Observation of second sound in graphite at temperatures above 100 K

Modeling heat conduction with dual-dissipative variables: A mechanism-data fusion method

Many macroscopic non-Fourier heat conduction models have been developed in the past decades based on Chapman-Enskog, Hermite, or other small perturbation expansion methods. These macroscopic models have achieved great success in capturing non-Fourier thermal behaviors in solid materials, but most of them are limited by small Knudsen numbers and incapable of capturing highly nonequilibrium or ballistic thermal transport. In this paper, we provide a different strategy for constructing macroscopic non-Fourier heat conduction modeling, that is, using data-driven deep-learning methods combined with nonequilibrium thermodynamics instead of small perturbation expansion. We present the mechanism-data fusion method, an approach that seamlessly integrates the rigorous framework of conservation-dissipation formalism (CDF) with the flexibility of machine learning to model non-Fourier heat conduction. Leveraging the conservation-dissipation principle with dual-dissipative variables, we derive an interpretable series of partial differential equations, fine tuned through a training strategy informed by data from the phonon Boltzmann transport equation. Moreover, we also present the inner-step operation to narrow the gap from the discrete form to the continuous system. Through numerical tests, our model demonstrates excellent predictive capabilities across various heat conduction regimes, including diffusive, hydrodynamic, and ballistic regimes, and displays its robustness and precision even with discontinuous initial conditions.

Electron Drag Effect on Thermal Conductivity in Two-Dimensional Semiconductors

Two-dimensional (2D) materials have shown great potential in applications as transistors, where thermal dissipation becomes crucial because of the increasing energy density. Although the thermal conductivity of 2D materials has been extensively studied, interactions between nonequilibrium electrons and phonons, which can be strong when high electric fields and heat current coexist, are not considered. In this work, we systematically study the electron drag effect, where nonequilibrium electrons impart momenta to phonons and influence the thermal conductivity, in 2D semiconductors using ab initio simulations. We find that, at room temperature, electron drag can significantly increase thermal conductivity by decreasing phonon-electron scattering in 2D semiconductors while its impact in three-dimensional semiconductors is negligible. We attribute this difference to the large electron-phonon scattering phase space and larger contribution to thermal conductivity by drag-active phonons. Our work elucidates the fundamental physics underlying coupled electron-phonon transport in materials of various dimensionalities.

Quasiballistic thermal transport in submicron-scale graphene nanoribbons at room-temperature

Phonon transport in two-dimensional materials has been the subject of intensive studies both theoretically and experimentally. Recently observed unique phenomena such as Poiseuille flow at low temperature in graphene nanoribbons (GNRs) initiated strong interest in similar effects at higher temperatures. Here, we carry out massive molecular dynamics simulations to examine thermal transport in GNRs at room temperature (RT) and demonstrate that non-diffusive behaviors including Poiseuille-like local thermal conductivity and second sound are obtained, indicating quasiballistic thermal transport. For narrow GNRs, a Poiseuille-like thermal conductivity profile develops across the nanoribbon width, and wider GNRs exhibit a mixed nature of phonon transport in that diffusive transport is dominant in the middle region whereas non-uniform behavior is observed near lateral GNR boundaries. In addition, transient heating simulations reveal that the driftless second sound can propagate through GNRs regardless of the GNR width. By decomposing the atomic motion into out-of-plane and in-plane modes, it is further shown that the observed quasiballistic thermal transport is primarily contributed by the out-of-plane motion of C atoms in GNRs.

Thermal conduction force under standing and quasistanding temperature field

Thermal conduction force plays a crucial role in manipulating the local thermal conductivity of crystals. However, due to the diffusive nature of thermal conduction, investigating the force effect is challenging. Recently, researchers have explored the force effect based on the wavelike behavior of thermal conduction, specifically second sound. However, their focus has been primarily on the progressive case, neglecting the more complex standing temperature field case. Additionally, establishing a connection between the results obtained from the progressive case and the standing case poses a challenging problem. In this study, we investigate the force effect of standing and quasistanding temperature fields, revealing distinct characteristics of thermal conduction force. Moreover, we establish a link between the progressive and standing cases through the quasistanding case. Our findings pave the way for research in more intricate scenarios and provide an additional degree of freedom for manipulating the local thermal conductivity of dielectric crystals.

Exceptions to Fourier's Law at the Macroscale

The usual basis to analyze heat transfer within materials is the equation formulated 200 years ago, Fourier's law, which is identical mathematically to the mass diffusion equation, Fick's law. Revisiting this assumption regarding heat transport within translucent materials, performing the experiments in vacuum to avoid air convection, we compare the model predictions to infrared-based measurements with nearly mK temperature resolution. After heat pulses, we find macroscale non-Gaussian tails in the surface temperature profile. At steady state, we find macroscale anomalous hot spots when the sample is topographically rough, and this is validated by using two additional independent methods to measure surface temperature. These discrepancies from Fourier's law for translucent materials suggest that internal radiation whose mean-free-path is millimeters interacts with defects to produce small heat sources that by secondary emission afford an additional, non-local mode of heat transport. For these polymer and inorganic glass materials, this suggests unique strategies of heat management design.

