Extreme longitudinal thermal conductivity and non-diffusive heat transport in isotopic hBN.

Two-dimensional materials, such as graphene, boron nitride and transition metal dichalcogenides, have attracted increased interest due to their potential applications in electronics and optoelectronics. Thermal transport in two-dimensional materials could be quite different from three-dimensional bulk materials. This article reviews the progress on experimental measurements and theoretical modeling of phonon transport and thermal conductivity in two-dimensional materials. We focus our review on a few typical two-dimensional materials, including graphene, boron nitride, silicene, transition metal dichalcogenides, and black phosphorus. The effects of different physical factors, such as sample size, strain and defects, on thermal transport in Two-dimensional materials are summarized. We also discuss the environmental effect on the thermal transport of two-dimensional materials, such as substrate and when two-dimensional materials are presented in heterostructures and intercalated with inorganic components or organic molecules.

Deviations from Fourier's law emerge from numerical simulations of various lattices modelling solids. Non-integrability and moreover chaotic motion are considered to be conditions of normal heat conduction. However, these are not sufficient conditions. Using a simple model as an example, we show that non-diffusive transport could occur even in the presence of disorder in the lattice and completely chaotic dynamics. We conclude that diffusive and non-diffusive transport can coexist, while the system is moving along a chaotic trajectory in the phase space.

Thermal transport in two-dimensional (2D) materials has attracted great attention since the discovery of high thermal conductivity in graphene, which is closely related to the hydrodynamic phonon transport. In this Perspective, we briefly summarize the recent progresses in studying hydrodynamic phonon transport in 2D materials, including both theoretical and experimental works. First, the criterion and numerical methods for studying hydrodynamic phonon transport are reviewed. We then discuss the physical mechanism and peculiar phenomena related to hydrodynamic phonon transport in 2D materials and finally present the challenge for future studies. This Perspective aims to provide the physical understanding of the hydrodynamic phonon transport, which might be beneficial to the exploration of novel thermal transport behaviors in 2D materials.

The single mode relaxation time approximation has been demonstrated to greatly underestimate the lattice thermal conductivity of two-dimensional materials due to the collective effect of phonon normal scattering. Callaway's dual relaxation model represents a good approximation to the otherwise ab initio solution of the phonon Boltzmann equation. In this work we develop a discrete-ordinate-method (DOM) scheme for the numerical solution of the phonon Boltzmann equation under Callaway's model. Heat transport in a graphene ribbon with different geometries is modeled by our scheme, which produces results quite consistent with the available molecular dynamics, Monte Carlo simulations, and experimental measurements. Callaway's lattice thermal conductivity model with empirical boundary scattering rates is examined and shown to overestimate or underestimate the direct DOM solution. The length convergence of the lattice thermal conductivity of a rectangular graphene ribbon is explored and found to depend appreciably on the ribbon width, with a semiquantitative correlation provided between the convergence length and the width. Finally, we predict the existence of a phonon Knudsen minimum in a graphene ribbon only at a low system temperature and isotope concentration so that the average normal scattering rate is two orders of magnitude stronger than the intrinsic resistive one. The present work will promote not only the methodology for the solution of the phonon Boltzmann equation but also the theoretical modeling and experimental detection of hydrodynamic phonon transport in two-dimensional materials.

The approach of solving the Boltzmann transport equation (BTE) is widely used to evaluate the thermal conductivity and screen low thermal conductivity materials for thermoelectric applications, where phonon transport is approximated as particlelike propagation. Phonon transport through a wavelike tunneling channel, as described by the Wigner transport equation (WTE), will have a notable effect in some two-dimensional (2D) materials due to the parabolic out-of-plane acoustic modes and lower phonon energy, which is usually neglected, inducing an underestimation of thermal conductivity. Here, we investigate the phonon transport of four representative 2D structures by the WTE approach. Both the low-symmetry unit cell with heavy atoms and the strong anharmonicity will lead to a higher contribution from the tunneling channel. The total lattice thermal conductivity of low-symmetry KAgSe is only 0.34 ${\mathrm{W}\phantom{\rule{0.16em}{0ex}}\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ at 800 K, of which 26% is contributed by the wavelike tunneling. The strong lattice anharmonicity of 2D InSe with lone-pair electrons induces wide phonon linewidths for both acoustic and optical phonon modes, suppressing the conductivity through particlelike propagation channel. The coherence conductivity through wavelike tunneling accounts for 58% of the total one at 800 K. Our work helps to gain a better understanding of the dual-channel phonon transport in complex 2D structures. The strong anharmonic acoustic modes are crucial to achieve ultralow lattice thermal conductivity.

