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Fullerene-based sandwiches have emerged as new candidates for potential applications of two-dimensional nanomaterials in electronics or energy storage. Recently, experimentalists have observed the evolution of boundaries for fullerene clusters sandwiched by two graphene layers, while vacuum space with typical dimension of 30 {\AA} was found within the fullerene layer. Because the pattern of the fullerene cluster impacts the physical properties of the sandwiches, it is important to understand the mechanisms for their structural transformations. In the present work, we find that the graphene/fullerene/graphene sandwich structure transforms among three configurations, depending on the fullerene to graphene area ratio. Molecular dynamics simulations show that there are two critical values for the area ratio. The fullerene pattern transforms from circular to rectangular at the first critical area ratio of 1/{\pi}. The critical value of 1/{\pi} is successfully derived by comparing the geometrical perimeter of the circular and rectangular shapes for the fullerene cluster without any physical parameters. At the second critical area ratio, the graphene layers surrounding the fullerene cluster become separated due to the competition between the bending energy and the cohesive energy. Based on the analytic model, the vacuum space is predicted to be 34 {\AA}, which agrees quite well with the experimental result. These findings provide fundamental insights into the mechanisms driving structural transformation of fullerene-based sandwiches, which will enable the selection of appropriate structures and materials to guide the design of future electronic and energy storage applications.

Van der Waals heterostructures such as graphene/MoS$_2$ are promising candidates for plenty of optical or electronic applications, owing to advanced properties inherited from the constitutional atomic layers. Thermal expansion is an important phenomenon to be considered for the thermal stability of the van der Waals heterstructure as temperature commonly rises during the operation of nano devices. In the present work, the thermal expansion coefficient for the graphene/MoS$_2$ heterostructure is investigated by molecular dynamics simulations, and the effect from the unavoidable misfit strain on the thermal expansion coefficient is revealed. The misfit strain can tune the thermal expansion coefficient by a factor of six, and this effect is quite robust in sense that it is not sensitive to the size or direction of the heterostructure. An analytic formula is derived to directly relate the thermal expansion coefficient to the misfit strain of the heterostructure, which qualitatively agrees with the numerical results although the analytic formula underestimates the misfit strain effect. Further analysis discloses that the misfit strain can efficiently engineer the thermal induced ripples, which serves as the key mechanism for the misfit strain effect on the thermal expansion coefficient. These findings provide valuable information for the thermal stability of van der Waals heterostructures and shall be benefit for practical applications of van der Waals heterostructure based nano devices.

Zirconia is well-known for plenty of important morphologys with Zr coordination varying from sixfold in the octagonal phase to eightfold in the cubic or tetragonal phase. The development of empirical potentials to describe these zirconia morphologys is an important issue but a long-standing challenge, which becomes a bottleneck for the theoretical investigation of large zirconia structures. In contrast to the standard core-shell model, we develop a new potential for zirconia through the combination of long-range Coulomb interaction and bond order Tersoff model. The bond order characteristic of the Tersoff potential enables it to be well suited for the description of these zirconia morphologys with different coordination numbers. In particular, the complex monoclinic phase with two inequivalent oxygens, that is difficult to be described by most existing empirical potentials, can be well captured by this newly developed potential. It is shown that this potential can provide reasonable predictions for most static and dynamic properties of various zirconia morphologys. Besides its clear physical essence, this potential is at least one order faster than core-shell based potentials in the molecule dynamics simulation, as it discards the concept of the ultralight shell that demands for an extremely small time step. We also provide potential scripts for the widely used packages GULP and LAMMPS., Comment: Tersoff potential scripts for GULP and LAMMPS are available from www.jiangjinwu.org

We perform both molecular dynamics simulations and theoretical analysis to study the sensitivity of the graphene nanomechanical resonator based mass sensors, which are actuated following the global extended mode or the localized edge mode. We find that the mass detection sensitivity corresponding to the edge mode is about three times higher than that corresponding to the extended mode. Our analytic derivations reveal that the enhancement of the sensitivity originates in the reduction of the effective mass for the edge mode due to its localizing feature.

