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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 739 records · Page 41
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Generation of out-of-plane ferroelectric behavior in a one-atom-thick monolayer

Ferroelectricity with out-of-plane polarization has so far been found in several two-dimensional (2D) materials, including monolayers comprising three to five planes of atoms, e.g. α-In 2 Se 3 and MoTe 2 . Here, we explore the generation of out-of-plane polarization within a one-atom-thick monolayer material, namely hexagonal boron nitride. We performed density-functional-theory calculations to explore inducing ferroelectric-like distortions through incorporation of isovalent substitutional impurities that are larger than the host atoms. This disparity in bond lengths causes a buckling of the h-BN, either up or down, which amounts to a dipole with two equivalent energies and opposing orientations. We tested several impurities to explore the magnitude of the induced dipole and the switching energy barrier for dipole inversion. The effects of strain, dipole–dipole interactions, and vertical heterostructures with graphene are further explored. Our results suggest a highly-tunable system with ground state antiferroelectricity and metastable ferroelectricity. Finally, we expect that this work will help foster new ways to include functionality in layered 2D-material-based applications.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Room-temperature large magnetoelectricity in a transition metal doped ferroelectric perovskite

There is increasing interest in novel magnetoelectric (ME) materials that exhibit robust ME coupling at room-temperature (RT) for advanced memory, energy, spintronics, and other multifunctional device applications, by making use of the ability to control polarization with a magnetic field and/or magnetization via an electric field. Obtaining ME materials with strong ME coupling, understanding the origin, and manipulating its processing along with composition to realize large ME coefficients at RT constitute an important step in multiferroic research. To address this, we have investigated the multiferroic and ME properties of Ni-doped Pb(Zr 0.20 Ti 0.80 )O 3 (PZT). We find that the ferroelectric (T C ~ 700 K) and weak ferromagnetic (~ 602 K) phase transitions of Ni-doped PZT are well above RT, leading to a strong ME coupling coefficient (α E,31 ) of 11.7 mVcm -1 Oe -1 (H ac = 1 Oe and f = 1 kHz). While X-ray diffraction suggests a single-phase material, high resolution transmission electron microscopy reveals regions with and without Ni present; thus magnetoelectric coupling between two phases is possible. First-principle calculations suggest the (Ni Pb ) × defect is likely to be responsible for the experimental observed magnetism and ME coupling in Ni-doped PZT. Furthermore, we demonstrate that Ni-doped PZT exhibits low loss tangent, low leakage current, large saturation polarization and weak ferromagnetism. Ultimately, our work demonstrates that Ni-doped PZT is a cost-effective RT multiferroic with strong ME coupling.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Bandgap analysis and carrier localization in cation-disordered ZnGeN 2

The bandgap of ZnGeN 2 changes with the degree of cation site disorder and is sought in light emitting diodes for emission at green to amber wavelengths. By combining the perspectives of carrier localization and defect states, we analyze the impact of different degrees of disorder on electronic properties in ZnGeN 2 , addressing a gap in current studies, which largely focus on dilute or fully disordered systems. The present study demonstrates changes in the density of states and localization of carriers in ZnGeN 2 calculated using bandgap-corrected density functional theory and hybrid calculations on partially disordered supercells generated using the Monte Carlo method. We use localization and density of states to discuss the ill-defined nature of a bandgap in a disordered material and identify site disorder and its impact on the structure as a mechanism controlling electronic properties and potential device performance. Decreasing the order parameter results in a large reduction of the bandgap. The reduction in bandgap is due, in part, to isolated, localized states that form above the valence band continuum associated with nitrogen coordinated by more zinc than germanium. The prevalence of defect states in all but the perfectly ordered structure creates challenges for incorporating disordered ZnGeN 2 into optical devices, but the localization associated with these defects provides insight into the mechanisms of electron/hole recombination in the material.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Weak magnetic field-dependent photoluminescence properties of lead bromide perovskites

