Polarons in materials

Today our understanding of the vibrational thermodynamics of materials at low temperatures is emerging nicely, based on the harmonic model in which phonons are independent. At high temperatures, however, this understanding must accommodate how phonons interact with other phonons or with other excitations. We shall see that the phonon-phonon interactions give rise to interesting coupling problems, and essentially modify the equilibrium and non-equilibrium properties of materials, e.g., thermodynamic stability, heat capacity, optical properties and thermal transport of materials. Despite its great importance, to date the anharmonic lattice dynamics is poorly understood and most studies on lattice dynamics still rely on the harmonic or quasiharmonic models. There have been very few studies on the pure phonon anharmonicity and phonon-phonon interactions. The work presented in this thesis is devoted to the development of experimental and computational methods on this subject. Modern inelastic scattering techniques with neutrons or photons are ideal for sorting out the anharmonic contribution. Analysis of the experimental data can generate vibrational spectra of the materials, i.e., their phonon densities of states or phonon dispersion relations. We obtained high quality data from laser Raman spectrometer, Fourier transform infrared spectrometer and inelastic neutron spectrometer. With accurate phonon spectra data, we obtained the energy shifts and lifetime broadenings of the interacting phonons, and the vibrational entropies of different materials. The understanding of them then relies on the development of the fundamental theories and the computational methods. We developed an efficient post-processor for analyzing the anharmonic vibrations from the molecular dynamics (MD) calculations. Currently, most first principles methods are not capable of dealing with strong anharmonicity, because the interactions of phonons are ignored at finite temperatures. Our method adopts the Fourier transformed velocity autocorrelation method to handle the big data of time-dependent atomic velocities from MD calculations, and efficiently reconstructs the phonon DOS and phonon dispersion relations. Our calculations can reproduce the phonon frequency shifts and lifetime broadenings very well at various temperatures. To understand non-harmonic interactions in a microscopic way, we have developed a numerical fitting method to analyze the decay channels of phonon-phonon interactions. Based on the quantum perturbation theory of many-body interactions, this method is used to calculate the three-phonon and four-phonon kinematics subject to the conservation of energy and momentum, taking into account the weight of phonon couplings. We can assess the strengths of phonon-phonon interactions of different channels and anharmonic orders with the calculated two-phonon DOS. This method, with high computational efficiency, is a promising direction to advance our understandings of non-harmonic lattice dynamics and thermal transport properties. These experimental techniques and theoretical methods have been successfully performed in the study of anharmonic behaviors of metal oxides, including rutile and cuprite stuctures, and will be discussed in detail in Chapters 4 to 6. For example, for rutile titanium dioxide (TiO2), we found that the anomalous anharmonic behavior of the B1g mode can be explained by the volume effects on quasiharmonic force constants, and by the explicit cubic and quartic anharmonicity. For rutile tin dioxide (SnO2), the broadening of the B2g mode with temperature showed an unusual concave downwards curvature. This curvature was caused by a change with temperature in the number of down-conversion decay channels, originating with the wide band gap in the phonon dispersions. For silver oxide (Ag2O), strong anharmonic effects were found for both phonons and for the negative thermal expansion.

In some metal oxides, an excess electron can give rise to the formation of a small polaron localized on a single site. However, there are still some metal oxides that exhibit the formation of a large polaron. The underlying mechanism behind this phenomenon remains unclear. In this study, we investigate polaron formation in metal oxides favorable for polaron formation using different functionals and through a review of the literature. Our findings indicate that the s valence electrons in cations could serve as a descriptor to classify the polarons in materials. In metal oxides with cations having ns (n ⩾ 5) valence electrons, excess charges trend to localize on several sites or form a two-dimensional shape, and even a large polaron, as these s electrons are delocalized in nature and have a large effect on p or d state polarons. The delocalized nature of ns (n ⩽ 4) valence electrons in cations is relatively small and does not affect the localization condition of p or d state polarons. Therefore, the excess charges in these metal oxides with ns (n ⩽ 4) valence electrons prefer to form a small polaron localizing on a single site. This work unveils the impact of the s valence in cations on polaron formation and provides a fundamental understanding of various types of polarons in metal oxides.

