arXiv subjects

Michele Simoncelli

Publications and source records attributed to Michele Simoncelli.

23 records · Page 2Linked to original sources

arXiv2022

Thermal conductivity of glasses above the plateau: first-principles theory and applications

Predicting the thermal conductivity of glasses from first principles has hitherto been a prohibitively complex problem. In fact, past works have highlighted challenges in achieving computational convergence with respect to length and/or time scales using either the established Allen-Feldman or Green-Kubo formulations, endorsing the concept that atomistic models containing thousands of atoms -- thus beyond the capabilities of first-principles calculations -- are needed to describe the thermal conductivity of glasses. In addition, these established formulations either neglect anharmonicity (Allen-Feldman) or miss the Bose-Einstein statistics of atomic vibrations (Green Kubo), thus leaving open the question on the relevance of these effects. Here, we present a first-principles formulation to address the thermal conductivity of glasses above the plateau, which can account comprehensively for the effects of structural disorder, anharmonicity, and quantum Bose-Einstein statistics. The protocol combines the Wigner formulation of thermal transport with convergence-acceleration techniques, and is validated in vitreous silica using both first-principles calculations and a quantum-accurate machine-learned interatomic potential. We show that models of vitreous silica containing less than 200 atoms can already reproduce the thermal conductivity in the macroscopic limit and that anharmonicity negligibly affects heat transport in vitreous silica. We discuss the microscopic quantities that determine the trend of the conductivity at high temperature, highlighting the agreement of the calculations with experiments in the temperature range above the plateau where radiative effects remain negligible (50<T <450 K).

cond-mat.mtrl-sci↗

arXiv2022

Wigner formulation of thermal transport in solids

Two different heat-transport mechanisms are discussed in solids: in crystals, heat carriers propagate and scatter particle-like as described by Peierls' formulation of the Boltzmann transport equation for phonon wavepackets. In glasses, instead, carriers behave wave-like, diffusing via a Zener-like tunneling between quasi-degenerate vibrational eigenstates, as described by the Allen-Feldman equation. Recently, it has been shown that these two conduction mechanisms emerge from a Wigner transport equation, which unifies and extends the Peierls-Boltzmann and Allen-Feldman formulations, allowing to describe also complex crystals where particle-like and wave-like conduction mechanisms coexist. Here, we discuss the theoretical foundations of such transport equation as is derived from the Wigner phase-space formulation of quantum mechanics, elucidating how the interplay between disorder, anharmonicity, and the quantum Bose-Einstein statistics of atomic vibrations determines thermal conductivity. This Wigner formulation argues for a preferential phase convention for the dynamical matrix in the reciprocal Bloch representation and related off-diagonal velocity operator's elements; such convention is the only one yielding a conductivity which is invariant with respect to the non-unique choice of the crystal's unit cell and is size-consistent. We rationalize the conditions determining the crossover from particle-like to wave-like heat conduction, showing that phonons below the Ioffe-Regel limit (i.e. with a mean free path shorter than the interatomic spacing) contribute to heat transport due to their wave-like capability to interfere and tunnel. Finally, we show that the present approach overcomes the failures of the Peierls-Boltzmann formulation for materials with ultralow or glass-like thermal conductivity.

cond-mat.mtrl-sci↗

arXiv2022

Many-body Green's function approach to lattice thermal transport

Recent progress in understanding thermal transport in complex crystals has highlighted the prominent role of heat conduction mediated by interband tunneling processes, which emerge between overlapping phonon bands (i.e. with energy differences smaller than their broadenings). These processes have recently been described in different ways, relying on the Wigner or Green-Kubo formalism, leading to apparently different results which question the definition of the heat-current operator. Here, we implement a full quantum approach based on the Kubo formula, elucidating analogies and differences with the recently introduced Wigner or Green-Kubo formulations, and extending the description of thermal transport to the overdamped regime of atomic vibrations, where the phonon quasiparticle picture breaks down. We rely on first-principles calculations on complex crystals with ultralow conductivity to compare numerically the thermal conductivity obtained within the aforementioned approaches, showing that at least in the quasiparticle regime the differences are negligible for practical applications.

cond-mat.mtrl-sci↗

arXiv2019

Generalization of Fourier's law into viscous heat equations

Heat conduction in dielectric crystals originates from the propagation of atomic vibrations, whose microscopic dynamics is well described by the linearized phonon Boltzmann transport equation. Recently, it was shown that thermal conductivity can be resolved exactly and in a closed form as a sum over relaxons, $\mathit{i.e.}$ collective phonon excitations that are the eigenvectors of Boltzmann equation's scattering matrix [Cepellotti and Marzari, PRX $\mathbf{6}$ (2016)]. Relaxons have a well-defined parity, and only odd relaxons contribute to the thermal conductivity. Here, we show that the complementary set of even relaxons determines another quantity --- the thermal viscosity --- that enters into the description of heat transport, and is especially relevant in the hydrodynamic regime, where dissipation of crystal momentum by Umklapp scattering phases out. We also show how the thermal conductivity and viscosity parametrize two novel viscous heat equations --- two coupled equations for the temperature and drift-velocity fields --- which represent the thermal counterpart of the Navier-Stokes equations of hydrodynamics in the linear, laminar regime. These viscous heat equations are derived from a coarse-graining of the linearized Boltzmann transport equation for phonons, and encompass both limits of Fourier's law and of second sound, taking place, respectively, in the regimes of strong or weak momentum dissipation. Last, we introduce the Fourier deviation number as a descriptor that captures the deviations from Fourier's law due to hydrodynamic effects. We showcase these findings in a test case of a complex-shaped device made of graphite, obtaining a remarkable agreement with the very recent experimental demonstration of hydrodynamic transport in this material. The present findings also suggest that hydrodynamic behavior can appear at room temperature in micrometer-sized diamond crystals.

physics.comp-ph↗

arXiv2019

Unified theory of thermal transport in crystals and disordered solids

Crystals and glasses exhibit fundamentally different heat conduction mechanisms: the periodicity of crystals allows for the excitation of propagating vibrational waves that carry heat, as first discussed by Peierls; in glasses, the lack of periodicity breaks Peierls' picture and heat is mainly carried by the coupling of vibrational modes, often described by a harmonic theory introduced by Allen and Feldman. Anharmonicity or disorder are thus the limiting factors for thermal conductivity in crystals or glasses; hitherto, no transport equation has been able to account for both. Here, we derive such equation, resulting in a thermal conductivity that reduces to the Peierls and Allen-Feldman limits, respectively, in anharmonic-and-ordered or harmonic-and-disordered solids, while also covering the intermediate regimes where both effects are relevant. This approach also solves the long-standing problem of accurately predicting the thermal properties of crystals with ultralow or glass-like thermal conductivity, as we show with an application to a thermoelectric material representative of this class.

cond-mat.mtrl-sci↗