Session J44: Electrons, Phonons, Electron Phonon Scattering, and Phononics II

Quantifying Uncertainty in First-Principles Predictions of Phonon Properties and Thermal Conductivity

We present a robust method for quantifying the uncertainty in phonon properties and thermal conductivity predicted from density functional theory calculations using the BEEF-vdW exchange-correlation (XC) functional. The procedure starts by displacing atoms in an equilibrium structure and using the energies of the perturbed structures to determine harmonic and anharmonic force constants. BEEF-vdW generates an ensemble of energies for each perturbed structure as a computationally efficient post-processing step by perturbing the XC functional and solving for the energy non-self consistently. Thus, each perturbed structure yields an ensemble of energies. This energy ensemble is then used to determine an ensemble of force constants, which is then used as input to lattice dynamics calculations and a solution of the Boltzmann transport equation. This procedure results in ensembles for the phonon frequencies, group velocities, and lifetimes, and overall heat capacity and thermal conductivity, whose spreads can be used to quantify uncertainty. Results for silicon, graphene, and graphite are presented and compared to predictions from the PBE, RPBE, and PBEsol XC functionals.   

From Coherent State Statistics to the Frozen Phonon Model

We present a formalism for employing the basis of coherent states for analytical and numerical computations involving systems at thermal equilibrium. We identify an integration measure on the complex plane which may be understood as the weight function for a thermal distribution of coherent states. When applied to phonons in a thermally occupied harmonic crystal, this method yields an intuitive and rigorously quantum mechanical justification of the frozen phonon model of thermal diffuse scattering. In this and many other applications, the semiclassical dynamics of coherent states can mediate the application of classical reasoning to otherwise intractable quantum problems, including those involving anharmonic potentials. We also discuss and refine the concept of “quasi-elastic” scattering.   

Anomalous elasticity of 2D materials beyond self--consistent approximation

We study elastic properties of two--dimensional crystalline materials, such as graphene. It is known that in 2D membranes strong thermal fluctuations of flexural phonons lead to dramatic change of phonon spectrum and, as a result, in anomalous material--independent elastic properties, such as non--linear Hooke's law under the low stress and auxetic behavior.
We compute elastic moduli η and Poisson ratio ν of 2D membrane in the approximation of high embedded dimensionality d_c=2+d. We go beyond one-loop approximation and find that famous self--consistent screening approximation is only as good as first--order approximation.
Most remarkably, we analyze a case of disordered membrane and find new disorder--dominant phase, where all the critical exponents are different from the clean case. We find that phase transition happens at finite temperature in contrast to the prediction given by self--consistent screening approximation, that transition is only possible at absolute zero.

Presented work is a continuation of the results reported in papers PhysRevB.97.125402, PhysRevB.92.155428.   

Continuity of phonon dispersion curves in layered ionic crystals

We investigate in detail the origin of apparent discontinuities and mode disappearances in phonon band diagrams of ionic materials having hexagonal and other anisotropic structures.¹ The phenomenon is due to the coupling of some of the vibrational modes to long wavelength electromagnetic waves within the material as described in 1951 by Huang.² Modern analyses by Giannozzi, Gonze, Baroni, and others, based on density functional theory and density functional perturbation theory, have been implemented in several first principles code packages such as ABINIT and QUANTUM ESPRESSO. These use the so-called non-analytic correction to the dynamical matrix to correctly represent the modified longitudinal optical vibrational modes. In this work, we extend the analysis to include the transverse phonon-photon modes as well. The combination of the longitudinal and transverse phonon-photon mode dispersions are continuous functions of the wavevector q. These effects are demonstrated for cubic and hexagonal BN.
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¹https://doi.org/10.1088/1361-648X/ab4cc1
²K. Huang, Proc. R. Soc. A A208, 352 (1951)
  

Theoretical Analysis of Vibrational Lineshapes from Molecular Dynamics

The conventional spectral method for extracting anharmonic phonon properties from molecular dynamics (MD) requires prohibitively long simulations as the fitting function relies on the infinite time approximation. To that end, we derived the spectral lineshapes for arbitrary simulation lengths, while retaining the frequency shift and lifetime as fitting parameters. The theory was illustrated for graphene, hexagonal boron nitride, and silicon at the density functional theory (DFT) level, with up to nearly a factor of nine reduction in the required simulation time to reach convergence in the vibrational properties as compared to the standard approach. Such improvement in the convergence is expected in general provided the phonon anharmonicity is sufficiently weak, resulting in well-defined renormalized phonon quasiparticles. Application of the proposed approach has the potential to be far reaching as the theory applies equally well to ab initio MD based on DFT, time-dependent DFT dynamics, and parameterized force-fields and is thus expected to have important impact on topics ranging from strongly-correlated materials with sophisticated treatment of electron-electron interactions to biological systems.   

