Self-consistent Phonon Method Research Articles

Implementation of the self-consistent phonons method with abinitio potentials (AI-SCP).

The self-consistent phonon (SCP) method allows one to include anharmonic effects when treating a many-body quantum system at thermal equilibrium. The system is then described by an effective temperature-dependent harmonic Hamiltonian, which can be used to estimate its various dynamic and static properties. In this paper, we combine SCP with abinitio (AI) potential energy evaluation in which case the numerical bottleneck of AI-SCP is the evaluation of Gaussian averages of the AI potential energy and its derivatives. These averages are computed efficiently by the quasi-Monte Carlo method utilizing low-discrepancy sequences leading to a fast convergence with respect to the number, S, of the AI energy evaluations. Moreover, a further substantial (an-order-of-magnitude) improvement in efficiency is achieved once a numerically cheap approximation of the AI potential is available. This is based on using a perturbation theory-like (the two-grid) approach in which it is the average of the difference between the AI and the approximate potential that is computed. The corresponding codes and scripts are provided.

Electric-field-tunable thermal conductivity in anti-ferroelectric materials

Based on density functional theory (DFT) calculations, we evaluate the thermal conductivities of LiBeP in both the ferroelectric (FE) and anti-ferroelectric (AFE) phases by using the self-consistent phonon method (SCP) combined with the compressive sensing (CS) approach. It is observed that the thermal conductivities can be tailored by more than 50% at room temperature upon the FE-AFE phase transitions. Detailed analysis on the phonon modes and scattering space reveals that there are substantial anharmonic effects in LiBeP. The significant change of the thermal conductivity makes it a promising candidate for thermal management materials with tunable thermal conductivities by electric fields. Our work provides a proof-of-concept example for electric-field controllable thermal management, which is promising for future applications.

Ab-initio calculations of temperature dependent electronic structures of inorganic halide perovskite materials.

Despite wide interest in halide perovskite materials, it is still challenging to accurately calculate their electronic structure and its temperature dependence. In this work, we present ab-initio calculations of the temperature dependence of the electronic structure of CsPbX3 materials (X = Cl, Br or I) in the cubic form and of the zero temperature electronic structure of the orthorhombic phase of these materials. Phonon-induced temperature dependent band energy renormalization was calculated within the framework of Allen-Heine-Cardona theory, where we exploited the self-consistent procedure to determine both the energy level shifts and their broadenings. The phonon spectrum of the materials was obtained using the self-consistent phonon method since standard density functional perturbation theory calculations in harmonic approximation yield phonon modes with imaginary frequencies due to the fact that the cubic structure is not stable at zero temperature. Our results suggest that low energy phonon modes mostly contribute to phonon-induced band energy renormalization. The calculated values of the band gaps at lowest temperature where the material exhibits a cubic structure are in good agreement with experimental results from the literature. The same is the case for the slope of the temperature dependence of the band gap for the CsPbI3 material where reliable experimental data are available in the literature. We also found that phonon-induced temperature dependence of the band gap is most pronounced for the conduction band minimum and valence band maximum, while other bands exhibit a weaker dependence.

Effect of quartic anharmonicity on the carrier transport of cubic halide perovskites CsSnI3 and CsPbI3

Recent years have witnessed the rising of halide perovskites for potential applications in photovoltaic and optoelectric devices. Due to the tilting motions of the octahedrons and rattling of the filling atoms, cubic halide perovskites show strong anharmonicity and imaginary frequencies in the phonon dispersion, which brings a great challenge to the prediction of carrier transports based on many-body theory. We have investigated the effect of quartic lattice anharmonicity on the carrier transports of cubic ${\mathrm{CsSnI}}_{3}$ and ${\mathrm{CsPbI}}_{3}$ in a comparative perspective by first-principles calculations. The hybrid functional of HSE06 was employed to get accurate band gaps and the self-consistent phonon method was used to renormalize interatomic force constants. Based on the electron-phonon Wannier interpolation and Boltzmann transport equation, the carrier mobilities and mode-resolved scattering rates were calculated and the dominant scattering channels were analyzed. Our results reveal that the mobility takes 595.9 and 84.5 ${\mathrm{cm}}^{2}/\mathrm{Vs}$ at room temperature for cubic ${\mathrm{CsSnI}}_{3}$ and ${\mathrm{CsPbI}}_{3}$, respectively, in good agreement with the experiment results. The longitudinal stretching mode of the Sn(Pb)-I bond with frequency of 120 ${\mathrm{cm}}^{\ensuremath{-}1}$ plays a dominant role in carrier scattering. In comparison, the acoustic modes and the rattling modes have a negligible effect on carrier scattering. Calculations of the band scattering rates show that deep valleys emerge at the band edges for both the highest valence band and the lowest conduction band, which is responsible for the slow relaxation of hot carriers. The strength of intraband electron-phonon coupling (EPC) between the band edge and the Sn(Pb)-I bond stretching mode is far larger than those of other modes, which leads to the dominant scattering in carrier transport. Compared with the harmonic approximation of atom interactions, the inclusion of quartic anharmonicity leads to the enhancement of atom interactions, which decreases the EPC strength and consequently increases the carrier mobilities.

