Session D61: Electrons, Phonons, Electron-Phonon Scattering and Phononics II

Phonon anharmonicity in quantum paraelectrics beyond density-functional theory

The ABO₃ family of perovskite oxides exhibits a wide range of physical properties and technological applications, with structural instabilities associated with anharmonic potential energy surfaces playing a key role. In the case of SrTiO₃ and KTaO₃, the strongly anharmonic lattice dynamics lead to a quantum paraelectric behavior at low temperatures, whereby the ferroelectric instability is suppressed due to anharmonic quantum fluctuations. A detailed quantitative understanding of the phonon anharmonicity underpins the study of emergent properties in this class of materials, but poses significant challenges.

In this talk, I will discuss an approach for calculating the temperature-dependent anharmonic properties of these materials with beyond density-functional theory accuracy. Specifically, we employ machine-learned potentials in combination with the stochastic self-consistent harmonic approximation. I will show that this method seamlessly allows to fully capture strong anharmonicities while retaining first-principles accuracy, and furthermore opens up the possibility to perform many-body calculations beyond DFT via Δ-machine learning. I will show that the paraelectric phase in KTaO₃ and SrTiO₃ is stabilized by anharmonic quantum fluctuations down to 0 K. In the case of SrTiO₃, we further characterize the cubic to tetragonal transition by the softening of the antiferrodistortive instability. I will discuss how a quantitative description of the quantum paraelectric behavior requires a higher-level treatment of electronic correlation effects via the random phase approximation.   

Computing the phononic properties of the metal-insulator transition in LuNiO3

The rare earth nickelates (RNiO₃) undergo a novel metal-insulator transition dubbed the site selective Mott transition. While the electronic picture of this phase transition has been extensively studied, the vibrational properties have not been explored due to the associated complexity. Here, we present the first step in understanding and predicting the structural disproportionation transition in the rare earth nickelates. The efficient bundled irreducible derivative approach was used to compute the phonons of LuNiO₃ in both the Pbnm and P2₁/c phases within DFT+U as a function of the Hubbard U, and comparisons with the experimental Raman spectra are provided. Additionally, we present the energy landscape of the bond disproportionation distortion as a function of U. An estimate of the transition temperature is provided based on the anharmonic phonon free energy within the independent mode approximation.   

First-principles study of magnetic-field-dependent thermal conductivity in magnetic materials

Measurements of thermal conductivity in magnetic systems have demonstrated large magnetic-field-induced enhancements at low temperatures, for example, in the Kitaev quantum spin liquid candidate α-RuCl₃ [Phys. Rev. Lett. 120, 117204 (2018)] and the cleavable magnet CrCl₃ [Phys. Rev. Res. 2, 013059 (2020)]. Models based on suppression of spin-phonon interactions modulated by magnetic field were used to understand this peculiar thermal transport behavior. However, these models were built from simple isotropic Debye models and a Debye-Callaway formalism with empirical scattering terms based on a variety of fitting parameters to describe intrinsic phonon scattering and magnetic scattering, among others, which hinder the understanding of the complex physics. Here we study phonon transport by solving the Peierls-Boltzmann equation with inputs of harmonic and anharmonic phonon properties calculated from first principles. The phonon scattering mechanisms from boundaries, defects, and three-phonon interactions are explicitly included, and an alternative scattering term for spin-phonon coupling is proposed to replace the previously used resonance scattering. Our work provides physical insights into mechanisms of spin-phonon interactions under magnetic field and field-dependent behaviors of magnetic materials.   

Anharmonic phonon behavior via irreducible derivatives: molecular dynamics and self-consistent perturbation theory

