Mode-coupling theory of lattice dynamics for classical and quantum crystals.

The dynamical properties of nuclei, carried by the concept of phonon quasiparticles , are central to the field of condensed matter. While the harmonic approximation can reproduce a number of properties observed in real crystals, the inclusion of anharmonicity in lattice dynamics is essential to accurately predict properties such as heat transport or thermal expansion. For highly anharmonic systems, non-perturbative approaches are needed, which result in renormalized theories of lattice dynamics. In this article, we apply the Mori-Zwanzig projector formalism to derive an exact generalized Langevin equation describing the quantum dynamics of nuclei in a crystal. By projecting this equation on quasiparticles in reciprocal space, and with results from linear response theory, we obtain a formulation of vibrational spectra that fully accounts for the anharmonicity. Using a mode-coupling approach, we construct a systematic perturbative expansion in which each new order is built to minimize the following ones. With a truncation to the lowest order, we show how to obtain a set of self-consistent equations that can describe the lineshapes of quasiparticles. The only inputs needed for the resulting set of equations are the static Kubo correlation functions, which can be computed using (fully quantum) path-integral molecular dynamics or approximated with (classical or ab initio) molecular dynamics. We illustrate the theory with an application on fcc 4He, an archetypal quantum crystal with very strong anharmonicity.

A pre-time-zero spatiotemporal microscopy technique for the ultrasensitive determination of the thermal diffusivity of thin films.

Diffusion is one of the most ubiquitous transport phenomena in nature. Experimentally, it can be tracked by following point spreading in space and time. Here, we introduce a spatiotemporal pump-probe microscopy technique that exploits the residual spatial temperature profile obtained through the transient reflectivity when probe pulses arrive before pump pulses. This corresponds to an effective pump-probe time delay of 13 ns, determined by the repetition rate of our laser system (76 MHz). This pre-time-zero technique enables probing the diffusion of long-lived excitations created by previous pump pulses with nanometer accuracy and is particularly powerful for following in-plane heat diffusion in thin films. The particular advantage of this technique is that it enables quantifying thermal transport without requiring any material input parameters or strong heating. We demonstrate the direct determination of the thermal diffusivities of films with a thickness of around 15 nm, consisting of the layered materials MoSe2 (0.18 cm2/s), WSe2 (0.20 cm2/s), MoS2 (0.35 cm2/s), and WS2 (0.59 cm2/s). This technique paves the way for observing nanoscale thermal transport phenomena and tracking diffusion of a broad range of species.

Spectroscopic signatures of nonpolarons: the case of diamond.

Polarons are quasi-particles made from electrons interacting with vibrations in crystal lattices. They derive their name from the strong electron-vibration polar interactions in ionic systems, that induce spectroscopic and optical signatures of such quasi-particles. In this paper, we focus on diamond, a non-polar crystal with inversion symmetry which nevertheless shows interesting signatures stemming from electron-vibration interactions, better denoted "nonpolaron" signatures in this case. The (non)polaronic effects are produced by short-range crystal fields, while long-range quadrupoles only have a small influence. The corresponding many-body spectral function has a characteristic energy dependence, showing a plateau structure that is similar to but distinct from the satellites observed in the polar Fröhlich case. We determine the temperature-dependent spectral function of diamond by two methods: the standard Dyson-Migdal approach, which calculates electron-phonon interactions within the lowest-order expansion of the self-energy, and the cumulant expansion, which includes higher orders of electron-phonon interactions. The latter corrects the nonpolaron energies and broadening, providing a more realistic spectral function, which we examine in detail for both conduction and valence band edges.

Unraveling Heat Transport and Dissipation in Suspended MoSe2 from Bulk to Monolayer.

Understanding heat flow in layered transition metal dichalcogenide (TMD) crystals is crucial for applications exploiting these materials. Despite significant efforts, several basic thermal transport properties of TMDs are currently not well understood, in particular how transport is affected by material thickness and the material's environment. This combined experimental-theoretical study establishes a unifying physical picture of the intrinsic lattice thermal conductivity of the representative TMD MoSe2 . Thermal conductivity measurements using Raman thermometry on a large set of clean, crystalline, suspended crystals with systematically varied thickness are combined with ab initio simulations with phonons at finite temperature. The results show that phonon dispersions and lifetimes change strongly with thickness, yet the thinnest TMD films exhibit an in-plane thermal conductivity that is only marginally smaller than that of bulk crystals. This is the result of compensating phonon contributions, in particular heat-carrying modes around ≈0.1 THz in (sub)nanometer thin films, with a surprisingly long mean free path of several micrometers. This behavior arises directly from the layered nature of the material. Furthermore, out-of-plane heat dissipation to air molecules is remarkably efficient, in particular for the thinnest crystals, increasing the apparent thermal conductivity of monolayer MoSe2 by an order of magnitude. These results are crucial for the design of (flexible) TMD-based (opto-)electronic applications.