Anharmonic lattice dynamics and structural phase transition of SnTe monolayer from first principles

In this work we investigate the role of quartic anharmonicity on the lattice- and thermo-dynamic properties of rectangular () and square (β) phases of two-dimensional (2D) SnTe monolayer (ML) by using self-consistent phonon (SCP) theory, based on the first-principles calculations. For both phases, as compared to the usual harmonic approximation (HA), the renormalized phonon frequency at the optical modes (4–10) is found to be increased upon the inclusion of quartic anharmonicity via the SCP method, where the effects of cubic anharmonicity are neglected. At the experimentally observed transition temperature (T c = 270 K), the difference in the vibrational free-energy between the square and rectangular phases of SnTe ML, calculated by using the anharmonic SCP correction is found to be much closer to the structural energy gain as compared to that obtained by using only the quasi-harmonic contribution. This validates the significance of SCP approach over the HA to explain the lattice dynamics properties and predict the T c for SnTe ML and similar 2D compounds. The calculated lattice thermal conductivity of square SnTe ML (e.g. 10.67 W m−1K−1 at 300 K) is higher than that of the rectangular SnTe ML (e.g. 6.72 W m−1K−1 at 300 K) due to the relatively higher corresponding thermodynamic parameters: specific heat capacity, group velocity, and phonon lifetime obtained for the square SnTe ML. Particularly, the low energy phonon modes are found to transport most of the heat in the system and, hence, played major role to the total lattice thermal conductivity.

Lattice dynamics and elasticity for \u03b5-plutonium

Lattice dynamics and elasticity for the high-temperature ε phase (body-centered cubic; bcc) of plutonium is predicted utilizing first-principles electronic structure coupled with a self-consistent phonon method that takes phonon-phonon interaction and strong anharmonicity into account. These predictions establish the first sensible lattice-dynamics and elasticity data on ε-Pu. The atomic forces required for the phonon scheme are highly accurate and derived from the total energies obtained from relativistic and parameter-free density-functional theory. The results appear reasonable but no data exist to compare with except those from dynamical mean-field theory that suggest ε-plutonium is mechanically unstable. Fundamental knowledge and understanding of the high-temperature bcc phase, that is generally present in all actinide metals before melting, is critically important for a proper interpretation of the phase diagram as well as practical modeling of high-temperature properties.

Glassy Dynamics of Passive and Active Network Materials: A Microscopic Theory

Signatures of glassy dynamics have been identified experimentally for a rich variety of materials in which molecular networks provide rigidity. Here we present a theoretical framework to study the glassy behavior of both passive and active network materials. We construct a general microscopic network model that incorporates nonlinear elasticity of individual filaments and steric constraints due to crowding. By building constructive analogies between structural glass forming liquids and random field Ising magnets implemented using a heterogeneous self-consistent phonon method, we provide a microscopic approach to determine the mismatch surface tension and the configurational entropy, which compete in determining the barrier for structural rearrangements. This model recapitulates the influence of crosslinking on the fragility of inorganic network glass formers. For active network materials, the mapping, which correlates the glassy characteristics to the network architecture and properties of nonequilibrium motor processes, is shown to capture several key experimental observations on the cytoskeleton of living cells. Our calculations also identify a spinodal point where simultaneously the mismatch penalty vanishes and the mechanical stability of amorphous packing disappears.

Normal-ordered second-quantized Hamiltonian for molecular vibrations.

A normal-ordered second-quantized form of the Hamiltonian is derived for quantum dynamics in a bound potential energy surface expressed as a Taylor series in an arbitrary set of orthogonal, delocalized coordinates centered at an arbitrary geometry. The constant, first-, and second-order excitation amplitudes of this Hamiltonian are identified as the ground-state energy, gradients, and frequencies, respectively, of the size-extensive vibrational self-consistent field (XVSCF) method or the self-consistent phonon method. They display the well-defined size dependence of V(1-n/2), where V is the volume and n is the number of coordinates associated with the amplitudes. It is used to rapidly derive the equations of XVSCF and vibrational many-body perturbation methods with the Møller-Plesset partitioning of the Hamiltonian.