Misfit strain is inevitable in various heterostructures like the graphene/MoS 2 van der Waals heterostructure. Although the misfit strain effect on electronic and other physical properties have been well studied, it is still unclear how will the misfit strain affect the performance of the nanomechanical resonator based on the graphene/MoS 2 heterostructure. By performing molecular dynamics simulations, we disclose a misfit strain-induced decoupling phenomenon between the graphene layer and the MoS 2 layer during the resonant oscillation of the heterostructure. A direct relationship between the misfit strain and the decoupling mechanism is successfully established through the retraction force analysis. We further suggest to use the graphene/MoS 2 /graphene sandwich heterostructure for the nanomechanical resonator application, which is able to prevent the misfit strain-related decoupling phenomenon. These results provide valuable information for the future application of the graphene/MoS 2 heterostructure in the nanomechanical resonator field.

We derive analytical expressions for the Young's modulus and the Poisson's ratio of the graphene nanoribbon, in which free edges are warped by the compressive edge stress. Our analytical formulas explicitly illustrate the reduction of the Young's modulus by the warped free edges, leading to the obvious width dependence for the Young's modulus of the graphene nanoribbon. The Poisson's ratio is also reduced by the warped free edges, and negative Poisson's ratio can be achieved in the graphene nanoribbon with an ultra-narrow width. These results are comparable with previous theoretical works.

The valence force field (VFF) model is a concise physical interpretation of the atomic interaction in terms of the bond and angle variations in the explicit quadratic functional form, while the machine learning (ML) method is a flexible numerical approach to make predictions based on some pre-obtained training data without the need of any explicit functions. We propose a so-called ML-VFF model, by combining the clear physical essence of the VFF model and the numerical flexibility of the ML method. Instead of imposing any explicit functional forms for the atomic interaction, the ML-VFF model predicts the potential and force with the Gaussian regression approach. We take graphene as an example to illustrate the ability of the ML-VFF model to make accurate predictions with relatively low computational expenses. We also discuss some key advantages and drawbacks of the ML-VFF model., Comment: four figures

Fullerence encapsulation has been proven to be a powerful approach to enhance mechanical and electronic properties of the single-walled carbon nanotubes (SWCNTs). However, some discrepancies emerge in recent studies of the fullerence encapsulation effect on the thermal conductivity of SWCNTs. More specifically, most previous theoretical works predicted slightly enhancement of the thermal conductivity, but the recent experiment by Kodama et al. (Nat. Mat. 16, 892 (2017)) observed clear reduction of the thermal conductivity in SWCNTs by fullerence encapsulation. We perform molecular dynamics simulations to revisit this issue, by comparatively investigate the thermal conductivity of the SWCNT (n, n) and the corresponding peapod (n, n) with n = 8, 9, 10, and 11. We find that the fullerence encapsulation can reduce the thermal conductivity of narrower SWCNTs with n = 8 and 9, but it can slightly enhance the thermal conductivity of thicker SWCNTs with n = 10 and 11. The underlying mechanisms for these opposite effects are explored by analyzing the encapsulation induced structural deformation and the variation of the phonon dispersion of the SWCNT. We illustrate that the reduction effect observed in the recent experiment is related to the mechanism for reduction of the thermal conductivity for narrower SWCNTs here, while previous numerical works correspond to the enhancement effect for thicker SWCNTs found in the present work. Our findings shed lights on clarifying the discrepancy between previous numerical predictions and experimental observations on the effect of the fullerence encapsulation on the thermal conductivity of the SWCNT.