Cubic phonon interactions are now regularly computed from first principles, and the quartic interactions have begun to receive more attention. Given this realistic anharmonic vibrational Hamiltonian, the classical phonon Green's function can be precisely measured using molecular dynamics, which can then be used to rigorously assess the range of validity for self-consistent diagrammatic approaches in the classical limit. Here we use the bundled irreducible derivative approach to efficiently and precisely compute cubic and quartic phonon interactions in CaF$_2$ and ThO$_2$, systematically obtaining the vibrational Hamiltonian purely in terms of irreducible derivatives. We assess the fidelity of various bare and self-consistent diagrammatic approaches to the phonon Green's function as compared to the numerically exact solution. Specific attention is given to the phonon frequency shifts and linewidths, demonstrating that the 4-phonon bubble diagram has an important contribution to linewidth beyond $T=500$ K. Moreover, accurate results are obtained even at $T=900$ K when performing self-consistency using a 4-phonon loop and evaluating the 3-phonon and 4-phonon bubble post-self-consistency. Our demonstration of accurate computation of the classical Green's function for a realistic anharmonic vibrational Hamiltonian implies that comparison with experiment at sufficiently high temperatures can be reserved for scrutinizing the quality of the vibrational Hamiltonian and the underlying approximations to the many-electron problem.   

First-principles studies of the charge density wave transition in titanium diselenide (TiSe2)

Many transition metal dichalcogenides (TMDs) host interesting properties arising from charge and spin ordering, superconducting pairing, and topological electronic effects, among which charge density wave (CDW) formation is common, but the detailed mechanisms remain murky in many cases. Models including Fermi surface nesting, static or dynamic phonon coupling, excitonic interaction, and many-body correlation effects are potential candidates. Specifically, TiSe₂ in the bulk form shows a simple commensurate (2×2×2) CDW transition, while a single layer of TiSe₂ shows a similar (2×2×2)  transition but at a higher transition temperature. The underlying driving mechanism for the CDW formation is still under debate. To gain a better understanding, we have performed first-principles calculations of the electronic and phononic structures for various distorted structures. The goal is to develop a method to predict the CDW transition temperature and the nature of the CDW phase. This talk will report our results.

    

Hubbard U through polaronic defect states

Since the preliminary work of Anisimov and co-workers, the Hubbard corrected DFT+U functional has been used for predicting properties of correlated materials by applying on-site effective Coulomb interactions to specific orbitals. However, the determination of the Hubbard U parameter has remained under intense discussion despite the multitude of approaches proposed. Here, we define a selection criterion based on the use of polaronic defect states for the enforcement of the piecewise linearity of the total energy upon electron occupation. The values of U determined in this way are found to be robust upon variation of the considered state. The corresponding electronic and structural properties are in good agreement with results from piecewise linear hybrid functionals. In particular, defect formation energies are well reproduced, thereby validating the energetics achieved with our selection criterion. It is emphasized that the selection of U should be based on physical properties directly associated with the orbitals to which U is applied, rather than on more global properties such as band gaps. For comparison, we also determine U through a well-established linear response scheme finding noticeably different values of U and consequently different formation energies. Possible origins of these discrepancies are discussed. As case studies, we consider the self-trapped electron in BiVO₄, the self-trapped hole in MgO, the Li-trapped hole in MgO, and the Al-trapped hole in α-SiO₂.   

Theory of Phonon Mode Interactions from Current Correlations and Applications in Disordered Solids and Liquids

Phonons are characterized by the normal modes of vibration that arise from the motion of the atoms in a periodic lattice.  Traditionally, the theoretical treatment involves solving the dynamical matrix to obtain the normal modes and their respective dispersion relations.  This approach fails for disordered solids and liquids when there is a complete breakdown of translational symmetry even when there is a well-identifiable dispersion relationship for such systems. In this work, we propose a new approach that makes use of the spatial Fourier component of the particle current (or momenta) to obtain the dispersion relationship without directly working with the dynamical matrix.  By Taylor expanding the particle current with respect to the atomic displacements and without invoking a repeating unit cell, we first demonstrate that the leading term corresponds to the normal modes of vibration. We then show that higher orders of the current expansion correspond to the scattering of normal modes in anharmonic systems.  Along with a new theoretical approach, we will present results from atomistic simulations that highlight the attractiveness of the particle current approach in disordered solids and liquids.

    

Novel results obtained by modeling of dynamic processes in superconductors: phase-slip centers as cooling engines

Based on the time-dependent Ginzburg-Landau system of equations and finite element modeling, we present novel results related with physics of phaseslippage in superconducting wires surrounded by a non-superconductive environment. These results are obtained within our previously reported approach related to superconducting rings and superconductive gravitational wave detector transducers. It is shown that the phase-slip centers (PSCs) can be effective in originating not only positive but also negative thermal fluxes. With appropriate design utilizing thermal diodes, PSCs can serve as cryocooling engines. Operating at T ∼ 1 K cryostat coldfinger, they can achieve sub-Kelvin temperatures without using ³He.   