The strong spin–orbit coupling (SOC) in lead halide perovskites, when inversion symmetry is lifted, has provided opportunities for investigating the Rashba effect in these systems. Moreover, the strong orbital moment, which, in turn, impacts the spin-pair in singlet and triplet electronic states, plays a significant role in enhancing the optoelectronic properties in the presence of external magnetic fields in lead halide perovskites. Here, we investigate the effect of weak magnetic fields (<1 T) on the photoluminescence (PL) properties of CsPbBr 3 nanocrystals with and without Ruddlesden–Popper (RP) faults and single crystals of CH 3 NH 3 PbBr 3 . Along with an enhancement in the PL intensity as a function of an external magnetic field, which is observed in both lead bromide perovskites, the PL emission red-shifts in CsPbBr 3 nanocrystals. Density-functional theory calculations of the electronic band-edge in CsPbBr 3 show almost no change in the energy gap as a function of the external magnetic field. The experimental results, thus, suggest the role of mixing of the triplet and singlet excitonic states under weak magnetic fields. This is further deduced from an enhancement in PL lifetimes as a function of the field in CsPbBr 3 ⁠. In CH 3 NH 3 PbBr 3⁠ , an increase in PL intensity is observed under weak magnetic fields; however, no changes in the peak energy or PL lifetimes are observed. The internal magnetic fields due to SOC are characterized for all three samples and found to be the highest for CsPbBr 3 nanocrystals with RP faults.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Charge Density Wave Order and Electronic Phase Transitions in a Dilute d ‐Band Semiconductor

Abstract As one of the most fundamental physical phenomena, charge density wave (CDW) order predominantly occurs in metallic systems such as quasi‐1D metals, doped cuprates, and transition metal dichalcogenides, where it is well understood in terms of Fermi surface nesting and electron–phonon coupling mechanisms. On the other hand, CDW phenomena in semiconducting systems, particularly at the low carrier concentration limit, are less common and feature intricate characteristics, which often necessitate the exploration of novel mechanisms, such as electron–hole coupling or Mott physics, to explain. In this study, an approach combining electrical transport, synchrotron X‐ray diffraction, and density‐functional theory calculations is used to investigate CDW order and a series of hysteretic phase transitions in a dilute d ‐band semiconductor, BaTiS 3 . These experimental and theoretical findings suggest that the observed CDW order and phase transitions in BaTiS 3 may be attributed to both electron–phonon coupling and non‐negligible electron–electron interactions in the system. This work highlights BaTiS 3 as a unique platform to explore CDW physics and novel electronic phases in the dilute filling limit and opens new opportunities for developing novel electronic devices.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Near-room-temperature ferromagnetic ordering in the pressure-induced collapsed-tetragonal phase in SrC⁢o 2 ⁢P 2

We present high-pressure electrical transport, magnetization, and single-crystal x-ray diffraction data on SrC⁢o 2 ⁢P 2 single crystals, revealing a transition from the uncollapsed tetragonal (ucT) to the collapsed tetragonal (cT) phase >∼10 GPa. This structural transition is accompanied by ferromagnetic (FM) ordering with a Curie temperature up to 260 K. First-principles-based density functional theory calculations show that there is a first-order transition between ucT and cT phases, with an onset ∼10 GPa as well as the appearance of FM ordering in the cT phase. Above ∼30 GPa, the experimental signatures of the magnetic ordering vanish in a first-order-like manner, consistent with the theoretical calculation results, indicating that SrC⁢o 2 ⁢P 2 is another example of the avoidance of quantum criticality in FM intermetallic compounds with almost room-temperature critical temperature. SrC⁢o 2 ⁢P 2 provides clear evidence that the structural, electronic, and magnetic properties associated with the cT transition are strongly entangled and are not only qualitatively captured by our first-principles-based calculations but are quantitatively reproduced as well.