Ab initioinvestigation of the lattice dynamics and thermophysical properties of BCC vanadium and niobium

In the present work, we have performed the phonon dispersion calculations of body-centered cubic vanadium (V) and niobium (Nb) with the supercell approach using different supercell size. Using DFT method, the calculated phonon spectra of V and Nb are found to be in a good agreement with the available experimental data. Our calculated results show a 'dip'-like feature in the longitudinal acoustic phonon mode along the Γ-H high symmetric path for both transition metals in the case of supercell size4×4×4. However, in supercell size2×2×2and3×3×3, the 'dip'-like feature is not clearly visible. In addition to this, thermodynamical properties are also computed, which compare well with the experimental data. Apart from this, the phonon lifetime due to electron-phonon interactions (τephph) and phonon-phonon interactions (PPIs) (τphph) are calculated. The effect of PPIs is studied by computing the average phonon lifetime for all acoustic branches. The value ofτephphof V (Nb) is found to be 23.16 (24.70)×10-15s at 100 K, which gets decreased to 1.51 (1.85)×10-15s at 1000 K. Theτphphof V (Nb) is found to be 8.59 (18.09)×10-12and 0.83 (1.76)×10-12s at 100 and 1000 K, respectively. Nextly, the lattice thermal conductivity is computed using linearized phonon Boltzmann equation. The present work suggests that studying the variation of phonon dispersion with supercell size is crucial for understanding the phonon properties of solids accurately.

Tunable thermal conduction force without macroscopic temperature gradients

Ubiquitous thermal conduction makes its force effect particularly important in diverse fields, such as electronic engineering and biochemistry. However, regulating thermal conduction force is still challenging due to two stringent restrictions. First, a temperature gradient is essential for inducing the force effect. Second, the force direction is fixed to the temperature gradient in a specific material. Here, we demonstrate that thermal conduction force can exist unexpectedly at a zero average temperature gradient in dielectric crystals. The wavelike feature of thermal conduction is considered, i.e., the second sound mode. Based on the momentum conservation law for phonon gases, we analyze thermal conduction force with the plane, zeroth-order Bessel, and first-order Bessel second sounds. Remarkably, the force direction is highly tunable to be along or against the second sound direction. These results provide valuable insights into thermal conduction force in those environments with temperature fluctuations, and they open up possibilities for practical applications in manipulating the local thermal conductivity of crystals.

Phonon Hydrodynamic Transport: Observation of Thermal Wave-Like Flow and Second Sound Propagation in Graphene at 100 K

Several experimental and theoretical investigations confirm the failure of the classical Fourier's law in low-dimensional systems and ultrafast thermal transport. Hydrodynamic heat transport has been recently considered as a promising avenue to thermal management and phonon engineering in graphitic materials. Non-Fourier features are therefore required to describe and distinguish the hydrodynamic regime from other heat transport regimes. In this work, we provide an efficient framework for the identification of hydrodynamic heat transport and second sound propagation in graphene at 80 and 100 K. We solve both the dual-phase-lag model and the Maxwell-Cattaneo-Vernotte equation based on the finite element method with ab initio data as inputs. We emphasize on the detection of thermal wave-like behavior using macroscopic quantities including the Knudsen number and second sound velocity beyond Fourier's law. We present a clear observation of the crossover phenomena from the wave-like regime to diffusive heat transport predicted in terms of mesoscopic equations. This present formalism will contribute to a clear and deeper understanding of hydrodynamic heat transport in condensed systems for future experimental detection of second sound propagation above 80 K.

Super-Ballistic Width Dependence of Thermal Conductivity in Graphite Nanoribbons and Microribbons

The super-ballistic temperature dependence of thermal conductivity, facilitated by collective phonons, has been widely studied. It has been claimed to be unambiguous evidence for hydrodynamic phonon transport in solids. Alternatively, hydrodynamic thermal conduction is predicted to be as strongly dependent on the width of the structure as is fluid flow, while its direct demonstration remains an unexplored challenge. In this work, we experimentally measured thermal conductivity in several graphite ribbon structures with different widths, from 300 nm to 1.2 µm, and studied its width dependence in a wide temperature range of 10-300 K. We observed enhanced width dependence of the thermal conductivity in the hydrodynamic window of 75 K compared to that in the ballistic limit, which provides indispensable evidence for phonon hydrodynamic transport from the perspective of peculiar width dependence. This will help to find the missing piece to complete the puzzle of phonon hydrodynamics, and guide future attempts at efficient heat dissipation in advanced electronic devices.

Motion of localized disturbances in scalar harmonic lattices

We present analytical and numerical investigations of energy propagation in systems of massive particles that interact via harmonic (linear) forces. The particle motion is described by a scalar displacement, and the particles are arranged in a simple crystal lattice. For the systems under consideration we prove the conservation of the total energy flux analytically. Then, using a sample case of a square lattice, we confirm the analytical results numerically. We create disturbances of a special kind which can move with a predefined velocity with a minor change in their shape. We show that a clot of energy, associated with each disturbance, moves similarly to a free body of matter in classical mechanics. We also numerically study a simultaneous propagation of a number of energy clots as an analogy to the motion of point masses in the conventional mechanics of particles. The obtained results demonstrate that an energy flow in lattices can be described in terms of numerous separated energy bodies, making a step towards a linkage between lattice dynamics and the kinetic theory of heat transfer in solids.