The physics of transport of heat-carrying atomic vibrations in amorphous and semi-crystalline solids is a topic of fundamental interest. Diverse tools have been employed to study thermal transport in these materials, including cryogenic thermal conductivity measurements and various inelastic scattering tools. However, unambiguously identifying the damping mechanisms of few THz and smaller frequency excitations remains difficult owing to the lack of the experimental probes in the frequency band. As a result, debate has remained regarding the microscopic origin of weak acoustic damping in amorphous silicon (Si), the unusually high thermal conductivity of ultra-drawn polyethylene, and other topics. In this thesis, we investigate the transport properties of heat-carrying acoustic excitations in semi-crystalline and amorphous solids using transient grating spectroscopy. This optical method permits the creation of thermal gradients over sub-micron length scales which may be comparable to the attenuation lengths of the excitations. We show how these measurements can be used to constrain the damping mechanisms in the sub-THz range that has been historically inaccessible by typical methods such as inelastic scattering. First, we report measurements of the bulk thermal conductivity and elastic properties of MoS₂ thin films. Specifically, we use TG to measure the in-plane longitudinal sound velocity and thermal conductivity. We do not observe any size effects of thermal conductivity with grating period, indicating that the propagating distance of heat-carrying acoustic phonons are smaller than the thermal length scale accessible in the experiment. This result is consistent with the mean free paths predicted from ab-initio numerical methods. Second, we utilize the capability of TG to resolve the microscopic heat transport properties of phonons in highly oriented semi-crystalline polyethylene (PE). Earlier experimental studies have reported thermal conductivities of up to ~ 100 Wm⁻¹ K⁻¹ crystalline polyethylene, orders of magnitude larger than the bulk value of ~ 0.4 Wm⁻¹ K⁻¹. However, the microscopic origin of the high thermal conductivity remains unclear. We address this question by applying TG to highly oriented polyethylene to show that mean free paths on micron length scales are the dominant heat carriers. Using a low-energy anisotropic Debye model to interpret these data, we find evidence of one-dimensional phonon density of states for excitations of frequency less than ~ 2 THz. This transition frequency is consistent with the unique features of ultradrawn PE, in particular the stiff longitudinal branch leading to wavelengths of 8 nm at 2 THz frequency; and fiber diameters Finally, we report the measurements of the frequency-resolved mean free path of heat-carrying acoustic excitation in amorphous silicon (aSi), for the first time. The heat-carrying acoustic excitations of amorphous silicon are of interest because their mean free paths approach the micron scale at room temperature. Despite extensive investigation, the origin of the weak acoustic damping in the heat-carrying frequencies remains a topic of debate for decades. A prior study suggested a framework of classifying the vibrations into propagons, diffusons, and locons. Propagons were considered phonon-like, delocalized, propagating vibrations; locons as localized vibrations, and diffusons as delocalized yet non-propagating vibrations. Following the framework, numerous works have predicted mechanism of acoustic damping in aSi, but the predictions have contradicted to observations in experiments. In this work, we obtained measurements of the frequency-dependent mean free path in amorphous silicon thin films from ~0.1-3 THz and over temperatures from 60 - 315 K using picosecond acoustics (PSA) and transient grating spectroscopy. We first describe our PSA experiments to resolve the attenuation of 0.1 THz acoustic excitations in aSi. We then present our table-top approach to resolve MFP of heat-carrying acoustic excitation between ~ 0.1-3 using TG spectroscopy. The mean free paths are independent of temperature and exhibit a Rayleigh scattering trend over most of this frequency range. The observed trend is inconsistent with the predictions of numerical studies based on normal mode analysis, but agrees with diverse measurements on other glasses. The micron-scale MFPs in amorphous Si arise from the absence of Akhiezer and two-level system damping in the sub-THz frequencies, leading to heat-carrying acoustic excitations with room-temperature damping comparable to that of other glasses at cryogenic temperatures. Our results allow us to establish a clear picture for the origin of micron-scale damping in aSi by understanding vibrations as acoustic excitation rather than propagons, diffusons, and locons.

