We review our recent development of a first-principles lattice dynamics method that can treat anharmonic effects nonperturbatively. The method is based on the self-consistent phonon theory and temperature-dependent phonon frequencies can be calculated efficiently by incorporating recent numerical techniques to estimate anharmonic force constants. The validity of our approach is demonstrated through applications to cubic strontium titanate, where overall good agreements with experimental data are obtained for phonon frequencies and lattice thermal conductivity. We also show the feasibility of highly accurate calculations based on a hybrid exchange-correlation functional within the present framework. Our method provides a new way for studying lattice dynamics in severely anharmonic materials where the standard harmonic approximation and the perturbative approach break down.
Anharmonic effects in an atomic monolayer thin crystal with honeycomb lattice structure are investigated by analytical and numerical lattice dynamical methods. Starting from a semi-empirical model for anharmonic couplings of third and fourth order, we study the in-plane and out-of-plane (flexural) mode components of the generalized wave vector dependent Grüneisen parameters, the thermal tension and the thermal expansion coefficients as function of temperature and crystal size. From the resonances of the displacement-displacement correlation functions we obtain the renormalization and decay rat…
Vacancies are prevalent point defects in crystals, but their thermal responses are elusive. Herein, we formulate a simple theoretical model to shed light on the vacancy evolution during heating. Vibrational excitations are thoroughly investigated via moment recurrence techniques in quantum statistical mechanics. On that basis, we carry out numerical analyses for Ag, Cu, and Ni with the Sutton-Chen many-body potential. Our results reveal that the well-known Arrhenius law is insufficient to describe the proliferation of vacancies. Specifically, anharmonic effects lead to a strong nonlinearity in…
Anharmonic phonon-phonon scattering serves a critical role in heat conduction in solids. Previous studies have identified many selection rules for possible phonon-phonon scattering channels imposed by phonon energy and momentum conservation conditions and crystal symmetry. However, the crystal-symmetry-based selection rules have mostly been \textit{ad hoc} so far in selected materials, and a general formalism that can summarize known selection rules and lead to new ones in any given crystal is still lacking. In this work, we apply a general formalism for symmetry-based scattering selection rul…
Understanding and predicting lattice dynamics in strongly anharmonic crystals is one of the long-standing challenges in condensed matter physics. Here we propose a first-principles method that gives accurate quasiparticle (QP) peaks of the phonon spectrum with strong anharmonic broadening. On top of the conventional first-order self-consistent phonon (SC1) dynamical matrix, the proposed method incorporates frequency renormalization effects by the bubble self-energy within the QP approximation. We apply the developed methodology to the strongly anharmonic $α$-CsPbBr$_3$ that displays phonon ins…
Ultrafast vibrational dynamics of inorganic-organic hybrid lead halide perovskite CH3NH3PbI$ in the room-temperature tetragonal phase is investigated under moderate photoexcitation slightly below the band gap. Time-resolved optical Kerr effect signal exhibits periodic modulations due to the libration and twisting of the methylammonium molecule at 4 and 8 THz, in addition to the inorganic sublattice deformation at 1.2 THz. These oscillations are heavily damped, and their frequencies exhibit blueshifts with increasing pump density, contrary to the expectation from conventional laser heating. Our…
The calculations of thermal conductivity requires to know anharmonic properties of the crystal. For this purpose a non-perturbative anharmonic theory is applied, which do not make use of the potential energy expansion over atomic displacements, but instead, runs ab initio calculations of Hellmann-Feynman forces for atomic patterns of atoms with specific displacements to rebuild the anharmonic phonon frequencies, and group velocities. see [K.Parlinski, Phys.Rev. B 98, 054305 (2018),] The Green-Kubo equation for the thermal conductivity needs to know the above quantities and the phonon relaxatio…
We combine ab initio simulations and Raman scattering measurements to demonstrate explicit anharmonic effects in the temperature dependent dielectric response of a NaCl single crystal. We measure the temperature evolution of its Raman spectrum and compare it to both a quasi-harmonic and anharmonic model. Results demonstrate the necessity of including anharmonic lattice dynamics to explain the dielectric response of NaCl, as it is manifested in Raman scattering. Our model fully captures the linear dielectric response of a crystal at finite temperatures and may therefore be used to calculate the…
Halide perovskite (HP) semiconductors exhibit unique strong coupling between the electronic and structural dynamics. The high-temperature cubic phase of HPs is known to be entropically stabilized, with imaginary frequencies in the calculated phonon dispersion relation. Similar calculations, based on the static average crystal structure, predict a stable tetragonal phase with no imaginary modes. This work shows that in contrast to standard theory predictions, the room-temperature tetragonal phase of CH$_{3} $NH$_{3} $PbI$_{3}$ is strongly anharmonic. We use Raman polarization-orientation (PO) m…
The efficient and accurate calculation of how ionic quantum and thermal fluctuations impact the free energy of a crystal, its atomic structure, and phonon spectrum is one of the main challenges of solid state physics, especially when strong anharmonicy invalidates any perturbative approach. To tackle this problem, we present the implementation on a modular Python code of the stochastic self-consistent harmonic approximation method. This technique rigorously describes the full thermodyamics of crystals accounting for nuclear quantum and thermal anharmonic fluctuations. The approach requires the…
An approach to compute the anharmonic peaks of the phonon dispersion curves through the ab initio calculated Hellmann-Feynman forces from a series of supercells with realistic atomic displacements of all atoms, which correspond to a given temperature, is reported. Obtained phonon dispersion bands are able to represent the positions and shapes of the anharmonic peaks. As example, the approach to cubic PbTe and perovskite MgSiO3 crystals is applied.