Tunable electron-flexural phonon interaction in graphene heterostructures

Peculiar electron-phonon interaction characteristics underpin the ultrahigh mobility1, electron hydrodynamics2-4, superconductivity5 and superfluidity6,7 observed in graphene heterostructures. The Lorenz ratio between the electronic thermal conductivity and the product of the electrical conductivity and temperature provides insight into electron-phonon interactions that is inaccessible to past graphene measurements. Here we show an unusual Lorenz ratio peak in degenerate graphene near 60 kelvin and decreased peak magnitude with increased mobility. When combined with ab initio calculations of the many-body electron-phonon self-energy and analytical models, this experimental observation reveals that broken reflection symmetry in graphene heterostructures can relax a restrictive selection rule8,9 to allow quasielastic electron coupling with an odd number of flexural phonons, contributing to the increase of the Lorenz ratio towards the Sommerfeld limit at an intermediate temperature sandwiched between the low-temperature hydrodynamic regime and the inelastic electron-phonon scattering regime above 120 kelvin. In contrast to past practices of neglecting the contributions of flexural phonons to transport in two-dimensional materials, this work suggests that tunable electron-flexural phonon couping can provide a handle to control quantum matter at the atomic scale, such as in magic-angle twisted bilayer graphene10 where low-energy excitations may mediate Cooper pairing of flat-band electrons11,12.

Observation of phonon Poiseuille flow in isotopically purified graphite ribbons

In recent times, the unique collective transport physics of phonon hydrodynamics motivates theoreticians and experimentalists to explore it in micro- and nanoscale and at elevated temperatures. Graphitic materials have been predicted to facilitate hydrodynamic heat transport with their intrinsically strong normal scattering. However, owing to the experimental difficulties and vague theoretical understanding, the observation of phonon Poiseuille flow in graphitic systems remains challenging. In this study, based on a microscale experimental platform and the pertinent occurrence criterion in anisotropic solids, we demonstrate the existence of the phonon Poiseuille flow in a 5.5 μm-wide, suspended and isotopically purified graphite ribbon up to a temperature of 90 K. Our observation is well supported by our theoretical model based on a kinetic theory with fully first-principles inputs. Thus, this study paves the way for deeper insight into phonon hydrodynamics and cutting-edge heat manipulating applications.

Panoramic Mapping of Phonon Transport from Ultrafast Electron Diffraction and Scientific Machine Learning

One central challenge in understanding phonon thermal transport is a lack of experimental tools to investigate frequency-resolved phonon transport. Although recent advances in computation lead to frequency-resolved information, it is hindered by unknown defects in bulk regions and at interfaces. Here, a framework that can uncover microscopic phonon transport information in heterostructures is presented, integrating state-of-the-art ultrafast electron diffraction (UED) with advanced scientific machine learning (SciML). Taking advantage of the dual temporal and reciprocal-space resolution in UED, and the ability of SciML to solve inverse problems involving O ( 10 3 ) $\mathcal{O}({10^3})$ coupled Boltzmann transport equations, the frequency-dependent interfacial transmittance and frequency-dependent relaxation times of the heterostructure from the diffraction patterns are reliably recovered. The framework is applied to experimental Au/Si UED data, and a transport pattern beyond the diffuse mismatch model is revealed, which further enables a direct reconstruction of real-space, real-time, frequency-resolved phonon dynamics across the interface. The work provides a new pathway to probe interfacial phonon transport mechanisms with unprecedented details.

Design and fabrication of diffraction grating with optimized efficiency for transient grating spectroscopy

Transient grating spectroscopy (TGS) based on diffraction gratings is a powerful optical method for studying the transport of energy carriers such as phonons and electrons. The diffraction grating in a TGS system is a key component to form a large-area interference pattern, i.e., transient grating, and to study the mean free path distribution of energy carriers. In this work, a design method for polarization-insensitive diffraction gratings with periods in the range 2-50 µm for TGS by a combination of rigorous coupled wave analysis and genetic algorithm was discussed. The method was tested for pump/probe wavelength of 515/532 or 1030/808 nm. Each ±1st diffraction order carries 35%-40% of the incident energy and the diffraction efficiencies of the other orders are lower than 10%. The optimized diffraction gratings were fabricated by a combination of photolithography and inductively coupled plasma etching, with the processing parameters introduced in detail, and their optical characteristics were evaluated. Finally, as a demonstration, the diffraction gratings for 1030/808 nm were applied to TGS to study the thermal transport properties of Ge. This work provides a useful guide for future applications and the development of TGS.