Polarons, which arise from the intricate interplay between excess electrons and/or holes and lattice vibrations (phonons), represent quasiparticles pivotal to the electronic behavior of materials. This review reaffirms the established classification of small and large polarons, emphasizing its relevance in the context of recent advances in understanding lead halide perovskites' behavior. The distinct characteristics of large and small polarons stem from the electron–phonon interaction range, which exerts a profound influence on materials’ characteristics and functionalities. Concurrently, lead halides have emerged with exceptional opto‐electronic properties, featuring prolonged carrier lifetimes, low recombination rates, high defect tolerance, and moderate charge carrier mobilities; these characteristics make them a compelling contender for integration of optoelectronic devices. In this review, the formation of both small and large polarons within the lattice of lead halide perovskites, elucidating their role in protecting photogenerated charge carriers from recombination processes, is discussed. As optoelectronic devices continue to advance, this review underscores the importance of unraveling polaron dynamics to pave the way for innovative strategies for enhancing the performance of next‐generation photovoltaic technologies. Future research should explore novel polaronic effects using advanced computational and experimental techniques, enhancing our understanding and unlocking new applications in materials science and device engineering.

This work, presents a study of lifetime of carriers due to intrinsic scattering mechanisms viz. electron–electron interaction (EEI), electron–phonon interaction (EPI) and phonon–phonon interaction (PPI) in a promising half-Heusler thermoelectric FeVSb. Using the full-GW method, the effect of EEI and temperature on the valence and conduction band extrema and band gap are studied. The lifetime of carriers with temperature are estimated at these band extrema. At 300 K, estimated value of lifetime at VBM (CBM) is ∼1.91 × 10−14 s (∼2.05 × 10−14 s). The estimated ground state band gap considering EEI is ∼378 meV. Next, the effect of EPI on the lifetime of electrons and phonons with temperature are discussed. The comparison of two electron lifetimes suggests that EEI should be considered in transport calculations along with EPI. The average acoustic, optical and overall phonon lifetimes due to EPI are studied with temperature. Further, the effect of PPI is studied by computing average phonon lifetime for acoustic and optical phonon branches. The lifetime of the acoustic phonons are higher compared to optical phonons which indicates acoustic phonons contribute more to lattice thermal conductivity (κ ph). The comparison of phonon lifetime due to EPI and PPI suggests that, above 500 K EPI is the dominant phonon scattering mechanism and cannot be ignored in κ ph calculations. Lastly, a prediction of the power factor and figure of merit of n-type and p-type FeVSb is made by considering the temperature dependent carrier lifetime for the electronic transport terms. This study shows the importance of considering EEI in electronic transport calculations and EPI in phonon transport calculations in FeVSb. Our study is expected to provide results to further explore the thermoelectric transport in this material.