We propose a tubal van der Waals heterostructure by rolling up the graphene and MoS2 atomic layers into a tubal form. We illustrate that the interlayer space for the tubal van der Waals heterostructure can be varied in a specific range, which is determined by the competition between the interlayer van der Waals force and the mechanical properties of the atomic layers. The variability of the interlayer space can be utilized to efficiently tune mechanical properties of the tubal van der Waals heterostructure. More specifically, we demonstrate that the Poisson's ratio of the tubal van der Waals heterostructure can be manipulated by a factor of two by varying the interlayer space from 1.44 to 4.44. Our work promotes a new member with tunable Poisson's ratio to the van der Waals heterostructure family.

Molecular dynamics simulations are performed to investigate the misfit strain-induced buckling of the transition-metal dichalcogenide (TMD) lateral heterostructures, denoted by the seamless epitaxial growth of different TMDs along the in-plane direction. The Stillinger-Weber potential is utilized to describe both the interaction for each TMD and the coupling between different TMDs, i.e., MX2 (with M=Mo, W and X=S, Se, Te). It is found that the misfit strain can induce strong buckling of the free-standing TMD lateral heterostructures of large area, resulting from the TMDs' atomic-thick nature. The buckling phenomenon occurs in a variety of TMD lateral heterostructures of different compositions and in various patterns. Our findings raise a fundamental mechanical challenge for the structural stability of the free-standing TMD lateral heterostructures., Comment: accepted by Acta Mechanica Solida Sinica; Stillinger-Weber potential for MoS2/WSe2/MoSe2/... compound is provided and can be obtained at website http://jiangjinwu.org/sw

The field of topological mechanics has recently emerged due to the interest in robustly transporting various types of energy in a flaw and defect-insensitive fashion. While there have been a significant number of studies based on discovering and proposing topological materials and structures, very few have focused on tuning the resulting topological bandgaps, which is critical because the bandgap frequency is fixed once the structure has been fabricated. Here, we perform both lattice dynamical calculations and molecular dynamical simulations to investigate strain effects on the phononic topological bandgaps in two-dimensional monolayer hexagonal boron nitride. Our studies demonstrate that while the topologically protected phononic bandgaps are not closed even for severely deformed hexagonal boron nitride, and are relatively insensitive to uniaxial tension and shear strains, the position of the frequency gap can be efficiently tuned in a wide range through the application of biaxial strains. Overall, this work thus demonstrates that topological phonons are robust against the effects of mechanical strain engineering, and sheds light on the tunability of the topological bandgaps in nanomaterials., Comment: Journal of Applied Physics, accepted

We perform both lattice dynamics analysis and molecular dynamics simulations to demonstrate the existence of topologically protected phonon modes in a two-dimensional, monolayer hexagonal boron nitride sheet. The topological phonon modes are found to be localized at an in-plane interface that divides the system into two regions of distinct valley Chern numbers. The dispersion of this topological phonon mode crosses over the frequency gap [1123, 1278] cm^{-1}, which is opened through analogy with the quantum valley Hall effect by breaking inversion symmetry of the boron and nitride atoms in the primitive unit cell. Consequently, vibrational energy with frequency within this gap is topologically protected, resulting in wave propagation that exhibits minimal backscattering, is robust with regards to structural defects such as sharp corners, and exhibits excellent temporal stability. Our findings open up the possibility of realizing topological phonons and mechanics in two-dimensional nanomaterials., Comment: Nanoscale, accepted

The present work carries out molecular dynamics simulations to compute the thermal conductivity of the borophene nanoribbon and the borophene nanotube using the Muller-Plathe approach. We investigate the thermal conductivity of the armchair and zigzag borophenes, and show the strong anisotropic thermal conductivity property of borophene. We compare the results of the borophene nanoribbon and the borophene nanotube, and find the thermal conductivity of the borophene is structure dependent.