First-Order Dyson Coordinates and Geometry

The mathematical constructs of the Dyson coordinates and geometry are introduced. The former are a unitary transformation of the normal coordinates and the anharmonic vibrational counterpart of the Dyson orbitals in electronic structure theory. The first-order Dyson coordinates bring the sums of the harmonic force constants and their first-order diagrammatic perturbation corrections (the first-order Dyson self-energy) to a diagonal form. The first-order Dyson geometry has no counterpart in electronic structure theory. It is the point on the potential energy surface at which the sums of the energy gradients and their first-order diagrammatic perturbation corrections vanish. It agrees with the vibrationally averaged geometry of vibrational self-consistent field (VSCF) theory in the bulk limit. These constructs provide a unified view of the relationship of VSCF and its diagrammatically size-consistent modifications as well as the self-consistent phonon method widely used in solid-state physics.

Microscopic theory of the glassy dynamics of passive and active network materials

Signatures of glassy dynamics have been identified experimentally for a rich variety of materials in which molecular networks provide rigidity. Here we present a theoretical framework to study the glassy behavior of both passive and active network materials. We construct a general microscopic network model that incorporates nonlinear elasticity of individual filaments and steric constraints due to crowding. Based on constructive analogies between structural glass forming liquids and random field Ising magnets implemented using a heterogeneous self-consistent phonon method, our scheme provides a microscopic approach to determine the mismatch surface tension and the configurational entropy, which compete in determining the barrier for structural rearrangements within the random first order transition theory of escape from a local energy minimum. The influence of crosslinking on the fragility of inorganic network glass formers is recapitulated by the model. For active network materials, the mapping, which correlates the glassy characteristics to the network architecture and properties of nonequilibrium motor processes, is shown to capture several key experimental observations on the cytoskeleton of living cells: Highly connected tense networks behave as strong glass formers; intense motor action promotes reconfiguration. The fact that our model assuming a negative motor susceptibility predicts the latter suggests that on average the motorized processes in living cells do resist the imposed mechanical load. Our calculations also identify a spinodal point where simultaneously the mismatch penalty vanishes and the mechanical stability of amorphous packing disappears.

The Interplay of Nonlinearity and Architecture in Cytoskeletal Mechanics

The interplay between cytoskeletal architecture and the nonlinearity of the interactions due to bucklable filaments plays a key role in modulating the cell's mechanical stability and affecting its structural rearrangements. We study a model of cytoskeletal structure treating it as an amorphous network of hard centers rigidly cross-linked by nonlinear elastic strings. Using simulations along with a self-consistent phonon method, we show that this minimal model exhibits diverse thermodynamically stable mechanical phases that depend on excluded volume, crosslink concentration, filament length and stiffness. Within the framework set by the free energy functional formulation and making use of the random first order transition theory of structural glasses, we further estimate the characteristic densities for a kinetic glass transition to occur in this model system. Network connectivity strongly modulates the transition boundaries between various equilibrium phases, as well as the kinetic glass transition density. We also study the effects of motorization using a modeled kinetic rate that couples the chemical response to mechanical environment.

The interplay of nonlinearity and architecture in equilibrium cytoskeletal mechanics

The interplay between cytoskeletal architecture and the nonlinearity of the interactions due to bucklable filaments plays a key role in modulating the cell's mechanical stability and affecting its structural rearrangements. We study a model of cytoskeletal structure treating it as an amorphous network of hard centers rigidly cross-linked by nonlinear elastic strings, neglecting the effects of motorization. Using simulations along with a self-consistent phonon method, we show that this minimal model exhibits diverse thermodynamically stable mechanical phases that depend on excluded volume, cross-link concentration, filament length, and stiffness. Within the framework set by the free energy functional formulation and making use of the random first order transition theory of structural glasses, we further estimate the characteristic densities for a kinetic glass transition to occur in this model system. Network connectivity strongly modulates the transition boundaries between various equilibrium phases, as well as the kinetic glass transition density.

Independent anharmonic oscillator approximation in the theory of structural phase transitions in crystals

A new method in the microscopic theory of anharmonic crystal lattice dynamics—the independent anharmonic oscillator (IAO) approximation—is discussed. The method is compared with traditional approaches (such as the mean-field and renormalized self-consistent phonon methods) from the standpoint of the analysis of the main approximations. Different methods are applied to the description of the structural phase transition in a monoatomic anharmonic crystal, the results obtained are analyzed, and the numerical accuracy of different approximations is estimated. It is demonstrated that, for this model in the displacement-type instability range, the new method, unlike the self-consistent phonon method, adequately describes the phase transition as a second-order transition. The phase transition temperature calculated in the displacement limit monotonically tends to the exact value in contrast with the temperature obtained within the mean field approximation.

