Topological polarons in halide perovskites.

Halide perovskites emerged as a revolutionary family of high-quality semiconductors for solar energy harvesting and energy-efficient lighting. There is mounting evidence that the exceptional optoelectronic properties of these materials could stem from unconventional electron-phonon couplings, and it has been suggested that the formation of polarons and self-trapped excitons could be key to understanding such properties. By performing first-principles simulations across the length scales, here we show that halide perovskites harbor a uniquely rich variety of polaronic species, including small polarons, large polarons, and charge density waves, and we explain a variety of experimental observations. We find that these emergent quasiparticles support topologically nontrivial phonon fields with quantized topological charge, making them nonmagnetic analog of the helical Bloch points found in magnetic skyrmion lattices.

Excitonic Polarons and Self-Trapped Excitons from First-Principles Exciton-Phonon Couplings.

Excitons consist of electrons and holes held together by their attractive Coulomb interaction. Although excitons are neutral excitations, spatial fluctuations in their charge density couple with the ions of the crystal lattice. This coupling can lower the exciton energy and lead to the formation of a localized excitonic polaron or even a self-trapped exciton in the presence of strong exciton-phonon interactions. Here, we develop a theoretical and computational approach to compute excitonic polarons and self-trapped excitons from first principles. Our methodology combines the many-body Bethe-Salpeter approach with density-functional perturbation theory and does not require explicit supercell calculations. As a proof of concept, we demonstrate our method for a compound of the halide perovskite family.

Tuning commensurability in twisted van der Waals bilayers.

Moiré superlattices based on van der Waals bilayers1-4 created at small twist angles lead to a long wavelength pattern with approximate translational symmetry. At large twist angles (θt), moiré patterns are, in general, incommensurate except for a few discrete angles. Here we show that large-angle twisted bilayers offer distinctly different platforms. More specifically, by using twisted tungsten diselenide bilayers, we create the incommensurate dodecagon quasicrystals at θt = 30° and the commensurate moiré crystals at θt = 21.8° and 38.2°. Valley-resolved scanning tunnelling spectroscopy shows disparate behaviours between moiré crystals (with translational symmetry) and quasicrystals (with broken translational symmetry). In particular, the K valley shows rich electronic structures exemplified by the formation of mini-gaps near the valence band maximum. These discoveries demonstrate that bilayers with large twist angles offer a design platform to explore moiré physics beyond those formed with small twist angles.

Tunable electron-flexural phonon interaction in graphene heterostructures.

Peculiar electron-phonon interaction characteristics underpin the ultrahigh mobility1, electron hydrodynamics2-4, superconductivity5 and superfluidity6,7 observed in graphene heterostructures. The Lorenz ratio between the electronic thermal conductivity and the product of the electrical conductivity and temperature provides insight into electron-phonon interactions that is inaccessible to past graphene measurements. Here we show an unusual Lorenz ratio peak in degenerate graphene near 60 kelvin and decreased peak magnitude with increased mobility. When combined with ab initio calculations of the many-body electron-phonon self-energy and analytical models, this experimental observation reveals that broken reflection symmetry in graphene heterostructures can relax a restrictive selection rule8,9 to allow quasielastic electron coupling with an odd number of flexural phonons, contributing to the increase of the Lorenz ratio towards the Sommerfeld limit at an intermediate temperature sandwiched between the low-temperature hydrodynamic regime and the inelastic electron-phonon scattering regime above 120 kelvin. In contrast to past practices of neglecting the contributions of flexural phonons to transport in two-dimensional materials, this work suggests that tunable electron-flexural phonon couping can provide a handle to control quantum matter at the atomic scale, such as in magic-angle twisted bilayer graphene10 where low-energy excitations may mediate Cooper pairing of flat-band electrons11,12.

Erratum: Unified Approach to Polarons and Phonon-Induced Band Structure Renormalization [Phys. Rev. Lett. 129, 076402 (2022)].