We parametrize the Stillinger-Weber potential for 156 two-dimensional atomic crystals. Parameters for the Stillinger-Weber potential are obtained from the valence force field model following the analytic approach (Nanotechnology 26, 315706 (2015)), in which the valence force constants are determined by the phonon spectrum. The Stillinger-Weber potential is an efficient nonlinear interaction, and is applicable for numerical simulations of nonlinear physical or mechanical processes. The supplemental resources for all simulations in the present work are available online in Ref. 1, including a fortran code to generate crystals' structures, files for molecular dynamics simulations using LAMMPS, files for phonon calculations with the Stillinger-Weber potential using GULP, and files for phonon calculations with the valence force field model using GULP., Comment: 25 more crystals are included. All structure codes and simulation scripts (using LAMMPS and GULP) are available online at: http://jiangjinwu.org/sw

Black phosphorene is not stable at ambient conditions, so atomic defects and oxidation effects are unavoidable in black phosphorus samples in the experiment. The effects of these defects on the performance of the black phosphorus nanoresonators are still unclear. Here, we perform classical molecular dynamics to investigate the effects of the vacancy and oxidation on single-layer black phosphorus nanoresonators at different temperatures. We find that the vacancy causes strong reduction in the quality factor of the nanoresonators, while the oxidation has weaker effect on the nanoresonators. More specifically, a 2% concentration of randomly distributed single vacancies is able to reduce the quality factor by about 80% and 40% at 4.2K and 50K, respectively. We also find that the quality factor of the nanoresonator is not sensitive to the distribution pattern of the vacancy defects.

Auxetic materials (materials with negative Poisson's ratio) and nanomaterials have independently been for many years two of the most active research fields in material science. Recently, these formerly independent fields have begun to intersect in new and interesting ways due to the recent discovery of auxeticity in nanomaterials like graphene, metal nanoplates, black phosphorus, and others. Here we review the research emerging at the intersection of auxeticity and nanomaterials. We first survey the atomistic mechanisms, both intrinsic and extrinsic, that have been found, primarily through atomistic simulations, to cause auxeticity in nanomaterials. We then outline the available experimental evidence for auxetic nanomaterials. In order to lay the groundwork for future work in this exciting area, we close by discussing several future prospects as well as the current challenges in this field., Comment: Applied Physics Review, accepted

Buckling is one of the most common phenomena in atomic-thick layered structures like graphene. While the buckling phenomenon usually causes disaster for most nano-devices, we illustrate one positive application of the buckled graphene for energy harvest, storage, and conversion. More specifically, we perform molecular dynamical simulations to show that the buckled graphene can be used to collect the wasted mechanical energy and store the energy in the form of internal knotting potential. Through strain engineering, the knotting potential can be converted into useful kinetic (thermal) energy that is highly concentrated at the free edges of the buckled graphene. The present study demonstrates potential applications of the buckled graphene for converting the dispersed wasted mechanical energy into the concentrated useful kinetic (thermal) energy., Comment: Nanotechnology, accepted

We perform molecular dynamics simulations to investigate the effect of hydrogenation on the Poisson's ratio of graphene. It is found that the value for Poisson's ratio in graphene can be effectively tuned from positive to negative by varying the percentage of hydrogenation. Specifically, the Poisson's ratio decreases with the increase of the percentage of hydrogenation, and reaches a minimum value of -0.04 at the percentage of hydrogenation about 50%. The Poisson's ratio starts to increase with a further increase of the percentage of hydrogenation. The appearance of minimum negative Poisson's ratio in the hydrogenated graphene is attributed to the suppression of the hydrogenation-induced ripples during stretching of graphene. Our results demonstrate that hydrogenation is a valuable approach for the tuning of the Poisson's ratio from positive to negative in graphene., Comment: Nanoscale, accepted

The single-layer black phosphorus is characteristic for its puckered configuration that possesses the hinge-like mechanism, which leads to the highly anisotropic in-plane Poisson's ratios and the negative out-of-plane Poisson's ratio. We reveal that the hinge-like mechanism can be attributed to the angle-angle cross interaction, which, combined with the bond stretching and angle bending interactions, is able to provide a good description of the mechanical properties in the single-layer black phosphorus. We also propose a nonlinear angle-angle cross interaction, which follows the form of the Stillinger-Weber potential and is advantageous for molecular dynamics simulations of single-layer black phosphorous under large deformations., Comment: GULP, LAMMPS