Anomalous conduction in one-dimensional particle lattices: Wave-turbulence approach

One-dimensional particle chains are fundamental models to explain anomalous thermal conduction in low-dimensional solids such as nanotubes and nanowires. In these systems the thermal energy is carried by phonons, i.e., propagating lattice oscillations that interact via nonlinear resonance. The average energy transfer between the phonons can be described by the wave kinetic equation, derived directly from the microscopic dynamics. Here we use the spatially nonhomogeneous wave kinetic equation of the prototypical β-Fermi-Pasta-Ulam-Tsingou model, to study thermal conduction in one-dimensional particle chains on a mesoscale description. By means of numerical simulations, we study two complementary aspects of thermal conduction: in the presence of thermostats setting different temperatures at the two ends and propagation of a temperature perturbation over an equilibrium background. Our main findings are as follows. (i) The anomalous scaling of the conductivity with the system size, in close agreement with the known results from the microscopic dynamics, is due to a nontrivial interplay between high and low wave numbers. (ii) The high-wave-number phonons relax to local thermodynamic equilibrium transporting energy diffusively, in the manner of Fourier. (iii) The low-wave-number phonons are nearly noninteracting and transfer energy ballistically. These results present perspectives for the applicability of the full nonhomogeneous wave kinetic equation to study thermal propagation.

High ambipolar mobility in cubic boron arsenide

Semiconductors with high thermal conductivity and electron-hole mobility are of great importance for electronic and photonic devices as well as for fundamental studies. Among the ultrahigh-thermal conductivity materials, cubic boron arsenide (c-BAs) is predicted to exhibit simultaneously high electron and hole mobilities of >1000 centimeters squared per volt per second. Using the optical transient grating technique, we experimentally measured thermal conductivity of 1200 watts per meter per kelvin and ambipolar mobility of 1600 centimeters squared per volt per second at the same locations on c-BAs samples at room temperature despite spatial variations. Ab initio calculations show that lowering ionized and neutral impurity concentrations is key to achieving high mobility and high thermal conductivity, respectively. The high ambipolar mobilities combined with the ultrahigh thermal conductivity make c-BAs a promising candidate for next-generation electronics.

Nonmonotonic heat dissipation phenomenon in close-packed hotspot systems

Transient heat dissipation in close-packed quasi-two-dimensional nanoline and three-dimensional nanocuboid hotspot systems is studied based on the phonon Boltzmann transport equation. It is found that, counterintuitively, the heat dissipation efficiency is not a monotonic function of the distance between adjacent nanoscale heat sources but reaches the highest value when this distance is comparable to the phonon mean free path. This is due to the competition of two thermal transport processes: quasiballistic transport when phonons escape from the nanoscale heat source and the scattering among phonons originating from the adjacent nanoscale heat source.

Heat Transport on Ultrashort Time and Space Scales in Nanosized Systems: Diffusive or Wave-like?

The non-Fourier effects, such as wave-like temperature propagation and boundary temperature jumps, arise in nanosized systems due to the multiple time and space scales nature of out-of-equilibrium heat transport. The relaxation to equilibrium occurs in successive time and space scales due to couplings between different excitations, whose relaxation times have different physical meanings and may differ significantly in magnitude. The out-of-equilibrium temperature evolution is described by a hierarchy of partial differential equations of a higher order, which includes both the diffusive and wave modes of heat transport. The critical conditions of transition from wave to diffusive modes are identified. We demonstrate that the answer to the question concerning which of these modes would be detected by experimental measurements may also depend on the accuracy of the experimental setup. Comparisons between the proposed approach and other non-Fourier models, such as the Guyer–Krumhansl and Jeffreys type, are carried out. The results presented here are expected to be useful for the theoretical and experimental treatment of non-Fourier effects and particularly heat wave phenomena in complex nanosized systems and metamaterials.

Phonon hydrodynamics in crystalline materials

Phonon hydrodynamics is an exotic phonon transport phenomenon that challenges the conventional understanding of diffusive phonon scattering in crystalline solids. It features a peculiar collective motion of phonons with various unconventional properties resembling fluid hydrodynamics, facilitating non Fourier heat transport. Hence, it opens up several new avenues to enrich the knowledge and implementations on phonon physics, phonon engineering, and micro and nanoelectronic device technologies. This review aims at covering a comprehensive development as well as the recent advancements in this field via experiments, analytical methods, and state-of-the-art numerical techniques. The evolution of the topic has been realized using both phenomenological and material science perspectives. Further, the discussions related to the factors that influence such peculiar motion, illustrate the capability of phonon hydrodynamics to be implemented in various applications. A plethora of new ideas can emerge from the topic considering both the physics and the material science axes, navigating toward a promising outlook in the research areas around phonon transport in non-metallic solids.