We devise a framework to compute accurate phonons in molecular crystals even in case of strong quantum anharmonicity. Our approach is based on the calculation of the static limit of the phononic Matsubara Green's function from path integral molecular dynamics simulations. Our method enjoys a remarkably low variance, which allows one to compute accurate phonon frequencies after a few picoseconds of nuclear dynamics, and it is further stabilized by the use of appropriate constrained displacement operators. We applied it to solid hydrogen at high pressure. For phase III, our predicted infrared (I…
The intermolecular lattice vibrations in small-molecule organic semiconductors have a strong impact on their functional properties. Existing models treat the lattice vibrations within the harmonic approximation. In this work, we use polarization-orientation (PO) Raman measurements to monitor the temperature-evolution of the symmetry of lattice vibrations in anthracene and pentacene single crystals. Combined with first-principles calculations, we show that at 10 K the lattice dynamics of the crystals are indeed harmonic. However, as the temperature is increased specific lattice modes gradually …
We adopted and extended an efficient Grüneisen formalism to study the phonon anharmonicity and linear thermal expansion coefficients (TECs) of trigonal bismuth selenide (Bi$_2$Se$_3$) and antimony telluride (Sb$_2$Te$_3$). Anharmonicity of the systems is studied via extensive calculation of Grüneisen parameters that exploit symmetry-preserving deformations. Consistent with experimental findings, a large anisotropy between the TECs in the $a$ and $c$ directions is found. The larger anharmonicity inherent in Sb$_2$Te$_3$, as compared to Bi$_2$Se$_3$ is offset by the volumetric effect, resulting …
Knowledge of lattice anharmonicity is essential to elucidate distinctive thermal properties in crystalline solids. Yet, accurate \textit{ab initio} investigations of lattice anharmonicity encounter difficulties owing to the cumbersome computations. Here we introduce the phonon quasiparticle approach and review its application to various materials. This method efficiently and reliably addresses lattice anharmonicity by combining \textit{ab initio} molecular dynamics and lattice dynamics calculations. Thus, in principle, it accounts for full anharmonic effects and overcomes finite-size effects t…
Molecular crystals often exist in multiple competing polymorphs, showing significantly different physico-chemical properties. Computational crystal structure prediction is key to interpret and guide the search for the most stable or useful form: A real challenge due to the combinatorial search space, and the complex interplay of subtle effects that work together to determine the relative stability of different structures. Here we take a comprehensive approach based on different flavors of thermodynamic integration in order to estimate all contributions to the free energies of these systems wit…
We use first principles calculations to study structural, vibrational and superconducting properties of H$_2$S at pressures $P\ge 200$ GPa. The inclusion of zero point energy leads to two different possible dissociations of H$_2$S, namely 3H$_2$S $\to$ 2H$_3$S + S and 5H$_2$S $\to$ 3H$_3$S + HS$_2$, where both H$_3$S and HS$_2$ are metallic. For H$_3$S, we perform non-perturbative calculations of anharmonic effects within the self-consistent harmonic approximation and show that the harmonic approximation strongly overestimates the electron-phonon interaction ($λ\approx 2.64$ at 200 GPa) and T$…
Ab initio-based Deep-Learning Prediction of Carrier Mobility in Strongly Anharmonic Materials
The NOMAD Laboratory at BIFOLD Technical University of Berlin（柏林工业大学BIFOLD NOMAD实验室）；College of Future Information Technology and State Key Laboratory of Photovoltaic Science and Technology, Fudan University（复旦大学未来信息技术学院与光伏科学与技术国家重点实验室）；Department of Physics, Tsinghua University（清华大学物理系）；State Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University（清华大学低维量子物理国家重点实验室）；Frontier Science Center for Quantum Information, Tsinghua University（清华大学量子信息前沿科学中心）；School of Materials Science and Engineering, Chonnam National University（全南国立大学材料科学与工程学）
Iterative learning scheme for crystal structure prediction with anharmonic lattice dynamics
Centro de Física de Materiales (CFM-MPC), CSIC-UPV/EHU（材料物理中心）；University of the Basque Country (UPV/EHU)（巴斯克大学）；Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心）