This corrects the article DOI: 10.1103/PhysRevLett.129.076402.

Unified Approach to Polarons and Phonon-Induced Band Structure Renormalization.

Ab initio calculations of the phonon-induced band structure renormalization are currently based on the perturbative Allen-Heine theory and its many-body generalizations. These approaches are unsuitable to describe materials where electrons form localized polarons. Here, we develop a self-consistent, many-body Green's function theory of band structure renormalization that incorporates localization and self-trapping. We show that the present approach reduces to the Allen-Heine theory in the weak-coupling limit, and to total energy calculations of self-trapped polarons in the strong-coupling limit. To demonstrate this methodology, we reproduce the path-integral results of Feynman and diagrammatic Monte Carlo calculations for the Fröhlich model at all couplings, and we calculate the zero point renormalization of the band gap of an ionic insulator including polaronic effects.

Dynamic Rashba-Dresselhaus Effect.

The Rashba-Dresselhaus effect is the splitting of doubly degenerate band extrema in semiconductors, accompanied by the emergence of counterrotating spin textures and spin-momentum locking. Here we investigate how this effect is modified by lattice vibrations. We show that, in centrosymmetric nonmagnetic crystals, for which a bulk Rashba-Dresselhaus effect is symmetry-forbidden, electron-phonon interactions can induce a phonon-assisted, dynamic Rashba-Dresselhaus spin splitting in the presence of an out-of-equilibrium phonon population. In particular, we show how Rashba, Dresselhaus, or Weyl spin textures can selectively be established by driving coherent infrared-active phonons, and we perform ab initio calculations to quantify this effect for halide perovskites.

Efficient First-Principles Methodology for the Calculation of the All-Phonon Inelastic Scattering in Solids.

Inelastic scattering experiments are key methods for mapping the full dispersion of fundamental excitations of solids in the ground as well as nonequilibrium states. A quantitative analysis of inelastic scattering in terms of phonon excitations requires identifying the role of multiphonon processes. Here, we develop an efficient first-principles methodology for calculating the all-phonon quantum mechanical structure factor of solids. We demonstrate our method by obtaining excellent agreement between measurements and calculations of the diffuse scattering patterns of black phosphorus, showing that multiphonon processes play a substantial role. The present approach constitutes a step towards the interpretation of static and time-resolved electron, x-ray, and neutron inelastic scattering data.

Monolayer 1T-NbSe2 as a 2D-correlated magnetic insulator.

Monolayer group V transition metal dichalcogenides in their 1T phase have recently emerged as a platform to investigate rich phases of matter, such as spin liquid and ferromagnetism, resulting from strong electron correlations. Newly emerging 1T-NbSe2 has inspired theoretical investigations predicting collective phenomena such as charge transfer gap and ferromagnetism in two dimensions; however, the experimental evidence is still lacking. Here, by controlling the molecular beam epitaxy growth parameters, we demonstrate the successful growth of high-quality single-phase 1T-NbSe2. By combining scanning tunneling microscopy/spectroscopy and ab initio calculations, we show that this system is a charge transfer insulator with the upper Hubbard band located above the valence band maximum. To demonstrate the electron correlation resulted magnetic property, we create a vertical 1T/2H NbSe2 heterostructure, and we find unambiguous evidence of exchange interactions between the localized magnetic moments in 1T phase and the metallic/superconducting phase exemplified by Kondo resonances and Yu-Shiba-Rusinov­like bound states.

Phonon-Limited Mobility and Electron-Phonon Coupling in Lead-Free Halide Double Perovskites.