Unsteady two-temperature heat transport in mass-in-mass chains

We investigate the unsteady heat (energy) transport in an infinite mass-in-mass chain with a given initial temperature profile. The chain consists of two sublattices: the β-Fermi-Pasta-Ulam-Tsingou (FPUT) chain and oscillators (of a different mass) connected to each FPUT particle. Initial conditions are such that initial kinetic temperatures of the FPUT particles and the oscillators are equal. Using the harmonic theory, we analytically describe evolution of these two temperatures in the ballistic regime. In particular, we derive a closed-form fundamental solution and solution for a sinusoidal initial temperature profile in the case when the oscillators are significantly lighter than the FPUT particles. The harmonic theory predicts that during the heat transfer the temperatures of sublattices are significantly different, while initially and finally (at large times) they are equal. This may look like an artifact of the harmonic approximation, but we show that it is not the case. Two distinct temperatures are also observed in the anharmonic case, even when the heat transport regime is no longer quasiballistic. We show that the value of the nonlinearity coefficient required to equalize the temperatures strongly depends on the particle mass ratio. If the oscillators are much lighter than the FPUT particles, then a fairly strong nonlinearity is required for the equalization.

Unraveling Heat Transport and Dissipation in Suspended MoSe2 from Bulk to Monolayer

Understanding heat flow in layered transition metal dichalcogenide (TMD) crystals is crucial for applications exploiting these materials. Despite significant efforts, several basic thermal transport properties of TMDs are currently not well understood, in particular how transport is affected by material thickness and the material's environment. This combined experimental-theoretical study establishes a unifying physical picture of the intrinsic lattice thermal conductivity of the representative TMD MoSe₂ . Thermal conductivity measurements using Raman thermometry on a large set of clean, crystalline, suspended crystals with systematically varied thickness are combined with ab initio simulations with phonons at finite temperature. The results show that phonon dispersions and lifetimes change strongly with thickness, yet the thinnest TMD films exhibit an in-plane thermal conductivity that is only marginally smaller than that of bulk crystals. This is the result of compensating phonon contributions, in particular heat-carrying modes around ≈0.1 THz in (sub)nanometer thin films, with a surprisingly long mean free path of several micrometers. This behavior arises directly from the layered nature of the material. Furthermore, out-of-plane heat dissipation to air molecules is remarkably efficient, in particular for the thinnest crystals, increasing the apparent thermal conductivity of monolayer MoSe₂ by an order of magnitude. These results are crucial for the design of (flexible) TMD-based (opto-)electronic applications.

Unsteady ballistic heat transport in two-dimensional harmonic graphene lattice

We study the evolution of initial temperature profiles in a two-dimensional isolated harmonic graphene lattice. Two heat transfer problems are solved analytically and numerically. In the first problem, the evolution of a spatially sinusoidal initial temperature profile is considered. This profile is usually generated in real experiments based on the transient thermal grating technique. It is shown that at short times the amplitude of the profile decreases by an order magnitude and then it performs small decaying oscillations. A closed-form solution, describing the decay of the amplitude at short times is derived. It shows that due to symmetry of the lattice, the anisotropy of the ballistic heat transfer is negligible at short times, while at large times it is significant. In the second problem, a uniform spatial distribution of the initial temperature in a circle is specified. The profile is the simplest model of graphene heating by an ultrashort localized laser pulse. The corresponding solution has the symmetry of the lattice and many local maxima. Additionally, we show that each atom has two distinct temperatures corresponding to motions in zigzag and armchair directions. Presented results may serve for proper statement and interpretation of laboratory experiments and molecular dynamics simulations of unsteady heat transfer in graphene.

Observation of second sound in graphite over 200 K

Second sound refers to the phenomenon of heat propagation as temperature waves in the phonon hydrodynamic transport regime. We directly observe second sound in graphite at temperatures of over 200 K using a sub-picosecond transient grating technique. The experimentally determined dispersion relation of the thermal-wave velocity increases with decreasing grating period, consistent with first-principles-based solution of the Peierls-Boltzmann transport equation. Through simulation, we reveal this increase as a result of thermal zero sound-the thermal waves due to ballistic phonons. Our experimental findings are well explained with the interplay among three groups of phonons: ballistic, diffusive, and hydrodynamic phonons. Our ab initio calculations further predict a large isotope effect on the properties of thermal waves and the existence of second sound at room temperature in isotopically pure graphite.

Thermal dynamics and electronic temperature waves in layered correlated materials

Understanding the mechanism of heat transfer in nanoscale devices remains one of the greatest intellectual challenges in the field of thermal dynamics, by far the most relevant under an applicative standpoint. When thermal dynamics is confined to the nanoscale, the characteristic timescales become ultrafast, engendering the failure of the common description of energy propagation and paving the way to unconventional phenomena such as wave-like temperature propagation. Here, we explore layered strongly correlated materials as a platform to identify and control unconventional electronic heat transfer phenomena. We demonstrate that these systems can be tailored to sustain a wide spectrum of electronic heat transport regimes, ranging from ballistic, to hydrodynamic all the way to diffusive. Within the hydrodynamic regime, wave-like temperature oscillations are predicted up to room temperature. The interaction strength can be exploited as a knob to control the dynamics of temperature waves as well as the onset of different thermal transport regimes.