Understanding heat transport in semiconductors and insulators is of fundamental importance because of its technological impact in electronics and renewable energy harvesting and conversion. Anharmonic Lattice Dynamics provides a powerful framework for the description of heat transport at the nanoscale. One of the advantages of this method is that it naturally includes quantum effects due to atoms vibrations, which are needed to compute the thermal properties of semiconductors widely used in nanotechnology, like silicon and carbon, even at room temperature. While the heat transport picture subs…
We determine the frequency dependence of four independent CdWO$_4$ Cartesian dielectric function tensor elements by generalized spectroscopic ellipsometry within mid-infrared and far-infrared spectral regions. Single crystal surfaces cut under different angles from a bulk crystal, (010) and (001), are investigated. From the spectral dependencies of the dielectric function tensor and its inverse we determine all long wavelength active transverse and longitudinal optic phonon modes with $A_u$ and $B_u$ symmetry as well as their eigenvectors within the monoclinic lattice. We thereby demonstrate t…
The variational stochastic self-consistent harmonic approximation is combined with the calculation of third-order anharmonic coefficients within density-functional perturbation theory and the "$2n+1$" theorem to calculate anharmonic properties of crystals. It is demonstrated that in the perturbative limit the combination of these two methods yields the perturbative phonon linewidth and frequency shift in a very efficient way, avoiding the explicit calculation of fourth-order anharmonic coefficients. Moreover, it also allows calculating phonon lifetimes and inelastic neutron scattering spectra …
For Sn$_2$P$_2$S$_6$ family of uniaxial ferroelectrics, the anharmonic quantum oscillators model, based on local three-well potential for spontaneous polarization fluctuations, has been used for a description of anharmonic properties, namely thermal expansion. The calculated pseudospin fluctuations spectra in ferroelectric phase demonstrate negative Grüneisen parameters for excitations that satisfy Curie-Weiss-like temperature and pressure dependencies in the vicinity of second order phase transition. Thermal expansion coefficient is calculated by evaluation of pseudospins entropy baric depend…
We present the investigations on atomic dynamics and Li+ diffusion in crystalline and amorphous Li2Si2O5 using quasielastic (QENS) and inelastic neutron scattering (INS) studies supplemented by ab-initio molecular dynamics simulations (AIMD). The QENS measurements in the amorphous phase of Li2Si2O5 show a narrow temperature window (700 < T < 775 K), exhibiting significant quasielastic broadening corresponding to the fast Li+ diffusion and relaxation of SiO4 units to the crystalline phase. Our INS measurements clearly show the presence of large phonon density of states (PDOS) at low energy (low…
The phonon dispersion relations of crystal lattices can often be well-described with the harmonic approximation. However, when the potential energy landscape exhibits more anharmonicity, for instance, in case of a weakly bonded crystal or when the temperature is raised, the approximation fails to capture all crystal lattice dynamics properly. Phonon-phonon scattering mechanisms become important and limit the phonon lifetimes. We take a novel approach and simulate the phonon dispersion of a complex dynamic solid at elevated temperatures with Machine-Learning Force Fields of near-first-principle…
We calculate the lattice dielectric function of strongly anharmonic rutile $\mathrm{TiO}_2$ from ab initio anharmonic lattice dynamics methods. Since an accurate calculation of the $Γ$ point phonons is essential for determining optical properties, we employ the modified self-consistent approach, including third-order anharmonicity as well as fourth-order anharmonicity. The resulting optical phonon frequencies and linewidths at the $Γ$ point much better agree with experimental measurements than those from a perturbative approach. We show that the four-phonon scattering process contributes as mu…
Anharmonic free energies and phonon dispersions from the stochastic self-consistent harmonic approximation: application to platinum and palladium hydrides
The low-frequency range of vibrational spectra is sensitive to collective vibrations of the lattice. In molecular crystals, it can be decisive to identify the structure of different polymorphs, and in addition, it plays an important role on the magnitude of the temperature-dependent component of vibrational free energy differences between these crystals. In this work we study the vibrational Raman spectra and vibrational density of states of different polymorphs of the flexible Aspirin and Paracetamol crystals based on dispersion-corrected density-functional theory, density-functional perturba…