As the size of electric and optoelectronic devices is reduced to nanoscale, self-heating becomes a major reliability concern. Leveraging designs that could intrinsically remove or reduce the heat and in turn decrease temperature is desirable. In this work, twin nanoscale heater lines with four-probe electrical measurement combined with full-field thermal imaging are used to elucidate the departure from Fourier Law. Thermoreflectance thermal imaging is employed to obtain temperature distribution of twin nanoheater lines where one is a heat source and the second one is a thermometer. The temperature change, due to Joule heating, on the heater line as well as the temperature profile on the thermometer line 0.3–0.5gm away, is measured by thermoreflectance imaging. The average temperature change of the heater lines is also measured independently using temperature-dependent electrical resistivity. Experimental results suggest that the modified Fourier theory ceases to explain the thermal distribution of submicron size heat sources. As the width of heat sources decreases, the temperature of the heater lines exceeds predictions of Fourier equation while the temperature on the thermometer line is significantly lower than the Fourier prediction. This could potentially be beneficial in the design of compact multi-finger high power transistor structures.

Electron transport in ultraclean two-dimensional materials has received much attention. However, the sign of the magnetoresistance effect in various electron flow regimes remains controversial. In this work, the complete electron Boltzmann transport equation is numerically solved with the discrete ordinate method in the real space to clarify the condition of the negative magnetoresistance effect under a weak magnetic field. It turns out from the numerical results that this effect occurs only within the ballistic regime under a low electric field rather than the hydrodynamic regime. It is noteworthy that the existence of momentum-conserving scattering dramatically reverses the sign of magnetoresistance in the ballistic regime. When the electric field becomes strong enough compared to the magnetic field, its effect on the deflection of the electrons is not negligible and will lead to positive magnetoresistance in the whole parameter domain. The possible influence of boundary conditions and internal electric field models on the sign of magnetoresistance is also discussed. Our work provides insight into electron fluid transport under electromagnetic fields.

Graphene exhibits extraordinary electronic and mechanical properties, and extremely high thermal conductivity. Being a very stable atomically thick membrane that can be suspended between two leads, graphene provides a perfect test platform for studying thermal conductivity in two-dimensional systems, which is of primary importance for phonon transport in low-dimensional materials. Here we report experimental measurements and non-equilibrium molecular dynamics simulations of thermal conduction in suspended single-layer graphene as a function of both temperature and sample length. Interestingly and in contrast to bulk materials, at 300 K, thermal conductivity keeps increasing and remains logarithmically divergent with sample length even for sample lengths much larger than the average phonon mean free path. This result is a consequence of the two-dimensional nature of phonons in graphene, and provides fundamental understanding of thermal transport in two-dimensional materials.

Interlayer twisting provides a powerful geometric means to manipulate phonon-mediated heat transport in two-dimensional materials. However, its role under realistic substrate-supported conditions remains poorly understood. Here, we investigate thermal transport in twisted multilayer graphene by combining the neuroevolution potential (NEP) machine-learning framework with the homogeneous nonequilibrium molecular dynamics (HNEMD) method. The simulations reveal that interlayer twist strongly suppresses the contribution of out-of-plane phonons to thermal conductivity, with the suppression concentrated in the low-frequency regime below ~15 THz. This behavior originates from moiré-induced modulation of interlayer coupling, which enhances out-of-plane phonon scattering and disrupts long-wavelength coherence. Remarkably, the suppression persists even in the presence of substrate coupling, where out-of-plane phonons are already significantly damped. As a result, supported twisted graphene approaches its suspended thermal conductivity more rapidly with increasing layer number than untwisted counterparts. These findings elucidate the microscopic mechanism of twist–substrate interplay and establish interlayer twist as an effective structural degree of freedom for controlling phonon transport in van der Waals layered materials.

