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Very recently, a novel two-dimension (2D) MXene, MoSi2N4, was successfully synthesized with excellent ambient stability, high carrier mobility, and moderate band gap (2020 Science 369 670). In this work, the intrinsic lattice thermal conductivity of monolayer MoSi2N4 is predicted by solving the phonon Boltzmann transport equation based on the first-principles calculations. Despite the heavy atomic mass of Mo and complex crystal structure, the monolayer MoSi2N4 unexpectedly exhibits a quite high lattice thermal conductivity over a wide temperature range between 300 to 800 K. At 300 K, its in-plane lattice thermal conductivity is 224 Wm−1 K−1. The detailed analysis indicates that the large group velocities and small anharmonicity are the main reasons for its high lattice thermal conductivity. We also calculate the lattice thermal conductivity of monolayer WSi2N4, which is only a little smaller than that of MoSi2N4. Our findings suggest that monolayer MoSi2N4 and WSi2N4 are potential 2D materials for thermal transport in future nano-electronic devices.

Many low-thermal-conductivity (κ ) crystals show intriguing temperature (T) dependence of κ : κ  ∝ T (crystal-like) at intermediate temperatures whereas weak T-dependence (glass-like) at high temperatures. It has been in debate whether thermal transport can still be described by phonons at the Ioffe-Regel limit. In this work, we propose that most phonons are still well defined for thermal transport, whereas they carry heat via dual channels: normal phonons described by the Boltzmann transport equation theory, and diffuson-like phonons described by the diffusion theory. Three physics-based criteria are incorporated into first-principles calculations to judge mode-by-mode between the two phonon channels. Case studies on La Zr O and Tl VSe show that normal phonons dominate low temperatures while diffuson-like phonons dominate high temperatures. Our present dual-phonon theory enlightens the physics of hierarchical phonon transport as approaching the Ioffe-Regel limit and provides a numerical method that should be practically applicable to many materials with vibrational hierarchy.

The conceptual understanding of charge transport in conducting polymers is still ambiguous due to a wide range of paracrystallinity (disorder). Here, we advance this understanding by presenting the relationship between transport, electronic density of states and scattering parameter in conducting polymers. We show that the tail of the density of states possesses a Gaussian form confirmed by two-dimensional tight-binding model supported by Density Functional Theory and Molecular Dynamics simulations. Furthermore, by using the Boltzmann Transport Equation, we find that transport can be understood by the scattering parameter and the effective density of states. Our model aligns well with the experimental transport properties of a variety of conducting polymers; the scattering parameter affects electrical conductivity, carrier mobility, and Seebeck coefficient, while the effective density of states only affects the electrical conductivity. We hope our results advance the fundamental understanding of charge transport in conducting polymers to further enhance their performance in electronic applications.

Abstract Pristine graphene and graphene-based heterostructures can exhibit exceptionally high electron mobility if their surface contains few electron-scattering impurities. Mobility directly influences electrical conductivity and its dependence on the carrier density. But linking these key transport parameters remains a challenging task for both theorists and experimentalists. Here, we report numerical and analytical models of carrier transport in graphene, which reveal a universal connection between graphene’s carrier mobility and the variation of its electrical conductivity with carrier density. Our model of graphene conductivity is based on a convolution of carrier density and its uncertainty, which is verified by numerical solution of the Boltzmann transport equation including the effects of charged impurity scattering and optical phonons on the carrier mobility. This model reproduces, explains, and unifies experimental mobility and conductivity data from a wide range of samples and provides a way to predict a priori all key transport parameters of graphene devices. Our results open a route for controlling the transport properties of graphene by doping and for engineering the properties of 2D materials and heterostructures.

The boundary integral method for propagating solid/liquid interfaces is detailed with allowance for the thermo-solutal Stefan-type models. Two types of mass transfer mechanisms corresponding to the local equilibrium (parabolic-type equation) and local non-equilibrium (hyperbolic-type equation) solidification conditions are considered. A unified integro-differential equation for the curved interface is derived. This equation contains the steady-state conditions of solidification as a special case. The boundary integral analysis demonstrates how to derive the quasi-stationary Ivantsov and Horvay-Cahn solutions that, respectively, define the paraboloidal and elliptical crystal shapes. In the limit of highest Péclet numbers, these quasi-stationary solutions describe the shape of the area around the dendritic tip in the form of a smooth sphere in the isotropic case and a deformed sphere along the directions of anisotropy strength in the anisotropic case. A thermo-solutal selection criterion of the quasi-stationary growth mode of dendrites which includes arbitrary Péclet numbers is obtained. To demonstrate the selection of patterns, computational modelling of the quasi-stationary growth of crystals in a binary mixture is carried out. The modelling makes it possible to obtain selected structures in the form of dendritic, fractal or planar crystals. This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.