Influence of spin-orbit coupling and Rashba interaction on the electron-phonon renormalized electronic energy levels

Electron-phonon (e-p) interaction calculations from first-principles are well documented in the literature. The predominance of non-adiabatic effects in the zero-point renormalization (ZPR) of the band gap for polar materials has been recently assessed in the light of the Fröhlich interaction.

Yet, even for benchmark materials, spin-orbit coupling (SOC) is frequently neglected to reduce the numerical cost of calculations. SOC manifests itself in the electronic structure through the split-off energy and by lifting band degeneracies away from time-reversal invariant momenta (TRIM). This modification of the energy levels will affect both e-p coupling energies and ZPR. Materials lacking inversion symmetry also exhibit an in-plane shift of the band extrema away from the TRIM, known as Rashba splitting. This could lead to resonant couplings at finite phonon wavevectors, which will strengthen the EP coupling energies.

We explicitly compute e-p coupling energies and ZPR for binary semiconductors, using density-functional perturbation theory (DFPT), with and without SOC. We also investigate Rashba semiconductor BiTeI. We finally analyze our results in the light of a three-dimensional Fröhlich Hamiltonian, including both SOC and Rashba interaction.   

Anharmonicity in Zirconium Hydrides: a first-principles study combined with inelastic neutron scattering

Zirconium Hydrides and Deuterides are candidates for neutron moderators and fuel-rod cladding materials. We investigate anharmonic phenomena in these materials using inelastic neutron scattering (INS) and lattice dynamics calculations within the framework of density functional theory (DFT). We observe multiple sharp peaks below harmonic (free) multi-phonon bands in the experimental spectra, which do not show up in the simulated INS spectra based on the harmonic approximation. We have thus carried out a detailed study of the anharmonicity by exploring the 2D potential energy surface with DFT calculations and solving the corresponding 2D single-particle Schrodinger equation of the H/D atom in zirconium hydrides/deuterides to get the eigenfrequencies. The results describe well the experimental INS spectra, showing harmonic behavior of the fundamental modes and strong anharmonicity at higher energies. The DFT calculations were carried out with the real-space multigrid (RMG) and VASP codes, and the experimental INS spectra were measured with the VISION spectrometer at the Spallation Neutron Source, Oak Ridge National Laboratory.   

Phonon-induced topological phase transition in SnTe

Unlike the topologically trivial semiconductor PbTe, SnTe has an inverted band gap at the L point that gives rise to a topological crystalline insulating phase protected by mirror symmetry [1]. In this work, we calculate the temperature renormalization of the electronic band structure of SnTe. We account for the energy shift of the electronic states due to thermal expansion, and electron-phonon interaction using the nonadiabatic Allen-Heine-Cardona formalism within density functional perturbation theory [2,3]. Corrections to the electronic band structure due to electron-electron interaction are obtained using many-body perturbation theory (GW). We capture the decrease of the direct gap with temperature yielding a temperature-induced phase transition to a topologically trivial phase at ~800 K. We find that both thermal expansion and electron-phonon interaction have a considerable effect on these temperature variations. We also analyze the temperature dependence of the electron-phonon self-energy.

[1] T. H. Hsieh et al., Nat. Commun. 3, 982 (2012)
[2] S. Ponce et al, J. Chem. Phys. 143, 102813 (2015)
[3] J. D. Querales-Flores et al, Phys. Rev. Mater. 3, 055405 (2019)

  

Phonon renormalization and four-phonon scattering in semiconductors and insulators

In semiconductors and insulators, heat is carried by phonons. Conventional ab initio methods for thermal conductivity (k) of materials assume that the lowest order theory of 3-phonon scattering sufficiently describes thermal transport. Here we show that this is not the case for several materials where higher-order 4-phonon scattering can significantly affect k. Furthermore, we show that for many naturally occurring materials, phonon scattering is so strong that not only is 4-phonon scattering important, but the underlying phonon quasiparticle picture itself can break down. To address this issue, we present a novel ab initio method that features an anharmonic many-body renormalization scheme to create well-defined phonon quasiparticles with weakened interactions, and includes both 3-phonon and 4-phonon scattering to obtain k [1]. We demonstrate the method’s success by comparing with experimental data of k for many common semiconductors and insulators. Our work presents a unified ab initio framework to accurately predict the thermal properties of solids with varying bond strengths.