We present an $\textit{ab initio}$ study of the thermodynamic properties of cubic CaSiO$_3$ perovskite (CaPv) over the pressure and temperature range of the Earth's lower mantle. We compute the anharmonic phonon dispersions throughout the Brillouin zone by utilizing the phonon quasiparticle approach, which characterizes the intrinsic temperature dependence of phonon frequencies and, in principle, captures full anharmonicity. Such temperature-dependent phonon dispersions are used to calculate $\textit{ab initio}$ free energy in the thermodynamic limit ($N \rightarrow \infty$) within the framewo…
The self-consisted harmonic approximation (SCHA) allows the computation of free energy of anharmonic crystals considering both quantum and thermal fluctuations. Recently, a stochastic implementation of the SCHA has been developed, tailored for applications that use total energy and forces computed from first principles. In this work, we extend the applicability of the stochastic SCHA to complex crystals with many degrees of freedom, with the optimisation of both the lattice vectors and the atomic positions. To this goal, we provide an expression for the evaluation of the pressure and stress te…
We develop a first-principles approach for the treatment of vibronic interactions in solids that overcomes the main limitations of state-of-the-art electron-phonon coupling formalisms. In particular, anharmonic effects in the nuclear dynamics are accounted to all orders via ab initio molecular dynamics simulations. This non-perturbative, self-consistent approach evaluates the response of the wave functions along the computed anharmonic trajectory; thus it fully considers the coupling between nuclear and electronic degrees of freedom. We validate and demonstrate the merits of the concept by cal…
Lattice vibrations in CH$_3$NH$_3$PbI$_3$ are strongly interacting, with double well instabilities present at the Brillouin zone boundary. Analysis within a first-principles lattice dynamics framework reveals anharmonic potentials with short phonon quasi-particle lifetimes and mean-free paths. The phonon behaviour is distinct from the inorganic semiconductors GaAs and CdTe where three-phonon interaction strengths are three orders of magnitude smaller. The implications for the applications of hybrid halide perovskites arising from thermal conductivity, band-gap deformation, and charge-carrier s…
Measurements of thermal diffusivity in several insulators have been shown to reach a Planckian bound on thermal transport that can be thought of as the limit of validity of semiclassical phonon scattering. Beyond this regime, the heat transport must be understood in terms of incoherent motion of the atoms under strongly anharmonic interactions. In this work, we propose a model for heat transport in a strongly anharmonic system where the thermal diffusivity can be lower than the Planckian thermal diffusivity bound. Similar to the materials which exhibit thermal diffusivity close to this bound, …
The microscopic origin of the large negative thermal expansion of cubic scandium trifluorides (ScF3) is investigated by performing a set of anharmonic free-energy calculations based on density functional theory. We demonstrate that the conventional quasiharmonic approximation (QHA) completely breaks down for ScF3 and the quartic anharmonicity, treated nonperturbatively by the self-consistent phonon theory, is essential to reproduce the observed transition from negative to positive thermal expansivity and the hardening of the R4+ soft mode with heating. In addition, we show that the contributio…
At room temperature, PbTe and SnTe are efficient thermoelectrics with a cubic structure. At low temperature, SnTe undergoes a ferroelectric transition with a critical temperature strongly dependent on the hole concentration, while PbTe is an incipient ferroelectric. By using the stochastic self-consistent harmonic approximation, we investigate the anharmonic phonon spectra and the occurrence of a ferroelectric transition in both systems. We find that vibrational spectra strongly depends on the approximation used for the exchange-correlation kernel in density functional theory. If gradient corr…
We investigate the role of the quartic anharmonicity in lattice dynamics and thermal transport of type-I clathrate Ba$_{8}$Ga$_{16}$Ge$_{30}$ based on \textit{ab initio} self-consistent phonon calculations. We show that the strong quartic anharmonicity of rattling guest atoms causes the hardening of vibrational frequencies of low-lying optical modes and thereby affects calculated lattice thermal conductivities $κ_{L}$ significantly, resulting in an improved agreement with experimental results including the deviation from $κ_{L}\propto T^{-1}$ at high temperature. Moreover, our static simulatio…