Hot-Carrier Cooling in High-Quality Graphene Is Intrinsically Limited by Optical Phonons.

Many promising optoelectronic devices, such as broadband photodetectors, nonlinear frequency converters, and building blocks for data communication systems, exploit photoexcited charge carriers in graphene. For these systems, it is essential to understand the relaxation dynamics after photoexcitation. These dynamics contain a sub-100 fs thermalization phase, which occurs through carrier-carrier scattering and leads to a carrier distribution with an elevated temperature. This is followed by a picosecond cooling phase, where different phonon systems play a role: graphene acoustic and optical phonons, and substrate phonons. Here, we address the cooling pathway of two technologically relevant systems, both consisting of high-quality graphene with a mobility >10 000 cm2 V-1 s-1 and environments that do not efficiently take up electronic heat from graphene: WSe2-encapsulated graphene and suspended graphene. We study the cooling dynamics using ultrafast pump-probe spectroscopy at room temperature. Cooling via disorder-assisted acoustic phonon scattering and out-of-plane heat transfer to substrate phonons is relatively inefficient in these systems, suggesting a cooling time of tens of picoseconds. However, we observe much faster cooling, on a time scale of a few picoseconds. We attribute this to an intrinsic cooling mechanism, where carriers in the high-energy tail of the hot-carrier distribution emit optical phonons. This creates a permanent heat sink, as carriers efficiently rethermalize. We develop a macroscopic model that explains the observed dynamics, where cooling is eventually limited by optical-to-acoustic phonon coupling. These fundamental insights will guide the development of graphene-based optoelectronic devices.

Electron-Phonon beyond Fröhlich: Dynamical Quadrupoles in Polar and Covalent Solids.

We include the treatment of quadrupolar fields beyond the Fröhlich interaction in the first-principles electron-phonon vertex in semiconductors. Such quadrupolar fields induce long-range interactions that have to be taken into account for accurate physical results. We apply our formalism to Si (nonpolar), GaAs, and GaP (polar) and demonstrate that electron mobilities show large errors if dynamical quadrupoles are not properly treated.

ABINIT: Overview and focus on selected capabilities.

abinit is probably the first electronic-structure package to have been released under an open-source license about 20 years ago. It implements density functional theory, density-functional perturbation theory (DFPT), many-body perturbation theory (GW approximation and Bethe-Salpeter equation), and more specific or advanced formalisms, such as dynamical mean-field theory (DMFT) and the "temperature-dependent effective potential" approach for anharmonic effects. Relying on planewaves for the representation of wavefunctions, density, and other space-dependent quantities, with pseudopotentials or projector-augmented waves (PAWs), it is well suited for the study of periodic materials, although nanostructures and molecules can be treated with the supercell technique. The present article starts with a brief description of the project, a summary of the theories upon which abinit relies, and a list of the associated capabilities. It then focuses on selected capabilities that might not be present in the majority of electronic structure packages either among planewave codes or, in general, treatment of strongly correlated materials using DMFT; materials under finite electric fields; properties at nuclei (electric field gradient, Mössbauer shifts, and orbital magnetization); positron annihilation; Raman intensities and electro-optic effect; and DFPT calculations of response to strain perturbation (elastic constants and piezoelectricity), spatial dispersion (flexoelectricity), electronic mobility, temperature dependence of the gap, and spin-magnetic-field perturbation. The abinit DFPT implementation is very general, including systems with van der Waals interaction or with noncollinear magnetism. Community projects are also described: generation of pseudopotential and PAW datasets, high-throughput calculations (databases of phonon band structure, second-harmonic generation, and GW computations of bandgaps), and the library libpaw. abinit has strong links with many other software projects that are briefly mentioned.

Low-Energy Phases of Bi Monolayer Predicted by Structure Search in Two Dimensions.

We employ an ab-initio structure search algorithm to explore the configurational space of bismuth in quasi-two dimensions. A confinement potential is introduced to restrict the movement of atoms within a predefined thickness to find the stable and metastable forms of monolayer Bi. In addition to the two known low-energy structures (puckered monoclinic and buckled hexagonal), our calculations predict three new phases: α, ß, and γ. Each phase exhibits peculiar electronic properties, ranging from metallic (α and γ) to semiconducting (puckered monoclinic, buckled hexagonal, and ß) monolayers. Topologically nontrivial features are predicted for buckled hexagonal and γ phases. We also remark on the role of 5d electrons on the electronic properties of Bi monolayer. We conclude that Bi provides a rich playground to study distortion-mediated metal-insulator phase transitions in quasi-2D.

Spin States Protected from Intrinsic Electron-Phonon Coupling Reaching 100 ns Lifetime at Room Temperature in MoSe2.