A combined first principles and phenomenological approach for the modeling of coherent phonons in materials

Coherent phonons in materials can elucidate the interactions between electronic, optical, and lattice degrees of freedom, and have potential applications in nonlinear phononics and coherent lattice control. We study coherent phonons in bismuth and antimony using first principles density functional theory and a phenomenological classical equation of motion. By explicitly calculating and interpolating both the potential energy surface and the frequency-dependent macroscopic dielectric function across all three optical phonon modes in these materials, we are able to map out the landscape of interactions between the lattice and the optical response of the material. We apply this approach to reproduce classic results in the field and compare expressions for the coupling of lattice dynamics with electronic response. We comment on the range of applicability of our methodology and the potential for first-principles-informed surrogate models for material response.   

Thermal Conductivity and Theory of Inelastic Scattering of Phonons by Collective Fluctuations

We study the coupling of phonons to any general operator field and its consequences on the thermal conductivity of phonons. Using a scattering approach, we find that the lowest-order diagonal scattering rate, which determines the longitudinal conductivity, is controlled by two-point correlation functions of the collective fluctuations the phonons couple to, while the off-diagonal scattering rates involve a minimum of four-point correlation functions. We take up the challenge of computing analytically these two- and four-point correlation functions in an ordered antiferromagnet and fermionic spinon spin liquid, hence providing expressions for the longitudinal and Hall conductivities in such systems. By explicit numerical computation of the phonon conductivity tensor from a given realistic interacting model of spins, we relate thermal conduction properties to features of the spin dynamics and the magnetoelastic coupling.   

Spectral heat phonon blocking characteristics across inter-mixed and oxidized semiconductor interfaces

In this work, we spectrally investigate thermal transport characteristics across the interfaces formed between Al metal and various semiconductors, such as Si, Ge, and GaAs by exploiting an acoustic phonon transmission spectroscopy technique which provides full transmission spectra of three acoustic branches. We control the interface conditions by adjusting an air exposure time after the HF treatment, and observe that the phonon transmission becomes significantly reduced from the high frequency side. Considering that the wavelength of heat phonons ranges from about 0.5 nm to 10 nm, we discuss the variations of the phonon transmittance spectra based on electronic and phononic states as well as the interface morphology.   

Manipulating electron and phonon flow across interfaces using structural randomness

Understanding electron and phonon transport across interfaces is of great significance for designing efficient solid-state devices such as transistors, laser diodes and thermoelectric energy converters. Interface roughness is a common type of randomness in heterostructures, which strongly affects electron and phonon transport across interfaces. We find that atomically rough interfaces can scatter short-wavelength electrons and assist the transmission between mismatched valleys. The contact resistance is reduced by over an order of magnitude. Our study provides new insights on the conventional wisdom to improve the interfacial transport using graded interfaces. We also use the atomistic Green's function to simulate phonon transport across rough interfaces to show that the basic assumption that phonons lose memories in the often-used diffuse phonon scattering model is questionable. With a parallel treatment of electron and phonon transport, our study points to pathways of simultaneous manipulation of their flow across interfaces.   

Athermal charge effect of improving the plasticity of metals: first-principles study

High plasticity is one of the most required factors when manipulating metals. Among several methods that have been industrially used to increase the plasticity of metals, plasticity induced by an electric current flow, which is called electro-plasticity, is widely used, but its physical origin has not been fully understood. It was suggested that Joule heating due to electric currents would cause a temperature rise leading to high plasticity observed in several metals. Recent studies have, however, revealed that such Joule heating may not be enough to increase a local temperature to induce high plasticity. Here we propose that the electro-plasticity is induced by modified electronic structures due to the charge doping effect. Our study suggests that the effect of charge doping causes phonon softening at certain frequencies due to bond weakening. We also consider the effects of charge doping on stacking fault in metals. It is found that the energy barrier for the slipping process of metal planes is reduced by excess charges accumulating near the slip plane during the stacking fault process. It is the athermal effect rather than a thermal one that induces electro-plasticity caused by phonon softening and charge accumulation.