Session N48: Electrons, Phonons, Electron-Phonon Scattering, and Phononics III

Thermal transport in complex materials: from glasses to van der Waals heterostructures

Nanometer-thin thermal insulators and nanodevices that enable the dynamic control of thermal transport are long-sought-after in nanoelectronics and renewable energy technologies.   

To design such systems, it is necessary to understand and compute phonon transport in complex non-crystalline materials.

Here I will illustrate an approach, named Quasi-Harmonic Green-Kubo, to calculate the thermal conductivity of solids, which naturally bridges the Boltzmann kinetic theory in crystals and the Allen-Feldman model in glasses. This approach completes a set of lattice dynamics and molecular dynamics tools that allow us to address phonon transport at the atomic scale in a broad range of materials.

Applications to glassy alloys, alloy superlattices, intercalated layered materials, and van der Waals heterostructures show that our atomistic simulation toolbox provides a parameter-free framework to predict and interpret heat transport in a wide range of materials and (nano)devices across from the ballistic to the diffusive regime.   

First-principles phonon lifetimes validated via inelastic neutron scattering

Phonon linewidths are a key component of quasiparticle theories of transport, yet ab-initio linewidths are rarely directly compared to inelastic neutron scattering (INS) results. Existing comparisons show discrepancies even at temperatures where perturbation theory is expected to work. In this work, we demonstrate that the reciprocal space voxel (q-voxel), which is the minimum region in reciprocal space sampled by INS, must be explicitly accounted for within theory in order to have a meaningful comparison with INS. We illustrate this in two ionic insulators having the fluorite structure: CaF₂ and ThO₂.  The quadratic and cubic phonon interactions are computed from DFT, and leading order perturbation theory is used to construct the scattering function at q-points. When the first-principles scattering function is computed within the same q-voxel as INS, the resulting linewidths are in reasonable agreement. Passing this test implies high fidelity of the phonon interactions and the approximations used to compute the Green’s function, serving as a critical benchmark of theory, and implying that other material properties should be reasonably predicted.   

Thermal transport in solids beyond the Ioffe-Regel limit

Recently it has been shown that the two established heat conduction mechanisms—namely the propagation of atomic vibrational waves in anharmonic crystals elucidated by the phonon Boltzmann transport equation [R. Peierls, Ann. Phys. 395, 1055 (1929)], and the couplings between atomic vibrational modes in harmonic glasses rationalized by Allen and Feldman’s equation [P. B. Allen and J. L. Feldman, Phys. Rev. Lett. 62, 645 (1989)]—naturally emerge as limiting cases of a unified theory, derived from the Wigner formulation of quantum mechanics and describing on an equal footing solids ranging from crystals to glasses [M. Simoncelli, N. Marzari, and F. Mauri, Nat. Phys. 15, 809 (2019)]. Here, we combine this unified theoretical framework with first-principles calculations to investigate what happens when atomic vibrational waves reach the Ioffe-Regel limit (i.e. their mean free paths become comparable or shorter than the interatomic spacing), showing that they can still contribute to heat transport due to their wave-like capability to interfere and tunnel. We showcase these findings in various silica polymorphs with different degree of disorder, and in materials with ultralow thermal conductivity employed for thermal barrier coatings or thermoelectrics.   

A typical medium dynamical cluster approximation for studying Anderson localization of phonons in multi-branch mass-disordered systems

The phenomenon of Anderson localization (AL) has generated a lot of interest over many decades. Specifically, the AL of phonons has been viewed as a potential mechanism for improving the figure of merit of thermoelectric materials. Despite extensive work, the influence of the directional nature of phonons on the AL transition has not been well explored. In this talk, I will discuss the recently developed typical medium dynamical cluster approximation to investigate the AL of phonons considering three directions of lattice vibrations in the presence of mass disorder. We have validated the new formalism against several limiting cases and exact diagonalization results. A comparison of results for the single branch versus multiple branch case yields several interesting observations of the interplay of inter-branch mixing and diagonal disorder in the context of phonon localization.   

