Session L34: Thermal Transport Modeling - Novel Approaches

Car and Parrinello meet Green and Kubo: simulating atomic heat transport from equilibrium ab initio molecular dynamics

Modern simulation methods based on electronic-structure theory have long been deemed unfit to compute heat transport coefficients within the Green-Kubo formalism. This is so because the quantum-mechanical energy density from which the heat flux is derived is inherently ill defined, thus allegedly hampering the use of the Green-Kubo formula. While this objection would actually apply to classical systems as well, I will demonstrate that the thermal conductivity is indeed independent of the specific microscopic expression for the energy density and current from which it is derived. This fact results from a kind of \emph{gauge invariance} stemming from energy conservation and extensivity, which I will illustrate numerically for a classical Lennard-Jones fluid. I will then introduce an expression for the adiabatic energy flux, derived within density-functional theory, that allows simulating atomic heat transport using equilibrium \emph{ab initio} molecular dynamics. The resulting methodology is demonstrated by comparing results from ab-initio and classical molecular-dynamics simulations of a model liquid-Argon system, for which accurate inter-atomic potentials are derived by the force-matching method, and applied to compute the thermal conductivity of heavy water at ambient conditions. The problem of evaluating transport coefficients along with their accuracy from relatively short trajectories is finally addressed and discussed with a few representative examples.   

First principles calculations of thermal conductivity with out of equilibrium molecular dynamics simulations

The prediction of the thermal properties of solids and liquids is central to numerous problems in condensed matter physics and materials science, including the study of thermal management of opto-electronic and energy conversion devices. We present [1] a method to compute the thermal conductivity of solids by performing ab initio molecular dynamics at non equilibrium conditions. Our formulation is based on a generalization of the approach to equilibrium technique, using sinusoidal temperature gradients, and it only requires calculations of first principles trajectories and atomic forces. We discuss results and computational requirements for a representative, simple oxide, MgO, and compare with experiments and data obtained with classical potentials. [1] M. Puligheddu et al. Submitted 2016   

Ab initio thermal transport in strongly anharmonic materials

We present recent advances regarding the temperature dependent effective potential method (TDEP) and its application to thermoelectric materials. All orders of non-harmonic effects are implicitly included when calculating phonon dispersions, lattice thermal transport and finite temperature phase stability. Recent additions deal with thermal transport in disordered systems, complex crystal structures and numerical efficiency for high-throughput applications.   

Novel Electron-Phonon Relaxation Pathway in Graphite Revealed by Time-Resolved Raman Scattering and Angle-Resolved Photoemission Spectroscopy

Ultrafast dynamics of photo-excited electron-hole pairs has attracted a lot of attention in the last decade due to its importance for a number of technologies such as solar cells. We report dynamics of electron-hole excitations as well as G phonons in graphite after an excitation by an intense laser pulse investigated by the combination of ultrafast pump-probe Raman scattering and angle-resolved photoemission spectroscopy. We found that the increase of the G phonon population occurs about 65 fs later than the prediction of the accepted two-temperature model. This time-delay is also evidenced by the absence of the so-called self-pumping for G phonons. The unusual pump fluence dependence also contradicts the two-temperature model. These experimental observations imply a new relaxation pathway which we call Anharmonic Phonon Model (APM): Instead of hot carriers transferring energy to G-phonons directly, the energy is first transferred to optical phonons near the zone boundary K-points, which then decay into G-phonons via phonon-phonon scattering. The simulation results based on the APM will also be presented.   

First-Principles Simulations of Non-Equilibrium Phonon Dynamics in III-V Materials

Understanding non-equilibrium energy transfer between hot electrons and phonons is important to improving the efficiency of solar-energy conversion and nanoelectronic devices. As photo- or electrically-excited electrons excite non-thermal phonons, they generate transient and/or steady-state non-equilibrium phonon distributions known as "phonon bottlenecks", impacting thermal transport and structural properties. In this work, we develop a first-principles method that captures these effects, by computing the transient dynamics of non-equilibrium phonon distribution using the Bloch-Boltzmann-Peierls equations along with first-principles calculations of electron-phonon and phonon-phonon interactions. We apply our method to the description of phonon thermalization in III-V semiconductors. We examine the effects of polarity and phonon-phonon scattering phase space on the thermalization time, and discuss the deviation from simple two-temperature models that are commonly used to interpret ultrafast-laser experiments.   

Non-linear thermoelectric nano-device with electron-phonon interactions

We consider electron transport through a single (tight-binding Hamiltonian) site and a localized phonon, about which are placed two leads at disparate chemical potentials due to being at disparate temperatures (the usual thermoelectric regime). In a calculation patterned after the large body of zero-temperature work done in the driven regime (where an external agent maintains the chemical potential difference), non-equilibrium Green functions are used to obtain the nonlinear current-voltage characteristics. The Green functions are calculated using the self-consistent Born approximation to incorporate (at the Hartree-Fock-diagram level) interactions between the itinerant electrons and localized phonon-mode. In the thermoelectric regime, we evaluate the power and efficiency of the device as a function of the electron-phonon coupling at various temperature differences. In addition, we will report studies of a new regime where an external driving agent and a temperature-difference are both responsible for the chemical potential difference: the partially-driven thermoelectric regime.   