A microscopical model of the structural phase transitions in La2−xMxCuO4

Abstract A microscopical model of anharmonic lattice dynamics forLa2−xMxCuO4 crystals is considered. The model free energy and the soft tilting mode frequencies are calculated to describe the D 17 4h→ D 18 4h→ D 16 4h structural phase transitions in the framework of the self-consistent phonon method.

Self-consistent phonon approach to thermal vibrations in model small clusters.

Thermal atomic vibrations in small clusters have been studied theoretically using the self-consistent phonon method. We have calculated the free energy for model clusters in which constituent atoms interact with each other through a pairwise potential and are vibrating with a frequency ${\ensuremath{\omega}}_{n}$ for the nth atom. Thermal softening and thermal expansion are investigated as a function of temperature for different structures of cluster sizes, N=7, 9, and 13. A structure with pentagonal caps is shown to be more stable vibrationally than a section of cubic structure of the same size. The instability temperature in the present model clusters is discussed in the context of melting in small clusters.

Self-consistent phonons, thermal properties, and vibrational instability of the copper crystal.

We have studied the temperature-dependent phonon spectrum and other vibrational properties of copper using the self-consistent phonon method and also the quasiharmonic method. A model pair potential suitable for such a study has been constructed. We have also investigated the vibrational instability of the overheated perfect crystal by studying the system's free energy.

Lattice dynamics of solid N2 with an a b i n i t i o intermolecular potential

We have performed harmonic and self-consistent phonon lattice dynamics calculations for α and γ N2 crystals using an intermolecular potential from ab initio calculations. This potential contains electrostatic (multipole) interactions, up to all R−9 terms inclusive, anisotropic dispersion interactions up to all R−10 terms inclusive, and anisotropic overlap interactions caused by charge penetration and exchange between the molecules. The lattice constants, cohesion energy, the frequencies of the translational phonon modes and the Grüneisen parameters for the librational modes are in good agreement with experimental values, confirming the quality of the potential. The frequencies of the librational modes and those of the mixed modes are less well reproduced, especially at temperatures near the α–β phase transition. Probably, the self-consistent phonon method used does not fully account for the anharmonicity in the librations.

Dynamical aspects of the formation of the mesomorphic state structure

In terms of the self-consistent phonon field method generalized with regard to the orientational degrees of freedom the dynamics of the formation of the mesomorphic state structure at the activation of the molecular crystal oscillations is studied. The reasons for the existence and for the stability of the partially ordered media with liquid-crystalline and plastic packing of the molecules are substantiated. The dependencies of the dynamical crystal characteristics versus temperature are calculated. From the analysis of the librational and translational anharmonicities evolution at the temperature alteration the energetic relations for the transition of the molecular crystal into the mesostate are established. It is shown that the anharmonic processes bound-up with different degrees of the molecules freedom give an essentially unequal contribution to the development of the dynamical instability of the system. The mutual correlation between the structural instability type, the molecular crystalline anisotropy coefficient and the molecular interaction anisotropy factor are investigated. The behaviour of the critical values as functions of the system anisotropy parameters is considered. Conclusions are drawn regarding the crystal lattice disarrangement in the pretransitional regions of liquid-crystalline and plastic mesogeneity.

Self-consistent-phonon, random phase, and transfer-integral methods for a linear chain with anharmonic potential

The transfer-integral (TI) method, developed especially for hard-core potentials, is tested with anx 2 + α3x3 + α4x4 potential by a comparison with other methods: In the harmonic approximation the improvement of the TI method over the self-consistent phonon (SCP) method is about as great as that of the SCP method over the random phase approximation (RPA).

Self-consistent phonon calculation of the β phase and the α-β transition in solid nitrogen

The self-consistent phonon approximation of anharmonic lattice dynamics is applied to solid β nitrogen. Completely disordered molecular orientations and a Lennard-Jones 6–12 intermolecular potential are assumed. The quantities calculated are the phonon spectrum and the thermal expansion as a function of temperature at zero pressure. The α-β fcc-hcp transition temperature is estimated on the basis of two models for the molecular ordering in the β phase. Although the computations are intended primarily to explore the application of the self-consistent phonon method to a treatment of structural phase transitions in simple molecular crystals, comparison is made with existing experimental data.