predicted to be strongly adiabatic. It was found that transfer of a hole in the octahedral layer of annite had an adiabatic barrier of $0.311$ eV, and the transfer of an extra electron in hematite and goethite had adiabatic barriers of $0.242$ eV and $0.232$ eV respectively. The electronic coupling parameters,$V_{AB}$, were found to be $0.188$ eV, $0.196$ eV, and $0.102$ eV respectively for hematite, goethite, and annite. While similar bonding topologies pertain, the underlying basis for the differences is the subtle differences in local structures.
Polarons are entities of excess electrons dressed with local response of lattices, whose atomic-scale characterization is essential for understanding the many body physics arising from the electron-lattice entanglement, yet difficult to achieve. Here, using scanning tunneling microscopy and spectroscopy (STM/STS), we show the visualization and manipulation of single polarons in monolayer CoCl 2 , that are grown on HOPG substrate via molecular beam epitaxy. Two types of polarons are identified, both inducing upward local band bending, but exhibiting distinct appearances, lattice occupations and polaronic states. First principles calculations unveil origin of polarons that are stabilized by cooperative electron-electron and electron-phonon interactions. Both types of polarons can be created, moved, erased, and moreover interconverted individually by the STM tip, as driven by tip electric field and inelastic electron tunneling effect. This finding identifies the rich category of polarons in CoCl 2 and their feasibility of precise control unprecedently, which can be generalized to other transition metal halides.
We present a first-principles study of the short-time dynamics of excitons in hematite Fe 2 O 3 . We used time-dependent density functional theory (TD-DFT) with an underlying DFT+U treatment of electron interactions to characterize the electronic structure of excitons and nonadiabatic molecular dynamics theory (NA-MD) to determine their recombination (electronic ground-state recovery) and relaxation dynamics. Decoherence-corrected trajectory surface hopping approaches in NA-MD simulations yielded recovery times of ~1.1 to 1.8 ns and “higher-lying” exciton relaxation times of ~60 to 70 fs, in accord with experimentally derived lifetimes. With hematite phonons in the range of ~100 to 700 cm –1 , higher-lying excitons relax within one or two oscillations of the phonons before getting trapped into an electron–hole pair Exc-3 structure on the first excited state potential energy surface. This structure resembles already a pair of polarons (electron polaron plus hole polaron) with associated lattice distortions three (3) basal planes away. On longer time scales, the electron–hole bipolaronic pair hops to structures Exc-5, then Exc-7, then Exc-9, ... with the electron polaron and hole polaron separated by 5, 7, 9, ... basal planes in a process of charge separation. The largest frequency phonon ~672 cm –1 for the Exc-3 exciton structure is associated with the electron polaron moiety of the exciton. This phonon is a good candidate for giving rise to the recently observed and reported postexcitation transient IR absorption peak.
One of the serious challenges in all solid-state Li ion batteries is neutral Li intrusion into the solid-state electrolyte that can ultimately cause catastrophic failure. One possibility for this is due to n-type electron conductivity that induces the reaction Li + + e – → Li 0 at sites where the potential is less than the Li + /Li potential. This paper reports hybrid density functional theory calculations of the electronic conductivity in two prototype single crystalline solid-state electrolytes, cubic Li 7 La 3 Zr 2 O 12 (c-LLZO) and Li 7 P 3 S 11 (LPS). The formation energies of important point defects that can affect electron conductivity are determined, and we find that the mechanism of n-type electron conductivity for both solid-state electrolytes is via “small” electron polaron hopping, where the quotes signify that substantial Li ion rearrangement is associated with the polaron formation and its migration. In both electrolytes, the formation energies for the small polarons at the Fermi energy are too high to generate measurable electron conductivity at room temperature. For c-LLZO, the concentration of electron polarons necessary to ensure charge neutrality from positively charged oxygen vacancies formed in synthesis can be significantly higher. Hence, the electron conductivity could be significant when measured with ion-blocking metal electrodes, and we discuss how the synthesis conditions could affect this magnitude. However, in the solid-state battery, these polarons are replaced by negatively charged Li vacancies so that the electron conductivity should remain minimal. For LPS single crystals, the inherent minimal electron conductivity is independent of synthesis conditions. Here we also show that the cost of forming Li 0 in bulk c-LLZO is enormous due to strain effects so that it could only potentially form at voids, grain boundaries, or around vacancy defects which relax the lattice strain.