Thermal conductivity in dielectric crystals is the result of the relaxation of lattice vibrations described by the phonon Boltzmann transport equation. Remarkably, an exact microscopic definition of the heat carriers and their relaxation times is still missing: Phonons, typically regarded as the relevant excitations for thermal transport, cannot be identified as the heat carriers when most scattering events conserve momentum and do not dissipate heat flux. This is the case for two-dimensional or layered materials at room temperature, or three-dimensional crystals at cryogenic temperatures. In this work, we show that the eigenvectors of the scattering matrix in the Boltzmann equation define collective phonon excitations, which are termed here “relaxons”. These excitations have well-defined relaxation times, directly related to heat-flux dissipation, and they provide an exact description of thermal transport as a kinetic theory of the relaxon gas. We show why Matthiessen’s rule is violated, and we construct a procedure for obtaining the mean free paths and relaxation times of the relaxons. These considerations are general and would also apply to other semiclassical transport models, such as the electronic Boltzmann equation. For heat transport, they remain relevant even in conventional crystals like silicon, but they are of the utmost importance in the case of two-dimensional materials, where they can revise, by several orders of magnitude, the relevant time and length scales for thermal transport in the hydrodynamic regime.

A bstract We study quarkonium transport in the quark-gluon plasma by using the potential nonrelativistic QCD (pNRQCD) effective field theory and the framework of open quantum systems. We argue that the coupling between quarkonium and the thermal bath is weak using separation of scales, so the initial density matrix of the total system factorizes and the time evolution of the subsystem is Markovian. We derive the semiclassical Boltzmann equation for quarkonium by applying a Wigner transform to the Lindblad equation and carrying out a semiclassical expansion. We resum relevant interactions to all orders in the coupling constant at leading power of the nonrelativistic and multipole expansions. The derivation is valid for both weakly coupled and strongly coupled quark-gluon plasmas. We find reaction rates in the transport equation factorize into a quarkonium dipole transition function and a chromoelectric gluon distribution function. For the differential reaction rate, the definition of the momentum dependent chromoelectric gluon distribution function involves staple-shaped Wilson lines. For the inclusive reaction rate, the Wilson lines collapse into a straight line along the real time axis and the distribution becomes momentum independent. The relation between the two Wilson lines is analogous to the relation between the Wilson lines appearing in the gluon parton distribution function (PDF) and the gluon transverse momentum dependent parton distribution function (TMDPDF). The centrality dependence of the quarkonium nuclear modification factor measured by experiments probes the momentum independent distribution while the transverse momentum dependence and measurements of the azimuthal angular anisotropy may be able to probe the momentum dependent one. We discuss one way to indirectly constrain the quarkonium in-medium real potential by using the factorization formula and lattice calculations. The leading quantum correction to the semiclassical transport equation of quarkonium is also worked out. The study can be easily generalized to quarkonium transport in cold nuclear matter, which is relevant for quarkonium production in eA collisions in the future Electron-Ion Collider.

In this paper, we develop a new meshless method for solving a wide class of time-fractional partial differential equations with general space operators in 2D and 3D regular and irregular domains. These equations are usually used to model transport processes in anisotropic media with sub-diffusive phenomena. In this method, the spatial approximation is given in the form of the truncated series over a set of linearly independent functions. Then the system is solved by the use of an efficient backward substitution method which is based on the collocation procedure using modified basis functions. The main aim of the research is to show the accuracy and efficiency of the proposed algorithm over some of the existing methods. The numerical results of ten examples on 2D and 3D domains demonstrate the advantages of the presented approach.

The electronic transport and thermoelectric properties in n-type doped monolayer MoS2 are investigated by a parameter-free method based on first-principles calculations, electron-phonon coupling (EPC), and Boltzmann transport equation (BTE). Remarkably, the calculated electron mobility ∼ 47 cm2 V−1s−1 and thermoelectric power factor S2 ∼ 2.93 × 10−3 W m−1 K−2 at room temperature are much lower than the previous theoretical values (e.g. ∼ 130-410 cm2 V−1 s−1 and S2 ∼ 2.80 × 10−2 W m−1 K−2), but agree well with the most recent experimental findings of ∼ 37 cm2 V−1 s−1 and S2 ∼ 3.00 × 10−3 W m−1 K−2. The EPC projections on phonon dispersion and the phonon branch dependent scattering rates indicate that the acoustic phonons, especially the longitudinal acoustic phonons, dominate the carrier scattering. Therefore, a mobility of 68 cm2 V−1 s−1 is achieved if only the acoustic phonons induced scattering is included, in accordance with the result of 72 cm2 V−1 s−1 estimated from the deformation potential driven by acoustic modes. Furthermore, via excluding the scattering from the out-of-plane modes to simulate the EPC suppression, the obtained mobility of 258 cm2 V−1 s−1 is right in the range of 200-700 cm2 V−1 s−1 measured in the samples with top deposited dielectric layer. In addition, we also compute the lattice thermal conductivity κL of monolayer MoS2 using phonon BTE, and obtain a κL ∼ 123 W m−1 K−1 at 300 K.

The local fractional Burgers’ equation (LFBE) is investigated from the point of view of local fractional conservation laws envisaging a nonlinear local fractional transport equation with a linear non-differentiable diffusion term. The local fractional derivative transformations and the LFBE conversion to a linear local fractional diffusion equation are analyzed.