Thermal transport in graphene

Advanced materials for heat energy transfer, conversion, storage and utilization, are very much at the forefront of academic and industrial interest. Within this context, we are delighted to provide cutting-edge insight into the emerging materials that promote the utilization of heat energy, via a special issue with a selection of 19 review and original research articles. These papers summarize the recent advances in thermoelectric materials, phononic metamaterials, thermal interfacial materials, nanomaterials, and the applications in thermal management and renewable energy. Thermoelectric materials are important for renewable energy technology. The thermoelectric performance is determined by the Seebeck coefficient, electrical conductivity, and thermal conductivity. The strong interaction between the different heat carriers, including phonons and electrons, complicates the optimization of thermoelectric efficiency. Yu et al. (article number 1904862) contribute a review paper that helps us understand the outstanding thermoelectric performance of main-group chalcogenides from a chemical bonding perspective. It is suggested that large valley degeneracy, band convergence, and high band anisotropy can result in high power factors. Moreover, compared to covalent and ionic bonds, the bonds in main-group chalcogenides are soft, causing large anharmonicity and low thermal conductivity. Zhao et al. (article number 1903867) present the recent advances in the structure and properties of liquid-like thermoelectrics, focusing on their unusual electron and phonon transport behaviors. Commonly adopted strategies for further improving the thermoelectric properties are also summarized. In addition to inorganic thermoelectric materials, bio-friendly organic thermoelectric materials are becoming promising candidates for thermoelectric devices. Zeng et al. (article number 1903873) introduce important advances in the experimental and theoretical studies of organic thermoelectric materials, including molecular junctions, organic-inorganic heterojunctions, and single-molecule magnet. Various optimization strategies for organic thermoelectric devices are discussed. In an independent review article, Wang et al. (article number 1904534) provide a survey of recent advances and emerging experimental and theoretical methodologies in probing and tuning thermal and thermoelectric transport in molecular junctions. Amorphous materials have valuable applications in thermoelectrics, thermal protection, flexible electronics, and artificial intelligence chips. Zhou et al. (article number 1903829) systematically review the fundamental physical aspects of thermal conductivity in amorphous materials and discussed a number of open problems. Shin et al. (article number 1904815) review the state-of-the-art of high temperature thermal materials used in thermal barrier coating, including dense materials and porous materials. In addition to a comprehensive list of high temperature thermal materials, the unique mechanisms governing thermal transport processes at high temperatures are also elucidated. Composites based on phase change materials have received tremendous attention due to their application in thermal energy storage and management. Yuan et al. (article number 1904228) systematically introduce the methods to manipulate the thermal conductivity of phase change materials. Considering the importance of conductive polymers and their composites in smart devices such as touch screen displays, health monitoring sensors, and functional clothing, Xu et al. (article number 1904704) provide a comprehensive summary of the thermal properties of conductive polymers. The fundamental thermal transport mechanisms, up-to-date advancements in regulating their thermal conductivity and thermal-related applications are addressed. The technology of phononic crystal provides a strategy for controlling the thermal conductivity of solids, with applications in new information technology, thermal management, and thermoelectrics. Sledzinska et al. (article number 1904434) provide a systematic review of the recent experimental achievements in the fabrication of phononic crystals and their applications in thermal management. Hussein et al. (article number 1906718) introduce the new emerging concept of nanophononic metamaterials, and provide a comprehensive comparison with nanophononic crystals. Although thermal conductivity reduction can be achieved in both, the underlying mechanism is different. Graphene has ultrahigh thermal conductivity, which is expected to be utilized in the thermal management of nanoscale electronic devices. More interesting, by coupling different physical quantities, graphene is also demonstrated in other applications, such as thermoacoustic coupling devices, thermoelectric coupling devices, and thermooptical coupling devices. Li et al. (article number 1903888) provide a review of the recent progress in graphene-based thermal devices. Although graphene has attracted a lot of attention in thermal management owing to its ultrahigh thermal conductivity, the thermal conductivity of graphene-based composites still needs to be improved. Barani et al. (article number 1904008) demonstrate remarkable enhancement in the thermal conductivity of the epoxy-based hybrid composites with graphene and Cu-NP fillers, whose effect is attributed to the formation of highly thermally conductive percolation networks. On the other hand, with the number of interfaces increasing, interfacial thermal resistance is becoming even more important than the channel material itself. Giri and Hopkins (article number 1903857) summarize the recent experimental and computational advances in thermal transport across solid/solid interfaces. The role of localized vibrational modes is also clarified. Meng and Wang (article number 1904796) introduce the development of antiscaling interfacial materials towards highly efficient heat energy transfer and discuss the various effects on thermal conductivity such as surface energy, surface roughness, and surface wettability. Since the first discovery of graphene, two dimensional (2D) materials opened up numerous competitive applications because of their unique and highly tunable physical and chemical properties. Zhao et al. (article number 1903929) provide a thorough understanding of the thermal transport properties of various 2D semiconductors, including transition metal dichalcogenides, black phosphorus, and SnSe. The phonon-governed applications, including thermoelectric power generation and photoelectric and thermal devices, are also addressed. The thermal properties of borophene are summarized by Li et al. (article number 1904349). Zhan et al. (article number 1903841) summarize the thermal properties of different 3D nanostructures ranging from 3D nanoarchitectures to metal–matrix composites, which are constructed from different nanomaterials including nanoparticles, nanotubes, nanowires, nanoribbons, and nanosheets. In recent years, one emerging concept in physics is “topological phononics.” Using 2D materials as examples, Liu et al. (article number 1904784) introduce the novel concepts of Berry phase, topology, and pseudospin for phonons. The corresponding phenomena in one- and three-dimensional systems are also covered. Another important feature in terms of the thermal properties of 2D materials is the unusually high heat radiation. Although the amount of heat energy carried by radiation is usually lower than that through conduction, a significant enhancement of five orders of magnitude are demonstrated in 2D materials, contributed by the hyperbolic electromagnetic dispersion. Baudin et al. (article number 1904783) discuss the possibility of radiation cooling in 2D materials, focusing on the graphene and hexagonal boron nitride heterostructures. They introduce the concepts and mechanism of super-Planckian thermal emission and electroluminescent cooling. In conclusion, we would like to thank the authors for providing their important contributions to this special issue. We greatly appreciate Dr. Huan Wang for organizing this special issue, as well as the whole editorial team of Advanced Functional Materials, for their great support and kind cooperation. We sincerely hope that the readers of Advanced Functional Materials will enjoy reading this special issue.