Georgia Tech School of Chemistry and Biochemistry Special Summer Seminar Series, Prof Carlos Silva; 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 electron-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-degenerate resonances with constant inter-peak energy spacing. We highlight measurements of population and dephasing dynamics that point to the apparently deterministic role of polaronic effects in excitonic properties. We contend that an interplay of long-range and short-range exciton-lattice couplings give rise to exciton polarons, a character that fundamentally establishes their effective mass and radius, and consequently, their quantum dynamics. Given this complexity, a fundamentally far-reaching issue is how Coulomb-mediated many-body interactions---elastic scattering such as excitation-induced dephasing, inelastic exciton bimolecular scattering, and multi-exciton binding---depend upon the specific exciton-lattice coupling within the structured excitation lineshape. We measure the intrinsic and density-dependent exciton dephasing rates of the multiple excitons and their dependence on temperature by means of two-dimensional coherent excitation spectroscopy. We find that diverse excitons display distinct intrinsic dephasing rates mediated by phonon scattering involving different effective phonons, and contrasting rates of exciton-exciton elastic scattering. These findings establish specifically the consequence of distinct lattice dressing on exciton many-body quantum dynamics, which critically define fundamental optical properties that underpin photonics and quantum optoelectronics.
Combined experimental and theoretical investigations were performed to evaluate the potential of n-type BiFeO 3 as a photoanode. While previous experimental and theoretical studies on BiFeO 3 mainly focused on its ferroelectric properties, several studies have reported the advantages of BiFeO 3 as a photoelectrode for solar water splitting (e.g. bandgap energy and band edge positions relative to water reduction and oxidation potentials). However, the photoelectrochemical properties of n-type BiFeO 3 have not yet been thoroughly investigated. In our experimental investigation, we developed an electrodeposition-based synthesis to prepare uniform n-type BiFeO 3 thin-film electrodes. Furthermore, using a heat treatment under a N 2 environment, we intentionally introduced additional oxygen vacancies into the pristine n-type BiFeO 3 electrodes to increase the majority carrier density. The bandgaps, flatband potentials, photocurrent onset potentials, photocurrent generation, and photoelectrochemical stabilities of the pristine and N 2 -treated BiFeO 3 photoanodes were investigated comparatively to improve our understanding of BiFeO 3 photoanodes and to examine the effect of oxygen vacancies on the photoelectrochemical properties of BiFeO 3 . In our theoretical investigation, we performed first-principles calculations and demonstrated the formation of a small polaron when an extra electron was introduced into the BiFeO 3 lattice. Changes in electronic states cause by the small polaron formation were carefully investigated. We also examined the effects of oxygen vacancies on electron polaron formation and carrier concentration in BiFeO 3 . Using charge formation energy calculations and referencing charge transition levels to the free electron polaron level instead of to the conduction band minimum, we showed that the oxygen vacancy is capable of serving as a donor to enhance the carrier concentration of BiFeO 3 . Furthermore, our theoretical results agree well with our experimental findings. Together, the new experimental and theoretical results and discussion provided in this study have considerably improved our understanding of n-type BiFeO 3 as a photoanode.