Phonon transport beyond Rayleigh scattering in spatially correlated disorder

The performance and reliability of numerous technologies, from electronics and thermoelectrics to nuclear reactors, are constrained by the thermal conductivity of solid-state components. In many cases, these materials include substantial amounts of defects and nanostructures. Thus, understanding how disorder impacts phonon scattering and heat transport is a critical research challenge. It is known that the scattering rates of phonons due to point defects decrease as the fourth power of the mode frequency (Rayleigh scattering). Here, we demonstrate that this power law can be modified by introducing spatial correlations in the defect distribution, resulting in a substantial suppression of the thermal conductivity. To illustrate this, we apply a Chebyshev polynomial Green's function method to simple mass-disordered models for an exact treatment of disorder in large supercells (tens of millions of atoms).   

Strongly correlated phonons and the breakdown of phonon theory in MgO and BaTiO3

The phonon theory of lattice vibrations is exact in the limit of zero temperature. In this limit, phonons are non-interacting; but as the temperature is raised, anharmonic terms in the potential expansion become more important, giving rise to phonon-phonon interactions. If the strength of phonon-phonon interaction increases, strong correlation occurs and phonons themselves can become poorly defined. This can happen at very high temperatures, or in the vicinity of structural phase transitions, in cases exhibiting "rattler modes" in the material (i.e. atoms oscillating between local energy minima). 

We calculate the velocity-velocity correlation function from molecular dynamics simulations, obtaining (omega,k)-resolved power spectra at finite temperatures, to explore the breakdown of phonon theory with temperature in MgO and BaTiO₃. This breakdown is gradual in MgO but there are more sudden changes in BaTiO₃ near its phase transitions, when its central mode, which is a rattler mode, emerges.   

Phonon Modes in Supercritical Fluids

Phonons, which are collective vibrational excitations of atoms in a periodic lattice, can be described by

the normal mode of vibrations, and their dispersion can be determined through analysis of these modes.

Extending such an analysis to liquids is challenging due to the diffusive motion of atoms and the lack of

periodic structure in liquids. Theories of time correlation functions have been employed in the past to

describe the collective motion of atoms in liquids, and dispersion relationships can be extracted from

the Fourier spectra of these correlation functions. In this work, we present a direct method of

extracting phonon dispersion from the elementary excitations using the ratio of zero-time correlations

of acceleration and velocity modes. By applying it to supercritical fluids below the Frenkel line, where

solid-like characteristics are prominent, we show that the dispersion relations obtained through our

method agree with those obtained using current time correlation functions. We then determine the

speed of sound using the dispersion of longitudinal and transverse phonon modes.   

Modeling non-diffusive thermal transport in silicon with the phonon Boltzmann Transport Equation: Full Scattering Matrix vs Relaxation Time Approximation

In the past decade, non-diffusive heat transport by phonons at room temperature at the micro/nanoscale was reported in many single crystal materials. Many of these results have been modeled using the relaxation time approximation (RTA) to the Peierls-Boltzmann phonon transport equation (BTE). While the RTA has been shown to fail for high Debye temperature materials such as diamond and graphene, it has been considered accurate for lower Debye temperature materials such as silicon. The objective of the present study is to test this assumption by comparing the results obtained under RTA with the full scattering matrix BTE. We consider the problem of the transient thermal grating, i.e., the relaxation of a spatially periodic perturbation of the phonon distribution. Using silicon as an example, we present calculations with both the RTA and full scattering matrix over a wide range of the thermal grating periods covering the transition from diffusive to ballistic regime.  We find that the RTA performs reasonably well at the onset of non-diffusive transport, i.e., for the heat transport distances in the micron range, but becomes increasingly inaccurate on the nanometer scale when the phonon population in the thermal grating is far from equilibrium. We will discuss the relationship of the pseudo-temperature of the RTA with the thermodynamic temperature of the full scattering matrix BTE. The experimental relevance of the BTE calculations in the context of recent nanoscale transient grating experiments with extreme ultraviolet excitation will also be discussed.   

Response at finite temperature

We present recent developments using the temperature dependent effective potential technique (TDEP) to model vibrational properties of materials. The technique relies on explicitly temperature-dependent model Hamiltonians to capture all orders of non-harmonic effects. Recent developments include determination of high order Raman spectra, IR absorbtion, and thermal transport based on Green-Kubo formalism in contrast with the more established Boltzmann transport. In addition, we will present a generalisation of the TDEP technique to magnetic systems.   