Phonon-engineered extreme thermal conductivity materials

Materials with ultrahigh or low thermal conductivity are desirable for many technological applications, such as thermal management of electronic and photonic devices, heat exchangers, energy converters and thermal insulation. Recent advances in simulation tools (first principles, the atomistic Green's function and molecular dynamics) and experimental techniques (pump-probe techniques and microfabricated platforms) have led to new insights on phonon transport and scattering in materials and the discovery of new thermal materials, and are enabling the engineering of phonons towards desired thermal properties. We review recent discoveries of both inorganic and organic materials with ultrahigh and low thermal conductivity, highlighting heat-conduction physics, strategies used to change thermal conductivity, and future directions to achieve extreme thermal conductivities in solid-state materials.

Transient Hydrodynamic Lattice Cooling by Picosecond Laser Irradiation of Graphite

Recent theories and experiments have suggested hydrodynamic phonon transport features in graphite at unusually high temperatures. Here, we report a picosecond pump-probe thermal reflectance measurement of heat-pulse propagation in graphite. The measurement results reveal transient lattice cooling near the adiabatic center of a 15-μm-diameter ring-shape pump beam at temperatures between 80 and 120 K. While such lattice cooling has not been reported in recent diffraction measurements of second sound in graphite, the observation here is consistent with both hydrodynamic phonon transport theory and prior heat-pulse measurements of second sound in bulk sodium fluoride.

Room temperature second sound in cumulene

Second sound is known as the thermal transport regime occurring in a wave-like fashion, usually identified in a limited number of materials only at cryogenic temperatures. Here we show that second sound in a μm-long carbon chain (cumulene) might occur even at room temperature. To this aim, we calibrate a many-body force field on the first principles calculated phonon dispersion relations of cumulene and, through molecular dynamics, we mimic laser-induced transient thermal grating experiments. We provide evidence that by tuning temperature as well as the space modulation of its initial profile we can reversibly drive the system from a wave-like to a diffusive-like thermal transport. By following three different theoretical methodologies (molecular dynamics, the Maxwell-Cattaneo-Vernotte equation, and heat transport microscopic theory) we estimate for cumulene a second sound velocity in the range of 2.4-3.2 km s-1.

Observation of second sound in a rapidly varying temperature field in Ge

Second sound is known as the thermal transport regime where heat is carried by temperature waves. Its experimental observation was previously restricted to a small number of materials, usually in rather narrow temperature windows. We show that it is possible to overcome these limitations by driving the system with a rapidly varying temperature field. High-frequency second sound is demonstrated in bulk natural Ge between 7 K and room temperature by studying the phase lag of the thermal response under a harmonic high-frequency external thermal excitation and addressing the relaxation time and the propagation velocity of the heat waves. These results provide a route to investigate the potential of wave-like heat transport in almost any material, opening opportunities to control heat through its oscillatory nature.

Hot carriers in graphene - fundamentals and applications

Hot charge carriers in graphene exhibit fascinating physical phenomena, whose understanding has improved greatly over the past decade. They have distinctly different physical properties compared to, for example, hot carriers in conventional metals. This is predominantly the result of graphene's linear energy-momentum dispersion, its phonon properties, its all-interface character, and the tunability of its carrier density down to very small values, and from electron- to hole-doping. Since a few years, we have witnessed an increasing interest in technological applications enabled by hot carriers in graphene. Of particular interest are optical and optoelectronic applications, where hot carriers are used to detect (photodetection), convert (nonlinear photonics), or emit (luminescence) light. Graphene-enabled systems in these application areas could find widespread use and have a disruptive impact, for example in the field of data communication, high-frequency electronics, and industrial quality control. The aim of this review is to provide an overview of the most relevant physics and working principles that are relevant for applications exploiting hot carriers in graphene.

Moiré Patterns in 2D Materials: A Review

Quantum materials have attracted much attention in recent years due to their exotic and incredible properties. Among them, van der Waals materials stand out due to their weak interlayer coupling, providing easy access to manipulating electrical and optical properties. Many fascinating electrical, optical, and magnetic properties have been reported in the moiré superlattices, such as unconventional superconductivity, photonic dispersion engineering, and ferromagnetism. In this review, we summarize the methods to prepare moiré superlattices in the van der Waals materials and focus on the current discoveries of moiré pattern-modified electrical properties, recent findings of atomic reconstruction, as well as some possible future directions in this field.

Thermal oscillations, second sound and thermal resonance in phonon hydrodynamics

Recent observation of second sound in graphite at a temperature above 100 K has aroused a great interest in the study of thermal waves in non-metallic solid materials. In this article, based on the Guyer–Krumhansl model, we investigate the second sound and thermal resonance phenomena in phonon hydrodynamics. The occurrence condition for the second sound is derived. It shows that the smaller the relaxation time of N-scattering of the non-metallic solid with a large relaxation time of R-scattering, the more likely the second sound will occur. For the phonon transport in the non-metallic solid excited by an oscillatory heat source with a single frequency, the occurrence condition for thermal resonance and a formula for calculating the external heat source frequency at resonance are also derived. It is found that the low-dimensional materials with small size are prone to the occurrence of second sound and thermal resonance. These phenomena open up new avenues for thermal management and energy conversion.