Here, we investigate the thermodynamic driving-force dependences of photoinduced charge separation (CS) and subsequent charge transfer dynamics in single-walled carbon nanotube (SWNT)–perylenediimide (PDI) donor–acceptor (D–A) superstructures. Pump–probe spectroscopy reveals that [SWNT (•+)n ]-(PDI –• ) n CS states form on an ∼100 fs time scale following photoexcitation; these dynamics are invariant across an ∼400 mV driving force range, indicating that SWNT hole polaron formation time scales are determined by nanotube lattice and solvent relaxation. These CS states feature SWNT hole polarons adjacent to (geminate) and nearby (nongeminate) PDI radical anions. Analysis of the free energy dependence for charge recombination (CR) of [SWNT •+ ] geminate -(PDI –• ) CS states highlights an ∼2 meV value for D–A electronic coupling (HAB) and ∼0.93 eV for the total reorganization energy (λ T ). A corresponding driving force dependence of the CR dynamics for [SWNT •+ ] nongeminate -(PDI –• ) CS states indicates a diminished H AB value (∼0.6 meV) and a larger λ T (∼1.1 eV), consistent with larger transfer distances. SWNT excitons that persist following photoinduced CS drive photooxidation of PDI –• components of [SWNT (•+)n ]-(PDI –• ) n CS states ( 1 SWNT* + PDI •– → PDI + SWNT •– ); this reaction manifests a significantly reduced λ T value (∼0.67 eV) as the initially prepared SWNT reduced state bears the character of a conduction band injected electron ([SWNT •– ] CB ). This reaction thus gives rise to relaxed, nongeminate SWNT electron and hole polarons on the same nanotube; these polarons react on a 10 2 ps time scale independent of the electronic structure of these SWNT-PDI superstructures.
Hybrid (photo)cathodes consisting of conjugated polymer and hydrogen evolution reaction (HER) cocatalysts are an emerging platform for low-cost solar fuel generation. Poly{[N,N′-bis(2-octyldodecyl)-naphthalene-1,4,5,8-bis(dicarboximide)-2,6-diyl]-alt-5,5′-(2,2′-bithiophene)}, known as P(NDI2OD-T2) or N2200, is a promising electron accepting material for bulk heterojunction photocathodes. Unlike inorganic (photo)electrodes, much less is known about the energetic alignment of conjugated polymer electrode/metal/electrolyte junctions. Here, in this work, we investigate the electrical doping behavior in an N2200 cathode and its Fermi-level alignment with gold nanoparticles, which is used here as a model for the hydrogen evolution metal cocatalyst. Through UV/visible, Raman, and attenuated total-reflectance infrared spectroelectrochemistry, we observe the impact of electrical doping on the vibrational frequencies of neutral, anion, and dianion species in N2200, which suggests that electron density changes within the corresponding naphthalene-diimide (NDI) units. Upon one-electron reduction, the $C=O$ stretching frequency of the NDI anion unit (polaron) shows a red shift by ∼ 68 cm –1 . Additionally, the $C=O$ stretching frequency of neutral units in the doped N2200 shows a minor red shift of ∼ 5 cm –1 , suggesting charge transfer from neighboring polaron units. Surface-enhanced Raman spectroscopy measurements of a gold nanoparticle-functionalized N2200 electrode revealed that the Au Fermi level only shifts with that of N2200 upon polaron formation; thus, the formal potential of polymer polaron formation determines the behavior of the catalyst Fermi level, which we posit will modulate reaction capability. This mechanistic study provides a new approach for understanding the nanometer-scale energetics at the conjugated polymer/cocatalyst junction and provides critical insights for the future design of HER (photo)cathodes.
Anatase TiO 2 is an efficient water splitting photocatalyst using UV light, but solar energy harvesting requires the presence of midgap states to increase visible light absorption. Despite numerous studies, important questions remain regarding the photophysics in O vacancy doped TiO 2 . Here, by employing extreme ultraviolet reflection–absorption (XUV-RA) spectroscopy at the Ti M2,3-edge, spectral signatures of both large and small polaron states are identified, allowing ultrafast electron and hole dynamics in these states to be independently resolved. Results show that visible light absorption occurs via promotion of an electron from the small polaron state to the TiO 2 conduction band. In contrast, absorption of UV light results in direct band gap excitation followed by carrier relaxation during which hot holes trap as small polarons in 45 ± 42 fs, and hot electrons couple to polar optical phonons leading to vibrational coherence and large polaron formation in 945 ± 92 fs.