density functional theory↗
DOE OSTI2021

Ethane Dehydrogenation on Single and Dual Centers of Ga-modified γ-Al 2 O 3

Density-functional theory calculations and microkinetic analysis are used to investigate the efficacy of Ga-modified γ-Al 2 O 3 (110) surfaces for the catalytic dehydrogenation of ethane and elucidate the synergy between Ga and Al sites. The model surfaces are modified by either Ga grafting or doping. We consider and analyze numerous active sites and rank them using microkinetic analysis. The kinetic parameters obtained from microkinetic modelling are compared with experimental values for ethane dehydrogenation over Ga 2 O 3 -Al 2 O 3 mixed oxides prepared by co-precipitation. The dominant reaction pathway proceeds via heterolytic C-H bond dissociation to a surface proton and a metal-carbanion intermediate that undergoes β-hydride elimination. We find that grafted Ga sites are catalytically inactive. In contrast, Ga-doped sites exhibit fivefold enhancement in catalytic activity when compared to the sites on pristine Al 2 O 3 , owed to the synergy between neighboring AlIII and GaIV sites. Furthermore, we model and investigate the effect of surface hydroxylation, demonstrate how surface water interferes with the aforementioned synergy between AlIII and GaIV sites and discuss the implications for the catalytic activity of the modified surfaces. Here, an increase in the partial pressure of H 2 O significantly increases the apparent activation energies of dehydrogenation and interestingly changes the most active site.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Structural Distortions and Uniaxial Negative Thermal Expansion in the Polar Dion–Jacobson Oxide RbNdTa 2 O 7

We provide deeper insight into the crystal structures, sequential structural phase transitions (I2cm → Cmce → I4/mcm → P4/mmm), thermal expansion, and electronic properties of the n = 2 Dion–Jacobson polar oxide RbNdTa 2 O 7 , through X-ray powder diffraction, neutron powder diffraction, Raman studies, and density functional theory calculations. We observed a uniaxial negative thermal expansion (NTE) across the first-order transition, I2cm → Cmce, where the unit cell contracts along the c-axis, which is driven by a contraction of the NdTa 2 O 6 layer. Here, this NTE occurs within the temperature range of the first-order phase transition and contrasts with the corkscrew mechanism typically observed in Ruddlesden–Popper phases. In RbNdTa 2 O 7 , the I2cm (hybrid improper ferroelectric) → Cmce (antipolar) transition involves crucial changes in the bond lengths of Nd and Ta polyhedra, coupled with polar to antipolar displacement of the Nd ions, leading to a net contraction in the NdTa 2 O 6 layer along the c-axis, while preserving the overall octahedral tilting magnitude. This transition highlights the intricate interplay between the Nd and Ta coordination and the associated TaO 6 distortions. Temperature-dependent Raman spectra analysis further confirms the first-order structural transition and associated NTE, providing evidence for increased bond stiffness across this transition. Additionally, using neutron powder diffraction, we have determined that the transition I4/mcm → P4/mmm occurs at approximately 1150 K. Finally, we have calculated from DFT + U, the partial density of states, the energy bandgaps, and effective masses of the charge carriers of the polar ground structure.

Chemical structure↗
DOE OSTI2023

Migration of Ga vacancies and interstitials in β – Ga 2 O 3

Pathways and energy barriers for the migration of Ga vacancies (V Ga ) and Ga interstitials (Ga i ) in β–Ga 2 O 3 are explored using hybrid functional calculations and the nudged elastic band method. Considering β–Ga 2 O 3 as primarily being an n-type semiconductor, we focus on defect charge states relevant under such conditions: $V^{3 –}_{Ga}$, Ga$^{3+}_{i}$, and Ga$^{+}_{i}$. Notably, we describe a mechanism by which V Ga can transform between its different split configurations. In all cases, the intermediate state consists of a vacancy split between three Ga sites—a three-split vacancy—which enables passage over a significantly lower energy barrier. This is because it avoids the unfavorable simple vacancy at the tetrahedral Ga site. The proposed mechanism lowers the overall barrier for $V^{3–}_{Ga}$ diffusion along the [001] crystal direction from 1.73 to 0.97 eV, whereas the 2.08 eV barrier for the [100] and [010] directions is unaffected. For Ga$^{3+}_{i}$, we obtain similar overall migration barriers of 0.72, 0.80, and 1.02 eV for the [010], [001], and [100] directions, respectively. Ga$^{+}_{i}$ exhibits a strong preference for diffusion within the large eight-sided channel; the overall migration barrier is 0.92 eV for the [010] direction, and 2.16 eV for the [001] and [100] directions. The limiting step for the two latter directions involves ionization of Ga$^{+}_{i}$ followed by a jump to an adjacent large eight-sided channel as Ga$^{3+}_{i}$. Finally, our results are discussed in light of experimental observations of thermally activated recovery processes in irradiated material.