Temperonic Crystal: A Superlattice for Temperature Waves in Graphene

The temperonic crystal, a periodic structure with a unit cell made of two slabs sustaining temperature wavelike oscillations on short timescales, is introduced. The complex-valued dispersion relation for the temperature scalar field is investigated for the case of a localized temperature pulse. The dispersion discloses frequency gaps, tunable upon varying the slabs' thermal properties. Results are shown for the paradigmatic case of a graphene-based temperonic crystal. The temperonic crystal extends the concept of superlattices to the realm of temperature waves, allowing for coherent control of ultrafast temperature pulses in the hydrodynamic regime at above liquid nitrogen temperatures.

Time-Domain Investigations of Coherent Phonons in van der Waals Thin Films

Coherent phonons can be launched in materials upon localized pulsed optical excitation, and be subsequently followed in time-domain, with a sub-picosecond resolution, using a time-delayed pulsed probe. This technique yields characterization of mechanical, optical, and electronic properties at the nanoscale, and is taken advantage of for investigations in material science, physics, chemistry, and biology. Here we review the use of this experimental method applied to the emerging field of homo- and heterostructures of van der Waals materials. Their unique structure corresponding to non-covalently stacked atomically thin layers allows for the study of original structural configurations, down to one-atom-thin films free of interface defect. The generation and relaxation of coherent optical phonons, as well as propagative and resonant breathing acoustic phonons, are comprehensively discussed. This approach opens new avenues for the in situ characterization of these novel materials, the observation and modulation of exotic phenomena, and advances in the field of acoustics microscopy.

Generalized Cattaneo (telegrapher's) equations in modeling anomalous diffusion phenomena

We study generalized Cattaneo (telegrapher's) equations involving memory effects introduced by smearing the time derivatives. Consistency conditions where the smearing functions obey restrict freedom in their choice but the proposed scheme goes beyond the approach based on using fractional derivatives. We find conditions under which solutions of the equations considered so far can be recognized as probability distributions, i.e., are normalizable and nonnegative on their domains. Nonnegativity of solutions is demonstrated by methods of positive definite and completely monotonic functions with the Bernstein theorem being the cornerstone of the ongoing proofs. Analysis of exactly solvable examples and relevant mean-squared displacements enables us to classify diffusion processes described by such got solutions and to identify them with either ordinary or anomalous diffusion which character may change over time. To complete the present research we compare our results with those obtained using the continuous-time random-walk and the continuous-time persistent random-walk approaches.

Phononics of Graphene and Related Materials

In this Perspective, I present a concise account concerning the emergence of the research field investigating the phononic and thermal properties of graphene and related materials, covering the refinement of our understanding of phonon transport in two-dimensional material systems. The initial interest in graphene originated from its unique linear energy dispersion for electrons, revealed in exceptionally high electron mobility, and other exotic electronic and optical properties. Electrons are not the only elemental excitations influenced by a reduction in dimensionality. Phonons-quanta of crystal lattice vibrations-also demonstrate an extreme sensitivity to the number of atomic planes in the few-layer graphene, resulting in unusual heat conduction properties. I outline recent theoretical and experimental developments in the field and discuss how the prospects for the mainstream electronic application of graphene, enabled by its high electron mobility, gradually gave way to emerging real-life products based on few-layer graphene, which utilize its unique heat conduction rather than its electrical conduction properties.

Heat vortex in hydrodynamic phonon transport of two-dimensional materials

We study hydrodynamic phonon heat transport in two-dimensional (2D) materials. Starting from the Peierls-Boltzmann equation with the Callaway model approximation, we derive a 2D Guyer-Krumhansl-like equation describing hydrodynamic phonon transport, taking into account the quadratic dispersion of flexural phonons. In addition to Poiseuille flow, second sound propagation, the equation predicts heat current vortices and negative non-local thermal conductance in 2D materials, which are common in classical fluids but have not yet been considered in phonon transport. Our results also illustrate the universal transport behaviors of hydrodynamics, independent of the type of quasi-particles and their microscopic interactions.

Phonon hydrodynamics and ultrahigh-room-temperature thermal conductivity in thin graphite

Allotropes of carbon, such as diamond and graphene, are among the best conductors of heat. We monitored the evolution of thermal conductivity in thin graphite as a function of temperature and thickness and found an intimate link between high conductivity, thickness, and phonon hydrodynamics. The room-temperature in-plane thermal conductivity of 8.5-micrometer-thick graphite was 4300 watts per meter-kelvin-a value well above that for diamond and slightly larger than in isotopically purified graphene. Warming enhances thermal diffusivity across a wide temperature range, supporting partially hydrodynamic phonon flow. The enhancement of thermal conductivity that we observed with decreasing thickness points to a correlation between the out-of-plane momentum of phonons and the fraction of momentum-relaxing collisions. We argue that this is due to the extreme phonon dispersion anisotropy in graphite.