Light engineering of correlated states in topological materials provides a new avenue of achieving exotic topological phases inaccessible by conventional tuning methods. Here we demonstrate a light control of correlation gaps in a model charge-density-wave (CDW) and polaron insulator (TaSe 4 ) 2 I recently predicted to be an axion insulator. Our ultrafast terahertz photocurrent spectroscopy reveals a two-step, non-thermal melting of polarons and electronic CDW gap via the fluence dependence of a longitudinal circular photogalvanic current. This helicity-dependent photocurrent reveals continuous ultrafast phase switches from the polaronic state to the CDW (axion) phase, and finally to a hidden Weyl phase as the pump fluence increases. Additional distinctive attributes aligning with the light-induced switches include: the mode-selective coupling of coherent phonons to the polaron and CDW modulation, and the emergence of a non-thermal chiral photocurrent above the pump threshold of CDW-related phonons. The demonstrated ultrafast chirality control of correlated topological states here holds large potentials for realizing axion electrodynamics and advancing quantum-computing applications.
Polarons are quasiparticles formed as a result of lattice distortions induced by charge carriers. The single-electron Holstein model captures the fundamentals of single polaron physics. We examine the power of the exponential ansatz for the polaron ground-state wavefunction in its coupled cluster, canonical transformation, and (canonically transformed) perturbative variants across the parameter space of the Holstein model. Our benchmark serves to guide future developments of polaron wavefunctions beyond the single-electron Holstein model.
“Hidden” phases, generated using ultrafast laser pulses (few hundred femtoseconds), with distinct properties than at the thermodynamic equilibrium, are appealing for technologies, as they can be long-lived, with a lifetime of hours or weeks, and reversible with temperature sweeping or extra pulses. In this regard, La 2/3 Ca 1/3 MnO 3 (LCMO) stands out due to its tunability through epitaxial strain, which can drive the bulk ferromagnetic metal into an antiferromagnetic insulator (AFI), and its susceptibility to photoinduced transitions. Indeed, AFI LCMO displays a long-lived photoinduced transition into a putative hidden phase whose exact nature and excitations are still largely unknown. Here, we combine ultrafast photoexcitation in the near infrared with in situ transport, x-ray absorption, and resonant inelastic x-ray scattering (RIXS) to investigate the excitations (polarons, phonons, and orbital) of the photoexcited phase of LCMO and contrast them with the thermodynamic phases achieved through strain and temperature. In the thermodynamic regime, we establish the correlation between polarons and transport placing them in the “strong coupling” regime of the Holstein model. Upon photoexcitation of LCMO-AFI, we uncover a long-lived phase characterized by the softening of the polaron excitations, the partial suppression of the Jahn-Teller distortion, and nearly unchanged phonons, showing the emergence of a photoexcited state absent in the equilibrium phase diagram. Finally, by varying temperature, epitaxial strain, and photoexcitation fluence, we construct a polaron phase diagram and identify the key spectroscopic signatures of each phase. Our laser-RIXS approach establishes a versatile platform for exploring photoinduced hidden phases in quantum materials in nonstroboscopic conditions.