Electron-phonon (e-ph) interactions quantify the strength of interplay between charge carriers and lattice vibrations and critically determine the transport properties in materials near room temperature. Depending on the coupling strength, charge carriers can exhibit behaviors ranging from propagating waves extending across crystals to trapped particles localized in space. Therefore, accurately describing e-ph interactions plays a central role in quantitative transport studies on real materials. Over the last few years, first-principles methods combining density functional theory (DFT) and related techniques with the Boltzmann transport equation (BTE) have rapidly risen and reached maturity for investigating transport in various metals, semiconductors, and insulators with weak e-ph coupling. The lowest-order e-ph scattering process can be investigated starting from e-ph interactions from DFT calculations; this first-principles approach provides unambiguous quantitative prediction of transport properties such as the conductivity and mobility in common semiconductors and metals over a wide temperature range without using any empirical parameter. Encouraged by the agreement of the computed transport properties with experiment for many simple materials, this thesis aims to extend the applicability of this first-principles methodology and to further our understanding of microscopic transport mechanisms, especially in the wide temperature window near room temperature where transport is governed by e-ph scattering. We present research that expands the state of the art in three distinct ways, focusing on three research directions we pursue in this work. First, we employ the BTE to calculate the hole carrier mobility of naphthalene, an organic molecular crystal containing 36 atoms in a unit cell, the record largest system for first-principles charge transport calculations to date. The results are in excellent agreement with experiments, demonstrating that transport in some high-mobility organic semiconductors can still be explained within the band theory framework, and show that low-frequency rigid molecular motions control the electrical transport in organic molecular semiconductors in the bandlike regime. The second topic is an attempt to go beyond the lowest-order theory of e-ph interactions and quantify the importance of higher-order e-ph processes. We derive the electron-two-phonon scattering rates using many-body perturbation theory, compute them in GaAs, and quantify their impact on the electron mobility. We show that these next-to-leading order e-ph scattering rates, although smaller than the lowest-order contribution, are not negligible, and can compensate the overestimation of mobility generally made by the lowest-order BTE calculation in weakly-polar semiconductors. In the third part of the thesis, we explore the opposite extreme case in which e-ph interactions are strong and lead to the formation of localized (so-called polaron) electronic states that become self-trapped by the interactions with the atomic vibrations. We derive a rigorous approach based on canonical transformations to compute the energetics of self-localized (small) polarons in materials with strong e-ph interactions. With the aid of \textit{ab initio} e-ph interactions, we carry out the corresponding numerical calculations to investigate the formation energy of small polaron and determine whether the charge carriers favor localized states over the Bloch waves. Due to the low computational cost of our approach, we are able to apply these calculations to various compounds, focusing on oxides, predicting the presence of small polaron in agreement with experiments in various materials. Our work paves the way to understanding small polaron formation and extending these calculations to predict transport in the polaron hopping mechanism in materials with strong e-ph coupling.

The study of electrons and holes confined to two, one, and even zero dimensions has uncovered a rich variety of new physics and applications. This book describes the interaction between these confined carriers and the optic and acoustic phonons within and around the confined regions. Phonons provide the principal channel of energy transfer between the carriers and their surroundings and also the main restriction to their room temperature mobility. However, they also have many other roles; they contribute, for example, an essential feature to the operation of the quantum cascade laser. Since their momenta at relevant energies are well matched to those of electrons, they can also be used to probe electronic properties such as the confinement width of two-dimensional (2-D) electron gases and the dispersion curve of quasiparticles in the fractional quantum Hall effect. The book describes both the physics of the electron-phonon interaction in the different confined systems and the experimental and theoretical techniques that have been used in its investigation. The experimental methods include optical and transport techniques as well as techniques in which phonons are used as the experimental probe. This book provides an up-to-date review of the physics and its significance in device performance.

Phonons, quantized lattice vibrations, govern most of the thermophysical properties of solid-state materials such that understanding the temperature dependent lattice dynamics is of great technological importance. I performed inelastic neutron scattering measurements at the Spallation Neutron Source on ARCS, a wide-angular chopper spectrometer, to measure phonon dispersions and density of states over a wide range of temperatures. Large phonon anharmonicities manifested by phonon energy shifts and broadenings were observed in both measured phonon dispersions and phonon density of states. The sources of deviations from the simple harmonic model with temperature were elucidated using experimentally assessed lattice dynamics coupled with ab initio methods. Pure anharmonicity dominates the changes in lattice dynamics with temperature and therefore drive the entropy and thermophysical properties of thermal expansion and thermal conductivity. Crystal structure, anharmonicity, and nuclear quantum effects all play important roles in the thermal expansion of silicon, and a simple mechanical explanation is inappropriate. The quantum effect of nuclear vibrations is also expected to be important for thermal expansion of many materials. My experimental techniques capture the linewidth broadenings from phonon anharmonicity needed to calculate thermal conductivity. The methods developed for data reduction on single crystal inelastic neutron scattering data and predicting macroscopic quantities should also be useful for understanding microscopic mechanisms behind thermophysical properties for materials.