Lead-free halide double perovskites have attracted considerable attention as complements to lead-based halide perovskites in a range of optoelectronic applications. Experiments on Cs2AgBiBr6 indicate carrier mobilities in the range of 0.3-11 cm2/(V s) at room temperature, considerably lower than in lead-based perovskites. The origin of low mobilities is currently unclear, calling for an atomic-scale investigation. We report state-of-the-art ab initio calculations of the phonon-limited mobility of charge carriers in lead-free halide double perovskites Cs2AgBiX6 (X = Br, Cl). For Cs2AgBiBr6, we obtain room-temperature electron and hole mobilities of 17 and 14 cm2/(V s), respectively, in line with experiments. We demonstrate that the cause for the lower mobility of this compound, compared to CH3NH3PbI3, resides in the heavier carrier effective masses. A mode-resolved analysis of scattering rates reveals the predominance of Fröhlich electron-phonon scattering, similar to lead-based perovskites. Our results indicate that, to increase the mobility of lead-free perovskites, it is necessary to reduce the effective masses, for example by cation engineering.

Exciton-Phonon Interactions in Monolayer Germanium Selenide from First Principles.

We investigate from first principles exciton-phonon interactions in monolayer germanium selenide, a direct gap two-dimensional semiconductor. By combining the Bethe-Salpeter approach and the special displacement method, we explore the phonon-induced renormalization of the exciton wave functions, excitation energies, and oscillator strengths. We determine a renormalization of the optical gap of 0.1 eV at room temperature, which results from the coupling of the exciton with both acoustic and optical phonons, with the strongest coupling to optical phonons at ∼100 cm-1. We also find that the exciton-phonon interaction is similar between monolayer and bulk GeSe. Overall, we demonstrate that the combination of many-body perturbation theory and special displacements offers a new route to investigate electron-phonon couplings in excitonic spectra, the resulting band gap renormalization, and the nature of phonons that couple to the exciton.

Limits to Electrical Mobility in Lead-Halide Perovskite Semiconductors.

Semiconducting polycrystalline thin films are cheap to produce and can be deposited on flexible substrates, yet high-performance electronic devices usually utilize single-crystal semiconductors, owing to their superior charge-carrier mobilities and longer diffusion lengths. Here we show that the electrical performance of polycrystalline films of metal-halide perovskites (MHPs) approaches that of single crystals at room temperature. Combining temperature-dependent terahertz conductivity measurements and ab initio calculations we uncover a complete picture of the origins of charge-carrier scattering in single crystals and polycrystalline films of CH3NH3PbI3. We show that Fröhlich scattering of charge carriers with multiple phonon modes is the dominant mechanism limiting mobility, with grain-boundary scattering further reducing mobility in polycrystalline films. We reconcile the large discrepancy in charge-carrier diffusion lengths between single crystals and films by considering photon reabsorption. Thus, polycrystalline films of MHPs offer great promise for devices beyond solar cells, including light-emitting diodes and modulators.

Ruddlesden-Popper-Phase Hybrid Halide Perovskite/Small-Molecule Organic Blend Memory Transistors.

Controlling the morphology of metal halide perovskite layers during processing is critical for the manufacturing of optoelectronics. Here, a strategy to control the microstructure of solution-processed layered Ruddlesden-Popper-phase perovskite films based on phenethylammonium lead bromide ((PEA)2 PbBr4 ) is reported. The method relies on the addition of the organic semiconductor 2,7-dioctyl[1]benzothieno[3,2-b]benzothiophene (C8 -BTBT) into the perovskite formulation, where it facilitates the formation of large, near-single-crystalline-quality platelet-like (PEA)2 PbBr4 domains overlaid by a ≈5-nm-thin C8 -BTBT layer. Transistors with (PEA)2 PbBr4 /C8 -BTBT channels exhibit an unexpectedly large hysteresis window between forward and return bias sweeps. Material and device analysis combined with theoretical calculations suggest that the C8 -BTBT-rich phase acts as the hole-transporting channel, while the quantum wells in (PEA)2 PbBr4 act as the charge storage element where carriers from the channel are injected, stored, or extracted via tunneling. When tested as a non-volatile memory, the devices exhibit a record memory window (>180 V), a high erase/write channel current ratio (104 ), good data retention, and high endurance (>104 cycles). The results here highlight a new memory device concept for application in large-area electronics, while the growth technique can potentially be exploited for the development of other optoelectronic devices including solar cells, photodetectors, and light-emitting diodes.