The advance of soft, polymer-based (photo)electrochemical energy transformation and storage applications requires a framework for polymer and electrolyte design that includes a deep understanding of the polymer–electrolyte interphase. Here, we report on the investigations of two napthalenediimide (NDI)–bithiophene (T2)-based semiconducting copolymers using computational modeling and in situ, ex situ, and operando techniques to reveal how changes in electrolyte and polymer chemistry modulate the electronic and structural properties of polymer electrodes during electrochemical (de)doping. These systems are shown to host an ensemble of polarons, in contrast with the single polaron-like character often reported, whose properties vary with the nature of the local environment. Importantly, these polarons serve as reporters of the nanoscale environments in which they reside. We demonstrate that controlling the polymer and electrolyte chemistry regulates the nature of the charge carriers generated upon electrochemical doping and/or exciton dissociation in a photoelectrochemical solar cell: For instance, divalent counterions enable polaron and bipolaron formation at lower reducing potentials, while supporting more bipolaron formation than monovalent counterions. A novel application of NEXAFS reveals insights into charge (de)localization, providing a pathway for future investigation of electron transport mechanisms. Finally, simulations of polymer swelling of an amorphous interphase show that charge formation has a large impact on polymer swelling and ion penetration. These studies deliver insights to enable the control of charge-carrier and ion transport, the rates of electron transfer and catalytic efficiency, device stability, and overall device performance.
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. In this study, time-of-flight inelastic neutron scattering experiments and first-principles density-functional theory calculations were employed to investigate the lattice vibrations (or phonon dynamics) in methylammonium lead iodide, a prototypical example of MHPs. Our findings are that optical phonons lose temporal coherence gradually with increasing temperature which vanishes at the orthorhombic-to-tetragonal structural phase transition. Surprisingly, however, we found that the spatial coherence is still retained throughout the decoherence process. We argue that the temporally decoherent and spatially coherent vibrations contribute to the formation of large polarons in this metal halide perovskite.
Carrier mobility in doped conjugated polymers is limited by Coulomb interactions with dopant counterions. This complicates studying the effect of the dopant’s oxidation potential on carrier generation because different dopants have different Coulomb interactions with polarons on the polymer backbone. In this work, dodecaborane (DDB)-based dopants are used, which electrostatically shield counterions from carriers and have tunable redox potentials at constant size and shape. DDB dopants produce mobile carriers due to spatial separation of the counterion, and those with greater energetic offsets produce more carriers. Neutron reflectometry indicates that dopant infiltration into conjugated polymer films is redox-potential-driven. Remarkably, X-ray scattering shows that despite their large 2-nm size, DDBs intercalate into the crystalline polymer lamellae like small molecules, indicating that this is the preferred location for dopants of any size. These findings elucidate why doping conjugated polymers usually produces integer, rather than partial charge transfer: dopant counterions effectively intercalate into the lamellae, far from the polarons on the polymer backbone. Finally, it is shown that the IR spectrum provides a simple way to determine polaron mobility. Overall, higher oxidation potentials lead to higher doping efficiencies, with values reaching 100% for driving forces sufficient to dope poorly crystalline regions of the film.
The reversal of halide ions is studied under various conditions. However, the underlying mechanism of heat-induced reversal remains unclear. This work finds that dynamic disorder-induced localization of self-trapped polarons and thermal disorder-induced strain (TDIS) can be co-acting drivers of reverse segregation. Localization of polarons results in an order of magnitude decrease in excess carrier density (polaron population), causing a reduced impact of the light-induced strain (LIS – responsible for segregation) on the perovskite framework. Meanwhile, exposing the lattice to TDIS exceeding the LIS can eliminate the photoexcitation-induced strain gradient, as thermal fluctuations of the lattice can mask the LIS strain. Under continuous 0.1 W cm -2 illumination (upon segregation), the strain disorder is estimated to be 0.14%, while at 80 °C under dark conditions, the strain is 0.23%. However, in situ heating of the segregated film to 80 °C under continuous illumination (upon reversal) increases the total strain disorder to 0.25%, where TDIS is likely to have a dominant contribution. Therefore, the contribution of entropy to the system's free energy is likely to dominate, respectively. Various temperature-dependent in situ measurements and simulations further support the results. These findings highlight the importance of strain homogenization for designing stable perovskites under real-world operating conditions.