36 MATERIALS SCIENCE↗
DOE OSTI2021

A new metric to control nucleation and grain size distribution in hybrid organic–inorganic perovskites by tuning the dielectric constant of the antisolvent

In perovskite research, there is a widely exploited but poorly explained phenomenon in which the addition of “antisolvents (ATS)” to precursor solutions results in higher-quality films. We explain the mechanism and driving force underlying an antisolvent-driven solvent extraction process. Density functional theory calculations uncover the defining effects of antisolvent choice on the extent of complexation between a lead salt and a methylammonium cation in solution. We experimentally validate the computational results using ultraviolet-visible spectroscopy and 207 Pb nuclear magnetic spectroscopy of methylammonium lead iodide solutions, containing both a processing solvent and an antisolvent. Furthermore, we uncover, and subsequently identify, the appearance of new species in solution as a result of the addition of the antisolvent. Furthermore, we observe that the choice of antisolvent has a substantial effect on the nature of the complexation of the methylammonium lead iodide (MAPbI 3 ) precursor species, whose origin we explain at an atomic level; specifically, the lower the dielectric of the antisolvent, the stronger the intermolecular binding energy between methylammonium cation (MA + ) cation and PbI 3 - plumbate, independent of the solvent or antisolvent interaction with the lead salt. Thin films were characterized using scanning electron microscopy; images of the films show how the addition of an antisolvent influences and, importantly, can be used to alter thin-film grain size. Grain size and distribution in thin films is reflected by the choice of antisolvent, promoting slower nucleation rates, a lower nucleation density, and hence larger final grain size.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Microstructure‐Dependent Sodium Storage Mechanisms in Hard Carbon Anodes

Sustainable energy storage is essential to support the transition to renewables and meet the increasing demand for energy. Sodium‐ion batteries (NIBs) are attractive for grid‐scale energy storage due to the abundance and low cost of sodium, sustainability of other battery components, and electrochemical performance. Hard carbon (HC) is a leading anode material for NIBs, but its complex microstructure complicates the understanding of sodium storage mechanisms. Using X‐ray total scattering and density functional theory calculations, this study clarifies how HC's microstructural variations influence sodium storage across the slope (high potential) and plateau (low potential) regions of the potential capacity curve. In the slope region, sodium initially adsorbs at high‐binding energy defect sites and subsequently intercalates between graphene layers, adsorbing at low‐binding energy defect sites, correlating with different slopes observed during initial sodiation. Initial irreversibility arises from sodium trapping at surface defects and solid electrolyte interface formation. In the plateau region, sodium simultaneously intercalates and fills pores, influenced by pore size, interlayer spacing, and defect concentration. HCs with larger pore sizes form larger sodium clusters. In conclusion, the proposed mechanism underscores the role of microstructure engineering in enhancing HC performance and advancing NIBs for grid‐scale energy storage.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Chern numbers of topological phonon band crossing determined with inelastic neutron scattering

Topological invariants in the band structure, such as Chern numbers, are important for the understanding and classification of the topological properties of matter and dictate the occurrence of exotic behaviors, yet their direct spectroscopic determination has been largely limited to electronic bands. Here, we use inelastic neutron scattering in conjunction with ab initio calculations to identify a variety of topological phonon band crossings in MnSi and CoSi single crystals. We find a distinct relation between the Chern numbers of a band-crossing node and the scattering intensity modulation in momentum space around the node. Given sufficiently high resolution, our method can be used to determine arbitrarily large Chern numbers of topological phonon band-crossing nodes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Tuning the structure and superconductivity of SrNi 2⁢ P 2 by Rh substitution