The development of halide perovskite semiconductors led to various technological breakthroughs in optoelectronics, in particular in the areas of photovoltaics and light-emitting diodes. Additionally, the study of their fundamental properties has uncovered intriguing puzzles that demand explanation. Polaronic effects associated with the coupling of electrons and holes to polar lattice vibrations are often invoked as a microscopic mechanism to explain various unusual experimental observations. While some form of polaronic behavior undoubtedly exists in these systems, several assumptions underlying standard models used to describe a polaron mechanism appear to be strongly violated in these materials. In this Perspective, we investigate the role of polaronic effects in halide perovskites and summarize signatures and failures of the polaron picture to explain physical characteristics of the materials. We highlight the importance of the complementary dynamic disorder concept that can rationalize various key properties of halide perovskites for which standard polaron and band-theory pictures of carrier transport fail.

Polaron dephasing processes are investigated in InAs/GaAs dots using far-infrared transient four wave mixing (FWM) spectroscopy. We observe an oscillatory behaviour in the FWM signal shortly (< 5 ps) after resonant excitation of the lowest energy conduction band transition due to coherent acoustic phonon generation. The subsequent single exponential decay yields long intraband dephasing times of 90 ps. We find excellent agreement between our measured and calculated FWM dynamics, and show that both real and virtual acoustic phonon processes are necessary to explain the temperature dependence of the polarization decay. PACS numbers: 78.67.Hc, 78.47.+p, 42.50.Md, 71.38.-k The strong spatial confinement of carriers in semiconductor quantum dots (QDs) leads to striking differences in the carrier-phonon interaction compared with systems of higher dimensionality. In particular, the discrete energy level s tructure in QDs results in long exciton and electron dephasing times [1, 2, 3, 4], making these semiconductor nanostructures highly attractive for implementation in quantum information processing applications. The study of dephasing mechanisms in QDs is commonly carried out using transient four wave mixing (FWM) spectroscopy. Using resonant interband excitation, FWM measurements have revealed the absorption lineshape of single QDs to consist of a narrow zero phonon line (ZPL) and an acoustic phonon-related broadband centred at the same energy. The only intraband FWM study [5] involved resonant excitation of high energy transitions in th e valence band of p-doped QDs yielding dephasing times ∼ 15 ps. However it was not possible to determine the dephasing mechanisms in this case. Intraband studies of the well-resolved lowest energy conduction band electron transitions in InAs/GaAs QDs have provided deep insight into the electron-phonon interaction and carrier relaxation processes in n-doped samples. Clear evidence of strong coupling between electrons and phonons, resulting in polaron formation, has been demonstrated using magneto-transmission measurements [6]. Ultrafast studies [7, 8] of polaron decay have shown that the previously assumed ’phonon bottleneck’ picture is not valid. Compared with semiconductor quantum wells, the intraband population relaxation time in QDs is long (∼ 50 ps) suggesting relatively long dephasing times. However there have been no reports of direct dephasing measurements to date. In the present letter we present the first investigations of i ntraband dephasing in n-doped QDs using degenerate FWM. Our calculations of the absorption lineshape in this case sh ow marked differences in comparison with the interband absorption [9]. The intraband lineshape consists of peaked acoustic phonon sidebands separated by ∼ 1.5 meV from the ZPL, which corresponds to phonons with wavelength close to the dot size, and is reminiscent of the lineshape associated wit h impurity-bound electron transitions [10]. Using pulse durations short enough to excite both the ZPL and acoustic phonon sidebands we find damped oscillations in the FWM signal, indicative of coherent acoustic phonon generation, followed by a single exponential decay. In contrast with the interband case, where the origin of the strong temperature dependence of the excitonic linewidth is still subject to debate, the simple 3 -level structure of the lowest energy conduction band states in InAs QDs permits an accurate simulation of the temperature dependence of the FWM signal. The excellent agreement found between experiment and theory, shows that virtual transitions between the p-states is the dominant dephasing mechanism at high temperature. At low temperature, we have measured an intersublevel dephasing time of T2 ∼ 90 ps. It is also interesting to compare our results with previous intraband dephasing measurements in higher dimensional (quantum well) systems [11]. Here phonon-mediated processes are not significant with the intraband dephasing instead determined by electronelectron interactions, yielding typical dephasing times ∼ 0.3 ps which are approximately 2 orders of magnitude faster than for the QD samples studied here. The relatively long intraband dephasing time in QDs is key to the efficient operation of new types of mid-infrared QD-based devices, such as intersublevel polaron lasers [12] and may be relevant for potential device applications such as qubits for quantum information processors [13]. The investigated samples were grown on (100) GaAs substrates by molecular beam epitaxy in the Stranski-Krastranow mode. They comprise 80 layers of InAs self-assembled QDs separated by 50 nm wide GaAs barriers, thus preventing both structural and electronic coupling between QD layers. The polaron transitions were studied between s-like ground (s) and p-like first excited ( p) states within the conduction band. To populate the s state, the samples were delta-doped with Si 2 nm below each QD layer. The doping density was controlled in such a way that the average doping did not exceed 1 electron per dot (see Ref. [14] for more details). Absorp