[1] N. K. Ravichandran and D. Broido, Phys. Rev. B. 98, 085205, 2018.   

Ab-initio calculation of Seebeck coefficient of transition-metal elements

Ab-initio calculation of the Seebeck coefficient S of transition metal elements are performed within the framework of Kubo–Greenwood formula. The difficult points of calculating S are that, firstly, at T = 0K, the conductivity of pure metal diverges. Second, the Fermi surfaces of transition metals composed of many different states where the constant relaxation time approximation breaks down. To overcome the difficulties, we included the effects of electron-phonon scattering in the calculation of S. We exploited the Korringa–Kohn–Rostoker (KKR) Green's function method combined with the Kubo–Greenwood formula. The electron-phonon scattering was taken into account through ab-initio phonon calculations and an alloy analogy applied to the local static phonons. The KKR coherent potential approximation (KKR–CPA) was used for the latter. The calculated Cu resistivity and the Seebeck coefficients for various transition-metal elements at finite temperature show reasonable overall agreements with experiments. The present approach provides us with a framework applicable to a wide range of materials, including pure metals, compounds, ordered and disordered alloys.   

Understanding the Restoring Force From a Local Bonding Perspective: A First-Principles Picture of Phonons and Elasticity

Though the calculation of bulk elastic quantities and phonon frequencies using modern ab-initio techniques is now routine, understanding the crystal chemical origins of these properties is still an open question. How do we relate the value of a specific bulk elastic constant or vibrational mode to chemically intuitive ideas about local structure and bonding, especially when our calculations are often done in a spatially delocalized Bloch basis? Using a basis of maximally localized Wannier functions, we partition the total electronic energy onto real space representations of occupied states, as well of the curvature of that energy with respect to mechanical deformations and phonon distortions. By understanding how the energy of each individual bond changes with these distortions, we can obtain orbitally decomposed, chemically specific understanding of bulk properties. We use this approach to explore various perovskite oxides, exploring the chemical origins of elasticity, structural phase transitions, Grüneisen parameters, and thermal expansion properties, and discuss the possibility of enhancing or controlling these properties.   

Finite temperature electronic properties of diamond and diamondoids

Accurate calculations of electron-phonon coupling are essential to predict the finite temperature (T) properties of materials and molecules, especially those containing light-atoms. We present an approach to compute electron-phonon coupling which treats the motion of ions quantum mechanically, through the use of path-integral calculations, and the electronic states at the DFT or many-body-perturbation theory (MBPT) level. In particular, we carried out simulations for diamond and diamondoids by coupling the first-principle molecular dynamics code Qbox (http://qboxcode.org) with i-PI (http://ipi-code.org), a path integral simulation package, and we obtained single-particle energy levels within MBPT using the WEST code (http://west-code.org). We present results for different cluster sizes and surface terminations and we compare the zero-temperature limit of our simulations with results recently reported for electron-phonon coupling at T=0 [1].

[1] R.McAvoy, M. Govoni and G. Galli, J. Chem. Theory Comput, 14, 6269 (2018).   

Electronic structure and phonons in FeTi at high pressure

The FeTi system is amenable to computational investigations due to its simple crystal structure and minimalist Fermi surface. A thermally-driven electronic topological transition that results in anomalous phonon softening was recently reported to occur in FeTi at elevated temperatures as new features appear in the Fermi surface and new spanning vectors increase electronic screening of particular phonon modes. We investigated the pressure dependence of the electronic structure and the phonon dispersions using density functional theory and uncovered an octahedral splitting with an energy difference that increases with pressure and a Kohn anomaly with a wavevector that decreases with pressure. The calculated Fe partial phonon density of states are in agreement with nuclear-resonant inelastic x-ray scattering measurements and show that the phonons stiffen at different rates.