Theory and Computation of Hall Scattering Factor in Graphene.

The Hall scattering factor, r, is a key quantity for establishing carrier concentration and drift mobility from Hall measurements; in experiments, it is usually assumed to be 1. In this paper, we use a combination of analytical and ab initio modeling to determine r in graphene. Although at high carrier densities r ≈ 1 in a wide temperature range, at low doping the temperature dependence of r is very strong with values as high as 4 below 300 K. These high values are due to the linear bands around the Dirac cone and the carrier scattering rates due to acoustic phonons. At higher temperatures, r can instead become as low as 0.5 due to the contribution of both holes and electrons and the role of optical phonons. Finally, we provide a simple analytical model to compute accurately r in graphene in a wide range of temperatures and carrier densities.

Intrinsic quantum confinement in formamidinium lead triiodide perovskite.

Understanding the electronic energy landscape in metal halide perovskites is essential for further improvements in their promising performance in thin-film photovoltaics. Here, we uncover the presence of above-bandgap oscillatory features in the absorption spectra of formamidinium lead triiodide thin films. We attribute these discrete features to intrinsically occurring quantum confinement effects, for which the related energies change with temperature according to the inverse square of the intrinsic lattice parameter, and with peak index in a quadratic manner. By determining the threshold film thickness at which the amplitude of the peaks is appreciably decreased, and through ab initio simulations of the absorption features, we estimate the length scale of confinement to be 10-20 nm. Such absorption peaks present a new and intriguing quantum electronic phenomenon in a nominally bulk semiconductor, offering intrinsic nanoscale optoelectronic properties without necessitating cumbersome additional processing steps.

First-principles calculations of charge carrier mobility and conductivity in bulk semiconductors and two-dimensional materials.

One of the fundamental properties of semiconductors is their ability to support highly tunable electric currents in the presence of electric fields or carrier concentration gradients. These properties are described by transport coefficients such as electron and hole mobilities. Over the last decades, our understanding of carrier mobilities has largely been shaped by experimental investigations and empirical models. Recently, advances in electronic structure methods for real materials have made it possible to study these properties with predictive accuracy and without resorting to empirical parameters. These new developments are unlocking exciting new opportunities, from exploring carrier transport in quantum matter to in silico designing new semiconductors with tailored transport properties. In this article, we review the most recent developments in the area of ab initio calculations of carrier mobilities of semiconductors. Our aim is threefold: to make this rapidly-growing research area accessible to a broad community of condensed-matter theorists and materials scientists; to identify key challenges that need to be addressed in order to increase the predictive power of these methods; and to identify new opportunities for increasing the impact of these computational methods on the science and technology of advanced materials. The review is organized in three parts. In the first part, we offer a brief historical overview of approaches to the calculation of carrier mobilities, and we establish the conceptual framework underlying modern ab initio approaches. We summarize the Boltzmann theory of carrier transport and we discuss its scope of applicability, merits, and limitations in the broader context of many-body Green's function approaches. We discuss recent implementations of the Boltzmann formalism within the context of density functional theory and many-body perturbation theory calculations, placing an emphasis on the key computational challenges and suggested solutions. In the second part of the article, we review applications of these methods to materials of current interest, from three-dimensional semiconductors to layered and two-dimensional materials. In particular, we discuss in detail recent investigations of classic materials such as silicon, diamond, gallium arsenide, gallium nitride, gallium oxide, and lead halide perovskites as well as low-dimensional semiconductors such as graphene, silicene, phosphorene, molybdenum disulfide, and indium selenide. We also review recent efforts toward high-throughput calculations of carrier transport. In the last part, we identify important classes of materials for which an ab initio study of carrier mobilities is warranted. We discuss the extension of the methodology to study topological quantum matter and materials for spintronics and we comment on the possibility of incorporating Berry-phase effects and many-body correlations beyond the standard Boltzmann formalism.