The compound SrNi 2⁢ P 2 is unique among the ThCr 2 ⁢Si 2 class since it exhibits a temperature-induced transition upon cooling from an uncollapsed tetragonal (ucT) state to a one-third-collapsed orthorhombic (tcO) state where one out of every three P-rows bond across the Sr layers. This compound is also known for exhibiting bulk superconductivity below 1.4 K at ambient pressure. Here, in this paper, we report on the effects of Rh substitution in Sr⁢(Ni 1-x ⁢Rh x ) 2 ⁢P 2 on the structural and superconducting properties. We studied the variation of the nearest P-P distances as a function of the Rh fraction at room temperature, as well as its temperature dependence for selected compositions. We find that increasing the Rh fraction leads to a decrease in the transition temperature between the ucT and tcO states, until a full suppression of the tcO state for x ≥ 0.166. The superconducting transition first remains nearly insensitive to the Rh fraction, and then it increases to 2.3 K after the tcO state is fully suppressed. These results are summarized in a phase diagram, built upon the characterization by energy dispersive x-ray spectroscopy, x-ray diffraction, resistance, magnetization, and specific heat measurements done on crystalline samples with varying Rh content. The relationship between band structure, crystal structure, and superconductivity is discussed based on previously reported band structure calculations on SrRh 2 ⁢P 2 . Moreover, the effect of Rh fraction on the stress-induced structural transitions is also addressed by means of strain-stress studies done by uniaxial compression of single-crystalline micropillars of Sr⁢(Ni 1-x ⁢Rh x ) 2 ⁢P 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Spin Splitting Energy of Transition Metals: A New, More Affordable Wave Function Benchmark Method and Its Use to Test Density Functional Theory

Accurately predicting the spin splitting energy of chemical species is important for understanding their reactivity and magnetic properties, but it is very challenging, especially for molecules containing transition metals. One impediment to progress is the scarcity of accurate benchmark data. Here we report a set of calculations designed to yield reliable benchmarks for simple transition-metal complexes that can be used to test density functional methods that are affordable for large systems of more practical interest. Various wave function methods are tested against experiment for Fe 2+ , Fe 3+ , and Co 3+ , including CASSCF, CASPT2, CASPT3, MRCISD, MRCISD+Q, ACPF, AQCC, CCSD(T), and CASPT2/CCSD(T) and also a new method called CASPT2.5, which is performed by taking the average of the CASPT2 and CASPT3 energies. Furthermore, we find that MRCISD+Q, ACPF, and AQCC require smaller active spaces for good accuracy than are required by CASPT2 and CASPT3, and this aspect may be important for calculations on larger molecules; here we find that CASPT2.5 extrapolated to a complete basis set is the most suitable method—in terms of computational cost and in terms of accuracy on monatomic systems—and therefore we chose this method for molecular benchmarks. Then Kohn–Sham density functional calculations with 60 exchange-correlation functionals are tested for FeF 2 , FeCl 2 , and CoF 2 . We find that MN15-L, M06-SX, and revM06 have very good agreement with CASPT2.5 benchmarks in terms of both the spin splitting energy and the optimized geometry for each spin state. In addition, we recommend def2-TZVP as the most suitable basis set to perform density functional calculations for molecular spin splitting energies; extra polarization functions in the basis set do not help to increase the accuracy of the spin splitting energy in KS calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Energy Migration Processes in Re(I) MLCT Complexes Featuring a Chromophoric Ancillary Ligand

We present herein the synthesis, structural characterization, electronic structure calculations, and ultrafast and supra-nanosecond photophysical properties of a series of five Re(I) bichromophores exhibiting metal to ligand charge transfer (MLCT) excited states based on the general formula fac -[Re(N ^ N)(CO) 3 (PNI-py)]PF 6, where PNI-py is 4-piperidinyl-1,8-naphthalimidepyridine and N ^ N is a diimine ligand ( Re1 – 5 ), along with their corresponding model chromophores where 4-ethylpyridine was substituted for PNI-py ( Mod1 – 5 ). The diimine ligands used include 1,10-phenanthroline (phen, 1 ), 2,9-dimethyl-4,7-diphenyl-1,10-phenanthroline (bcp, 2 ), 4,4'-di- tert -butyl-2,2'-bipyridine (dtbb, 3 ), 4,4'-diethyl ester-2,2'-bipyridine (deeb, 4 ), and 2,2'-biquinoline (biq, 5 ). In these metal–organic bichromophores, structural modification of the diimine ligand resulted in substantial changes to the observed energy transfer efficiencies between the two chromophores as a result of the variation in 3 MLCT excited-state energies. The photophysical properties and energetic pathways of the model chromophores were explored in parallel to accurately track the changes that arose from introduction of the organic chromophore pendant on the ancillary ligand. All relevant photophysical and energy transfer processes were probed and characterized using time-resolved photoluminescence spectroscopy, ultrafast and nanosecond transient absorption spectroscopy, and time-dependent density functional theory calculations. Of the five bichromophores in this study, four ( Re1 – 4 ) exhibited a thermal equilibrium between the 3 PNI-py and the 3 MLCT excited state, drastically extending the lifetimes of the parent model chromophores.