Structural optimization at finite temperature based on anharmonic phonon theory

We develop a theory of ab-initio structural optimization at finite temperature based on the self-consistent phonon (SCP) theory[1], which nonperturbatively considers the anharmonic effect. We implement the theory to the ALAMODE package[2,3], which is an open-source package of anharmonic phonon calculation. By applying our method, we successfully calculate the structural transition of BaTiO₃, a prototypical ferroelectric material. Our method makes it possible to efficiently compute the structure of materials at finite temperature in a deterministic way. We expect that the method is effective in investigating a wide range of materials with multiple competing structures.

[1] D. J. Hooton. Phil. Mag. 3.25 (1958)

[2] T. Tadano, S. Tsuneyuki PRB 92.054301 (2015)

[3] Y. Oba, et al. PRMat 3.033601 (2019)   

Temperature-dependent phonons from ab initio molecular dynamics and density functional perturbation theory.

Phonons play an important role in understanding properties of materials. Quasiharmonic approximation (QHA) introduces an implicit dependence of phonon frequencies on temperature via volume, allowing reasonable prediction of thermal expansion coefficient and free energy of materials. On the other hand, QHA is insufficient in capturing anharmonic effects that occur in the absence of thermal expansion, and breaks down in dynamically unstable materials where the harmonic phonons are negative. Here we develop a method for computing temperature-dependent phonons by fitting interatomic force constants (FCs) to ab-initio molecular dynamics (AIMD) forces. While our method is equivalent to that of [1] and [2], it differs in two ways: the 0K FCs are from density functional perturbation theory rather than finite-difference in supercell, and they are decomposed on symmetrized orthogonal basis, which are the parameters that are minimized during the fitting. Thus, we use highly efficient reciprocal-space representation in order to minimize the number of degrees of freedom. We demonstrate the effectiveness of this technique by computing temperature-dependent phonon shift in fcc Aluminum, where the QHA also works, and temperature renormalized phonons in bcc Titanium, where QHA fails.   

Effect of fourth-order anharmonicity on the phonon lineshapes in strongly anharmonic insulating crystals from first principles

Our recent work shows that the inclusion of four-phonon scattering and phonon renormalization driven by the fourth-order anharmonicity of the crystal potential is important to accurately represent the thermal conductivities of strongly anharmonic insulating crystals like sodium chloride (NaCl) [1]. Here we show, using our recently-developed unified first-principles framework, that four-phonon scattering also critically affects the phonon lineshapes of NaCl that are typically observed in inelastic neutron scattering measurements. To capture these higher-order effects accurately, our calculations include the lowest-order three-phonon and higher-order four-phonon scattering processes, and a many-body self-consistent anharmonic phonon renormalization step to address the ill-defined nature of phonon quasiparticles. Using this approach, we show that these higher-order anharmonic processes significantly broaden the phonon lineshapes compared to their three-phonon counterparts even around room temperature, and their inclusion into the calculations is crucial to achieve agreement with the experimental measurements.

[1] Navaneetha K. Ravichandran and David Broido, Phys. Rev. B 98 (8), 085205 (2018).   

Phonon transport in ultrahigh thermal conductivity materials beyond the relaxation time approximation

In electrical insulators, heat is carried by the quantized collective lattice vibrations called phonons. Resistance to heat flow in these materials is caused by phonon scattering processes. Thermal phonon transport in these materials is governed by the semi-classical Boltzmann Transport Equation (BTE). Solutions of the BTE are commonly derived assuming the validity of relaxation time approximation (RTA), where all phonon scattering events are assumed to be momentum-dissipative in nature. While the RTA-based BTE solution describes the heat flow in several materials reasonably well, it fails to capture the ultrahigh thermal conductivity and the exceptional phonon transport properties of materials like diamond and boron nitride. Here we present the solutions of the BTE without the RTA for phonon transport through these ultrahigh thermal conductivity materials and demonstrate that accurately distinguishing momentum-conserving (Normal) and momentum-dissipative (Umklapp) scattering events in our formulation is crucial to correctly predict their thermal transport properties.