We present time-resolved Kerr rotation measurements, showing spin lifetimes of over 100 ns at room temperature in monolayer MoSe2. These long lifetimes are accompanied by an intriguing temperature-dependence of the Kerr amplitude, which increases with temperature up to 50 K and then abruptly switches sign. Using ab initio simulations, we explain the latter behavior in terms of the intrinsic electron-phonon coupling and the activation of transitions to secondary valleys. The phonon-assisted scattering of the photoexcited electron-hole pairs prepares a valley spin polarization within the first few ps after laser excitation. The sign of the total valley magnetization, and thus the Kerr amplitude, switches as a function of temperature, as conduction and valence band states exhibit different phonon-mediated intervalley scattering rates. However, the electron-phonon scattering on the ps time scale does not provide an explanation for the long spin lifetimes. Hence, we deduce that the initial spin polarization must be transferred into spin states, which are protected from the intrinsic electron-phonon coupling, and are most likely resident charge carriers, which are not part of the itinerant valence or conduction band states.

Electron-Beam Manipulation of Silicon Dopants in Graphene.

The direct manipulation of individual atoms in materials using scanning probe microscopy has been a seminal achievement of nanotechnology. Recent advances in imaging resolution and sample stability have made scanning transmission electron microscopy a promising alternative for single-atom manipulation of covalently bound materials. Pioneering experiments using an atomically focused electron beam have demonstrated the directed movement of silicon atoms over a handful of sites within the graphene lattice. Here, we achieve a much greater degree of control, allowing us to precisely move silicon impurities along an extended path, circulating a single hexagon, or back and forth between the two graphene sublattices. Even with manual operation, our manipulation rate is already comparable to the state-of-the-art in any atomically precise technique. We further explore the influence of electron energy on the manipulation rate, supported by improved theoretical modeling taking into account the vibrations of atoms near the impurities, and implement feedback to detect manipulation events in real time. In addition to atomic-level engineering of its structure and properties, graphene also provides an excellent platform for refining the accuracy of quantitative models and for the development of automated manipulation.

Two-Step Phase Transition in SnSe and the Origins of its High Power Factor from First Principles.

The interest in improving the thermoelectric response of bulk materials has received a boost after it has been recognized that layered materials, in particular SnSe, show a very large thermoelectric figure of merit. This result has received great attention while it is now possible to conceive other similar materials or experimental methods to improve this value. Before we can now think of engineering this material it is important we understand the basic mechanism that explains this unusual behavior, where very low thermal conductivity and a high thermopower result from a delicate balance between the crystal and electronic structure. In this Letter, we present a complete temperature evolution of the Seebeck coefficient as the material undergoes a soft crystal transformation and its consequences on other properties within SnSe by means of first-principles calculations. Our results are able to explain the full range of considered experimental temperatures.

Real-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems.

Real-space grids are a powerful alternative for the simulation of electronic systems. One of the main advantages of the approach is the flexibility and simplicity of working directly in real space where the different fields are discretized on a grid, combined with competitive numerical performance and great potential for parallelization. These properties constitute a great advantage at the time of implementing and testing new physical models. Based on our experience with the Octopus code, in this article we discuss how the real-space approach has allowed for the recent development of new ideas for the simulation of electronic systems. Among these applications are approaches to calculate response properties, modeling of photoemission, optimal control of quantum systems, simulation of plasmonic systems, and the exact solution of the Schrödinger equation for low-dimensionality systems.

Computational Benchmarking for Ultrafast Electron Dynamics: Wave Function Methods vs Density Functional Theory.

Attosecond electron dynamics in small- and medium-sized molecules, induced by an ultrashort strong optical pulse, is studied computationally for a frozen nuclear geometry. The importance of exchange and correlation effects on the nonequilibrium electron dynamics induced by the interaction of the molecule with the strong optical pulse is analyzed by comparing the solution of the time-dependent Schrödinger equation based on the correlated field-free stationary electronic states computed with the equationof-motion coupled cluster singles and doubles and the complete active space multi-configurational self-consistent field methodologies on one hand, and various functionals in real-time time-dependent density functional theory (TDDFT) on the other. We aim to evaluate the performance of the latter approach, which is very widely used for nonlinear absorption processes and whose computational cost has a more favorable scaling with the system size. We focus on LiH as a toy model for a nontrivial molecule and show that our conclusions carry over to larger molecules, exemplified by ABCU (C10H19N). The molecules are probed with IR and UV pulses whose intensities are not strong enough to significantly ionize the system. By comparing the evolution of the time-dependent field-free electronic dipole moment, as well as its Fourier power spectrum, we show that TD-DFT performs qualitatively well in most cases. Contrary to previous studies, we find almost no changes in the TD-DFT excitation energies when excited states are populated. Transitions between states of different symmetries are induced using pulses polarized in different directions. We observe that the performance of TD-DFT does not depend on the symmetry of the states involved in the transition.