Estimation of effective electron relaxation times in real thermoelectric materials

Good samples of thermoelectric materials should be Phonon-Glass-Electron-Crystal (PGEC) [1], which scatters phonons without scattering electrons. However, the actual values of electron relaxation time $\tau_{\mathrm{el}}$ are not well investigated, and $\tau _{\mathrm{el}}$ is simply set as 10$^{\mathrm{-14}}$ s in many first-principles calculations of thermoelectric properties. In this study, we attempted to estimate the effective values of $\tau _{\mathrm{el}}$ of various thermoelectric materials, by fitting the calculation results by WIEN2k [2] and BoltzTraP [3] with experimental Seebeck coefficient and electrical conductivity. When we fitted experimental thermoelectric properties of Si$_{\mathrm{0.8}}$Ge$_{\mathrm{0.2}}$ samples [4][5], $\tau_{\mathrm{el}}$'s at 300 K were 9x10$^{\mathrm{-15}}$ s in a highly crystalline sample [4], and 5-6x10$^{\mathrm{-15}}$ s in ball-milled polycrystalline samples [5]. Temperature dependences of $\tau _{\mathrm{el}}^{\mathrm{-1}}$ were also different between samples, implying the difference in dominant electron scattering mechanisms. Various samples of thermoelectric materials with fairly high figures of merit exhibited $\tau_{\mathrm{el}}$ of several 10$^{\mathrm{-15\thinspace }}$s at 300 K. [1] G. A. Slack, \textit{CRC Handbook of Thermoelectrics}, 407 (1995). [2] P. Blaha, \textit{et al}., \textit{WIEN2k Users' Guide}, Vienna Univ. of Technology, Austria (2001). [3] G.K.H. Madsen et al., \textit{Comp. Phys. Comm.} 175, 67 (2006). [4] J.P. Dismukes et al., \textit{J. Appl. Phys.} 10 2899 (1976). [5] C.B. Vining et al., \textit{J. Appl. Phys.} 69 4333 (1991).   

Emergent phenomena in phonon thermal transport

The thermal conductivity of insulating crystals originates from the energy transfer through lattice vibrations, as commonly described by the phonon Boltzmann transport equation. Since the pioneering work of Peierls, the prevalent hypothesis is that phonons are the heat carriers. However, it has long been known that this picture has shortcomings. For example, in materials of reduced dimensionality or at cryogenic temperatures, the scattering dynamics is dominated by momentum conserving - normal - processes, as opposed to momentum dissipating - Umklapp - processes. In these circumstances, heat flux is not lost at every scattering event. Instead, scattering shuttles heat flux through multiple phonon states, coupling them. As a result, collective phonon excitations arise, causing exotic phenomena: in 2D materials, they are responsible of high thermal conductivities and hydrodynamic behaviors, such as second sound, where temperature propagates as a damped wave, a phenomenon hitherto observed only in a few materials at cryogenic temperatures. I will show how these properties can be rationalized by introducing a gas of collective phonon excitations, called 'relaxons' [1]. Defined as the eigenvectors of the scattering matrix, relaxons allow for a simple - yet exact - interpretation of thermal conductivity in terms of a kinetic gas theory, where the relevant gas is made of such relaxons, the true heat carriers, and not phonons. These considerations provide a new explanation of the high conductivities of 2D materials, revise the time evolution of thermalization processes [2], correct the relevant time and length scale of heat flux dissipation, and provide a new viewpoint on semiclassical transport theories. \newline \newline [1] A. Cepellotti, and N. Marzari Phys. Rev. X 6, 041013 (2016) \newline [2] J. Hu, et al., PNAS 113, 43, E6555 (2016)   

Thermal insulator transition induced by interface scattering

The classic Bruggeman percolation model of thermal conductivity for composite materials is generalized to include the effects of interfacial scattering [1]. This generalized model accurately explains the measured variation of the composite thermal conductivity with loading and particle size. At high loadings, this model further predicts that strong interface scattering leads to a sharp decrease in thermal conductivity, or an insulator transition, when conduction through the matrix is restricted and heat is forced to diffuse through particles with large interface resistance. The closed form and accuracy of the model, and its ability to predict transitions between insulating and conducting states, suggest it can be a useful tool for designing composite materials with low or high thermal conductivity for a number of applications. [1] B. A. Slovick and S. Krishnamurthy, Appl. Phys. Lett. 109, 141905 (2016).   

Nanoscale Interface Scattering of Phonons in Multilayered Nanostructures

Nanostructures can be employed to control thermal and electrical properties and increase thermoelectric energy conversion efficiency. An insight into surface and interface scattering in nanostructures is essential in manipulating these properties, which in turn affect the thermoelectric figure of merit ZT. An understanding of the surface conditions is imperative for predicting the amount of specular reflection and transmission of phonons. A crucial challenge is to incorporate this along with different physical properties of constituents across an interface. We employ an extension of the electromagnetic wave scattering theory for rough surfaces developed by P. Beckmann and A. Spizzichino to account for thermal phonon interface scattering. This is supplemented with the Fuchs-Sondheimer theory to formulate thermal transport in layered nanostructures. A rigorous analysis incorporating complete layer coupling, reflection and refraction conditions, and surface shadowing effects is presented. Thermal conductivities of superlattices, bi-layers and sandwich-layered structures made of different constituent materials including Si-Ge, AlAs-GaAs and Si-Si$_{\mathrm{x}}$Ge$_{\mathrm{1-x}}$ are calculated. An evaluation of the amount of heat flow confined within a constituent, and extended over multiple layers is performed. A detailed analysis of the heat spectrum is also presented which allows to predict the amount of heat carried by phonons of different frequencies and mean free paths. The proposed accurate description of phonon surface scattering and prediction of heat spectra would allow for the design of nano-engineered materials and devices with improved thermoelectric properties.