14 SOLAR ENERGY↗
DOE OSTI2021

Unraveling the Intermediate Reaction Complexes and Critical Role of Support-Derived Oxygen Atoms in CO Oxidation on Single-Atom Pt/CeO 2

CeO 2 -supported Pt single-atom catalysts have been extensively studied due to their relevance in automobile emission control and for the fundamental understanding of CeO 2 -based catalysts. Though CeO 2 -supported Pt nanoparticles are often more active than their single-atom counterparts, the former could easily redisperse to Pt single atom under oxidizing diesel conditions. Therefore, to maximize the reactivity of every Pt atom, it is important to fully understand the reaction mechanism of CeO 2 -supported Pt single atoms. Here, we report a CO oxidation study on a Pt/CeO 2 single-atom catalyst, where we can account for all of the neighbors using in situ and operando spectroscopy techniques and microcalorimetric measurements. Coupled with density functional theory calculations, we present a comprehensive picture of the dynamics of the surface species, the role of surface intermediates, and explain the observed reaction kinetics. We started with a catalyst containing exclusively single atoms and used in situ/operando spectroscopy to provide evidence for their stability during the reaction and to identify the Pt 1 complexes before and during the reaction and their binding to CO. The results reveal that in the precatalyst, Pt is present as Pt(O) 4 on the CeO 2 (111) step edge sites, but during CO oxidation, we find that two Pt 1 complexes coexist, representing two states of the same active site in the reaction cycle. The dominant state/complex remains Pt(O) 4 , which adsorbs CO very weakly as shown by CO microcalorimetry. The second, minority state/complex, Pt(CO)(O) 3 is generated through the reaction of Pt(O) 4 with CO, and CO is bound strongly to Pt 1 . Labile oxygen adatoms from the CeO 2 surface play a major role in the regeneration of Pt(O) 4 either directly from Pt(O) 3 or by reaction with the strongly adsorbed CO in Pt(CO)(O) 3 . We show that the formation of an oxygen vacancy and generation of a labile O* are not barrierless, which explains the long lifetime of Pt(CO)(O) 3 and its detectability despite being a minority complex. The results help to develop a comprehensive view of the dynamic evolution of Pt 1 complexes along the reaction cycle and provide mechanistic insights to guide the design of Pt-based single-atom catalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Comparison of the canonical transformation and energy functional formalisms for ab initio calculations of self-localized polarons

In materials with strong electron-phonon (e-ph) interactions, charge carriers can distort the surrounding lattice and become trapped, forming self-localized (small) polarons. We recently developed an ab initio approach based on canonical transformations to efficiently compute the formation and energetics of small polarons A different approach based on a Landau-Pekar energy functional has been proposed in the recent literature. Here in this work, we analyze and compare these two methods in detail. We show that the small polaron energy is identical in the two formalisms when using the same polaron wave function. We also show that our canonical transformation formalism can predict polaron band structures and can properly treat zero- and finite-temperature lattice vibration effects, although at present using a fixed polaron wave function. Conversely, the energy functional approach can compute the polaron wave function, but as we show here, it neglects lattice vibrations and cannot address polaron self-localization and thermal band narrowing. Taken together, this work relates two different methods developed recently to study polarons from first-principles, highlighting their merits and shortcomings and discussing them both in a unified formalism.

36 MATERIALS SCIENCE↗