Are hydrogen-bonded charge transfer crystals room temperature ferroelectrics?

We present a theoretical investigation of the anomalous ferroelectricity of mixed-stack charge transfer molecular crystals, based on the Peierls-Hubbard model, and first-principles calculations for its parametrization. This approach is first validated by reproducing the temperature-induced transition and the electronic polarization of TTF-CA, and then applied to a novel series of hydrogen-bonded crystals, for which room temperature ferroelectricity has recently been claimed. Our analysis shows that the hydrogen-bonded systems present a very low degree of charge transfer and hence support a very small polarization. A critical reexamination of experimental data supports our findings, shedding doubts on the ferroelectricity of these systems. More generally, our modeling allows the rationalization of general features of the ferroelectric transition in charge transfer crystals and suggests design principles for materials optimization.

First principles explanation of the positive Seebeck coefficient of lithium.

Lithium is one of the simplest metals, with negative charge carriers and a close reproduction of free-electron dispersion. Experimentally, however, Li is one of a handful of elemental solids (along with Cu, Ag, and Au) where the sign of the Seebeck coefficient (S) is opposite to that of the carrier. This counterintuitive behavior still lacks a satisfactory interpretation. We calculate S fully from first principles, within the framework of Allen's formulation of Boltzmann transport theory. Here it is crucial to avoid the constant relaxation time approximation, which gives a sign for S which is necessarily that of the carriers. Our calculated S are in excellent agreement with experimental data, up to the melting point. In comparison with another alkali metal, Na, we demonstrate that within the simplest nontrivial model for the energy dependency of the electron lifetimes, the rapidly increasing density of states (DOS) across the Fermi energy is related to the sign of S in Li. The exceptional energy dependence of the DOS is beyond the free-electron model, as the dispersion is distorted by the Brillouin zone edge; this has a stronger effect in Li than other alkali metals. The electron lifetime dependency on energy is central, but the details of the electron-phonon interaction are found to be less important, contrary to what has been believed for several decades. Band engineering combined with the mechanism exposed here may open the door to new "ambipolar" thermoelectric materials, with a tunable sign for the thermopower even if either n- or p-type doping is impossible.

First-principles study of the lattice dynamical properties of strontium ruthenate.

By means of first-principles calculations, various properties of SrRuO3 are investigated, focusing on its lattice dynamical properties. Despite having a Goldschmidt tolerance factor very close to 1, the phonon dispersion curves of the high-temperature cubic phase of SrRuO3 show strong antiferrodistortive instabilities. The energetics of metastable phases with different tilt patterns are discussed, concluding that the coupling of oxygen rotation modes with anti-polar Sr motion plays a key role in stabilizing the Pnma phase with respect to alternative rotation patterns. Our systematic analysis confirms previous expectations and contributes to rationalizing better why many ABO3 perovskites, including metallic compounds, exhibit an orthorhombic ground state. The zone-center phonon modes of the Pnma phase have been computed, from which we propose partial reassignment of available experimental data. The full dispersion curves have also been obtained, constituting benchmark results for the interpretation of future measurements and providing access to thermodynamical properties.

Role of dynamical instability in the ab initio phase diagram of calcium.

In the 32-119 GPa pressure range and at room temperature, a simple cubic phase was reported for calcium in many different experiments. Standard linear response theory, both within density functional perturbation theory and frozen phonon calculations, presents dynamical instabilities for the simple cubic structure in the whole pressure range. Many other possible candidate phases, as well as several possible stabilization mechanisms for the simple cubic phase, have been proposed as the result of ab initio predictions but the role of temperature on the relative stability of the different phases has not been systematically investigated. We revisit the stability of the three most important candidate phases of calcium for the intermediate pressure range and for various temperatures, taking explicitly into account thermal corrections relative to electronic as well as phononic entropy and anharmonic contributions. This corrects the discrepancies among previous theoretical results and experiments and presents a different picture of the temperature driven phase transition, which results from dynamical anharmonic stabilization of simple cubic and destabilization of the tetragonal phase.

Ab initio calculation of spin-dependent electron-phonon coupling in iron and cobalt.

The spin-dependent coupling between electrons and phonons in ferromagnetic Fe and Co is calculated from first principles in a collinear-spin formalism. The added spin polarization is fundamental for the correct representation of the phonons, but also for obtaining good transport properties, and permits decomposition (e.g. of the resistivity) into the contributions of majority and minority spin. In Fe the minority spin coupling is only about 50% more important, but in Co the coupling between phonons and minority spin electrons is an order of magnitude larger than that with the majority spin, and both are strongly anisotropic.