We use first-principles calculations, at the density-functional-theory (DFT) and GW levels, to study both the electron-phonon interaction for acoustic phonons and the ``synthetic'' vector potential induced by a strain deformation (responsible for an effective magnetic field in case of a nonuniform strain). In particular, the interactions between electrons and acoustic phonon modes, the so-called gauge-field and deformation potential, are calculated at the DFT level in the framework of linear response. The zero-momentum limit of acoustic phonons is interpreted as a strain of the crystal unit cell, allowing the calculation of the acoustic gauge-field parameter (synthetic vector potential) within the GW approximation as well. We find that using an accurate model for the polarizations of the acoustic phonon modes is crucial to obtain correct numerical results. Similarly, in the presence of a strain deformation, the relaxation of atomic internal coordinates cannot be neglected. The role of electronic screening on the electron-phonon matrix elements is carefully investigated. We then solve the Boltzmann equation semianalytically in graphene, including both acoustic and optical phonon scattering. We show that, in the Bloch-Gr\"uneisen and equipartition regimes, the electronic transport is mainly ruled by the unscreened acoustic gauge field, while the contribution due to the deformation potential is negligible and strongly screened. We show that the contribution of acoustic phonons to resistivity is doping and substrate independent, in agreement with experimental observations. The first-principles calculations, even at the GW level, underestimate this contribution to resistivity by $\ensuremath{\approx}30%$. At high temperature ($T&gt;270$ K), the calculated resistivity underestimates the experimental one more severely, the underestimation being larger at lower doping. We show that, besides remote phonon scattering, a possible explanation for this disagreement is the electron-electron interaction that strongly renormalizes the coupling to intrinsic optical-phonon modes. Finally, after discussing the validity of the Matthiessen rule in graphene, we derive simplified forms of the Boltzmann equation in the presence of impurities and in a restricted range of temperatures. These simplified analytical solutions allow us the extract the coupling to acoustic phonons, related to the strain-induced synthetic vector potential, directly from experimental data.

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 CoCl2, 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 CoCl2 and their feasibility of precise control unprecedently, which can be generalized to other transition metal halides.

Cyclohexylamine an effective corrosion inhibitor for mild steel in 0.1 N H2SO4: Experimental and theoretical (molecular dynamics simulation and FMO) study

Tunable electronic interactions in small lanthanide(III) nanoclusters: The comparative effects of OH − and O 2− supramolecular glues on europium(III)-to-dysprosium(III) energy transfer

Angle-resolved photoemission spectroscopy (ARPES) is a powerful experimental technique for directly probing electron dynamics in solids. The energy versus momentum dispersion relations and the associated spectral broadenings measured by ARPES provide a wealth of information on quantum many-body interaction effects. In particular, ARPES allows studies of the Coulomb interaction among electrons (electron-electron interactions) and the interaction between electrons and lattice vibrations (electron-phonon interactions). Here, we report ab initio simulations of the ARPES spectra of graphene including both electron-electron and electron-phonon interactions on the same footing. Our calculations reproduce some of the key experimental observations related to many-body effects, including the indication of a mismatch between the upper and lower halves of the Dirac cone.