Slot-Die-Printed Two-Dimensional ZrS3 Charge Transport Layer for Perovskite Light-Emitting Diodes.

Liquid-phase exfoliation of zirconium trisulfide (ZrS3) was used to produce stable and ready-to-use inks for solution-processed semiconductor thin-film deposition. Ribbon-like layered crystals of ZrS3 were produced by the chemical vapor transport method and were then exfoliated in three different solvents: dimethylformamide, ethanol, and isopropyl alcohol. The resulting ZrS3 dispersions were compared for stability and the ability to form continuous films on top of the perovskite layer in light-emitting diodes with the ITO/PEDOT:PSS/MAPbBr3/2D-ZrS3/LiF/Al structure. Film deposition was performed by using either spray or slot-die coating methods. The slot-die coating route proved to produce better and more uniform films with respect to spray coating. We found that the 2D ZrS3 electron injection layer (EIL) stabilized the interface between the perovskite and LiF/Al cathode, reducing the turn-on voltage to 2.8 V and showing a luminance that does not degrade during voltage sweep. On the other hand, EIL-free devices show electroluminescence on the first voltage sweep that reduces almost to zero in the subsequent sweeps. Combining physical device simulation and density functional theory calculation, we are able to explain these results in terms of lowering the electron injection barrier at the cathode.

Route to High Hole Mobility in GaN via Reversal of Crystal-Field Splitting.

A fundamental obstacle toward the realization of GaN p-channel transistors is its low hole mobility. Here we investigate the intrinsic phonon-limited mobility of electrons and holes in wurtzite GaN using the ab initio Boltzmann transport formalism, including all electron-phonon scattering processes and many-body quasiparticle band structures. We predict that the hole mobility can be increased by reversing the sign of the crystal-field splitting in such a way as to lift the split-off hole states above the light and heavy holes. We find that a 2% biaxial tensile strain can increase the hole mobility by 230%, up to a theoretical Hall mobility of 120 cm^{2}/V s at room temperature and 620 cm^{2}/V s at 100 K.

Coexistence of Superconductivity with Enhanced Charge Density Wave Order in the Two-Dimensional Limit of TaSe2.

Bulk 2H-TaSe2 is a model charge density wave (CDW) metal with superconductivity emerging at extremely low temperature (Tc = 0.1 K). Here, by first-principles calculations including the explicit calculation of the screened Coulomb interaction, we demonstrate enhanced superconductivity in the CDW state of monolayer 1H-TaSe2 observed in recent experiments. Its ground-state 3 × 3 CDW phase features triangular clustering of Ta atoms and possesses a large electron-phonon coupling of λ = 0.74, yielding an order of magnitude higher superconducting Tc compared to the bulk. Upon lowering the thickness from bulk to monolayer TaSe2, the CDW intensifies with slightly decreased Fermi-level density of states, while superconductivity gets boosted via a largely increased intrinsic electron-phonon coupling strength, which overcomes both the CDW effect and naturally reinforced Coulomb repulsion. These results uncover the simultaneously enhanced CDW and superconducting orders in the two-dimensional limit for the first time and have key implications for other CDW metals like 2H-TaS2.

Polarons from First Principles, without Supercells.

We develop a formalism and a computational method to study polarons in insulators and semiconductors from first principles. Unlike in standard calculations requiring large supercells, we solve a secular equation involving phonons and electron-phonon matrix elements from density-functional perturbation theory, in a spirit similar to the Bethe-Salpeter equation for excitons. We show that our approach describes seamlessly large and small polarons, and we illustrate its capability by calculating wave functions, formation energies, and spectral decomposition of polarons in LiF and Li_{2}O_{2}.