Phonon hydrodynamics is a theoretical framework for predicting nondiffusive heat transport processes in solids at the nanoscale or under high-frequency excitations. This article presents the microscopic and thermodynamic foundations of the theory and reviews its applications. First, we discuss historical and modern derivations of hydrodynamic heat transport equations from the phonon Boltzmann transport equation (BTE), and highlight advanced methods to predict hydrodynamic effects from direct solutions of the BTE beyond the Relaxation Time Approximation. Then, we review the main experiments that uncovered nondiffusive heat transport effects and their interpretation from the hydrodynamic perspective. Overall, the developments summarized in this work establish phonon hydrodynamics as a vital tool for understanding and engineering thermal transport at the nanoscale in data-processing and energy-conversion devices.

Two-dimensional (2D) materials have captured the attention of the scientific community due to the wide range of unique properties at nanometer-scale thicknesses. While significant exploratory research in 2D materials has been achieved, the understanding of 2D electronic transport and carrier dynamics remains in a nascent stage. Furthermore, because prior review articles have provided general overviews of 2D materials or specifically focused on charge transport in graphene, here we instead highlight charge transport mechanisms in post-graphene 2D materials, with particular emphasis on transition metal dichalcogenides and black phosphorus. For these systems, we delineate the intricacies of electronic transport, including band structure control with thickness and external fields, valley polarization, scattering mechanisms, electrical contacts, and doping. In addition, electronic interactions between 2D materials are considered in the form of van der Waals heterojunctions and composite films. This review concludes with a perspective on the most promising future directions in this fast-evolving field.

Phonon heat conduction over length scales comparable to their mean free paths is a topic of considerable interest for basic science and thermal management technologies. Although the failure of Fourier's law beyond the diffusive regime is well understood, debate exists over the proper physical description of thermal transport in the ballistic to diffusive crossover. Here, we derive a generalized Fourier's law that links the heat flux and temperature fields, valid from ballistic to diffusive regimes and for general geometries, using the Peierls-Boltzmann transport equation within the relaxation time approximation. This generalized Fourier's law predicts that thermal conductivity not only becomes nonlocal at length scales smaller than phonon mean free paths, but also requires the inclusion of an inhomogeneous nonlocal source term that has been previously neglected. We demonstrate the validity of this generalized Fourier's law through direct comparison with time-domain thermoreflectance (TDTR) measurements in the nondiffusive regime without adjustable parameters. Furthermore, we show that interpreting experimental data without this generalized Fourier's law leads to inaccurate measurement of thermal transport properties.

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.