Thermal transport of carbon nanomaterials

The diversity of thermal transport properties in carbon nanomaterials enables them to be used in different thermal fields such as heat dissipation, thermal management, and thermoelectric conversion. In the past two decades, much effort has been devoted to study the thermal conductivities of different carbon nanomaterials. In this review, different theoretical methods and experimental techniques for investigating thermal transport in nanosystems are first summarized. Then, the thermal transport properties of various pure carbon nanomaterials including 1D carbon nanotubes, 2D graphene, 3D carbon foam, are reviewed in details and the associated underlying physical mechanisms are presented. Meanwhile, we discuss several important influences on the thermal conductivities of carbon nanomaterials, including size, structural defects, chemisorption and strain. Moreover, we introduce different nanostructuring pathways to manipulate the thermal conductivities of carbon-based nanocomposites and focus on the wave nature of phonons for controlling thermal transport. At last, we briefly review the potential applications of carbon nanomaterials in the fields of thermal devices and thermoelectric conversion.

Ballistic resonance and thermalization in the Fermi-Pasta-Ulam-Tsingou chain at finite temperature

We study conversion of thermal energy to mechanical energy and vice versa in an α-Fermi-Pasta-Ulam-Tsingou (FPUT) chain with a spatially sinusoidal profile of initial temperature. We show analytically that coupling between macroscopic dynamics and quasiballistic heat transport gives rise to mechanical vibrations with growing amplitude. This phenomenon is referred to as ballistic resonance. At large times, these mechanical vibrations decay monotonically, and therefore the well-known FPUT recurrence paradox occurring at zero temperature is eliminated at finite temperatures.

Thermomass Theory in the Framework of GENERIC

Thermomass theory was developed to deal with the non-Fourier heat conduction phenomena involving the influence of heat inertia. However, its structure, derived from an analogy to fluid mechanics, requires further mathematical verification. In this paper, General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) framework, which is a geometrical and mathematical structure in nonequilibrium thermodynamics, was employed to verify the thermomass theory. At first, the thermomass theory was introduced briefly; then, the GENERIC framework was applied in the thermomass gas system with state variables, thermomass gas density ρ_h and thermomass momentum m_h, and the time evolution equations obtained from GENERIC framework were compared with those in thermomass theory. It was demonstrated that the equations generated by GENERIC theory were the same as the continuity and momentum equations in thermomass theory with proper potentials and eta-function. Thermomass theory gives a physical interpretation to the GENERIC theory in non-Fourier heat conduction phenomena. By combining these two theories, it was found that the Hamiltonian energy in reversible process and the dissipation potential in irreversible process could be unified into one formulation, i.e., the thermomass energy. Furthermore, via the framework of GENERIC, thermomass theory could be extended to involve more state variables, such as internal source term and distortion matrix term. Numerical simulations investigated the influences of the convective term and distortion matrix term in the equations. It was found that the convective term changed the shape of thermal energy distribution and enhanced the spreading behaviors of thermal energy. The distortion matrix implies the elasticity and viscosity of the thermomass gas.

Spherically Restricted Random Hyperbolic Diffusion

This paper investigates solutions of hyperbolic diffusion equations in R3 with random initial conditions. The solutions are given as spatial-temporal random fields. Their restrictions to the unit sphere S2 are studied. All assumptions are formulated in terms of the angular power spectrum or the spectral measure of the random initial conditions. Approximations to the exact solutions are given. Upper bounds for the mean-square convergence rates of the approximation fields are obtained. The smoothness properties of the exact solution and its approximation are also investigated. It is demonstrated that the Hölder-type continuity of the solution depends on the decay of the angular power spectrum. Conditions on the spectral measure of initial conditions that guarantee short- or long-range dependence of the solutions are given. Numerical studies are presented to verify the theoretical findings.

Equilibration of energies in a two-dimensional harmonic graphene lattice

We study dynamical phenomena in a harmonic graphene (honeycomb) lattice, consisting of equal particles connected by linear and angular springs. Equations of in-plane motion for the lattice are derived. Initial conditions typical for molecular dynamic modelling are considered. Particles have random initial velocities and zero displacements. In this case, the lattice is far from thermal equilibrium. In particular, initial kinetic and potential energies are not equal. Moreover, initial kinetic energies (and temperatures), corresponding to degrees of freedom of the unit cell, are generally different. The motion of particles leads to equilibration of kinetic and potential energies and redistribution of kinetic energy among degrees of freedom. During equilibration, the kinetic energy performs decaying high-frequency oscillations. We show that these oscillations are accurately described by an integral depending on dispersion relation and polarization matrix of the lattice. At large times, kinetic and potential energies tend to equal values. Kinetic energy is partially redistributed among degrees of freedom of the unit cell. Equilibrium distribution of the kinetic energies is accurately predicted by the non-equipartition theorem. Presented results may serve for better understanding of the approach to thermal equilibrium in graphene. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 2)'.

Temperature wave-like oscillations on ultra-short and ultra-fast time scales -INVITED

Recent findings in the frame of temperature wave-like oscillations on the ultra-short, ultra-fast time scales in solid states devices are here reviewed. The possibility for wave-like temperature oscillations are investigated at the light of the pass-band characteristic in w-k space for the temperature scalar field. The bandpass filter characteristics are accessed in terms of the heat carriers scattering times. The concepts here reviewed are of interest for perspective design of novel thermal nano-devices.