Negative Poisson's ratio (NPR) materials have drawn significant interest because the enhanced toughness, shear resistance and vibration absorption that typically are seen in auxetic materials may enable a range of novel applications. In this work, we report that single-layer graphene exhibits an intrinsic NPR, which is robust and independent of its size and temperature. The NPR arises due to the interplay between two intrinsic deformation pathways (one with positive Poisson's ratio, the other with NPR), which correspond to the bond stretching and angle bending interactions in graphene. We propose an energy-based deformation pathway criteria, which predicts that the pathway with NPR has lower energy and thus becomes the dominant deformation mode when graphene is stretched by a strain above 6%, resulting in the NPR phenomenon., Comment: Nano Letters, published

The Poisson's ratio characterizes the resultant strain in the lateral direction for a material under longitudinal deformation. Though negative Poisson's ratios (NPR) are theoretically possible within continuum elasticity, they are most frequently observed in engineered materials and structures, as they are not intrinsic to many materials. In this work, we report NPR in single-layer graphene ribbons, which results from the compressive edge stress induced warping of the edges. The effect is robust, as the NPR is observed for graphene ribbons with widths smaller than about 10 nm, and for tensile strains smaller than about 0.5%, with NPR values reaching as large as -1.51. The NPR is explained analytically using an inclined plate model, which is able to predict the Poisson's ratio for graphene sheets of arbitrary size. The inclined plate model demonstrates that the NPR is governed by the interplay between the width (a bulk property), and the warping amplitude of the edge (an edge property), which eventually yields a phase diagram determining the sign of the Poisson's ratio as a function of the graphene geometry., Comment: 4 figures

Edge effects play an important role for many properties of graphene. While most works have focused on the effects from isolated free edges, we present a novel knotting phenomenon induced by the interactions between a pair of free edges in graphene, and investigate its effect on the buckling of monolayer graphene. Upon compression, the buckling of graphene starts gradually in the form of two buckling waves from the warped edges. The collision of these two buckling waves results in the creation of a knot structure in graphene. The knot structure enables the buckled graphene to exhibit two unique post-buckling characteristics. First, it induces a five-fold increase in graphene's mechanical stiffness during the buckling process. Second, the knotted structure enables graphene to exhibit a mechanically stable post-buckling regime over a large (3%) compressive strain regime, which is significantly larger than the critical buckling strain of about 0.5%. The combination of these two effects enables graphene to exhibit an unexpected post-buckling stability that has previously not been reported. We predict that numerical simulations or experiments should observe two distinct stress strain relations for the buckling of identical graphene samples, due to the characteristic randomness in the formation process of the knot structure., Comment: 16 figures

We perform classical molecular dynamics to investigate the effects of mechanical strain on single-layer black phosphorus nanoresonators at different temperatures. We find that the resonant frequency is highly anisotropic in black phosphorus due to its intrinsic puckered configuration, and that the quality factor in the armchair direction is higher than in the zigzag direction at room temperature. The quality factors are also found to be intrinsically larger than graphene and MoS2 nanoresonators. The quality factors can be increased by more than a factor of two by applying tensile strain, with uniaxial strain in the armchair direction being most effective. However, there is an upper bound for the quality factor increase due to nonlinear effects at large strains, after which the quality factor decreases. The tension induced nonlinear effect is stronger along the zigzag direction, resulting in a smaller maximum strain for quality factor enhancement.

We propose to parametrize the Stillinger-Weber potential for covalent materials starting from the valence force field model. All geometrical parameters in the Stillinger-Weber potential are determined analytically according to the equilibrium condition for each individual potential term, while the energy parameters are derived from the valence force field model. This parametrization approach transfers the accuracy of the valence force field model to the Stillinger-Weber potential. Furthermore, the resulting Stilliinger-Weber potential supports for stable molecular dynamics simulations, as each potential term is at energy minimum state separately at the equilibrium configuration. We employ this procedure to parametrize Stillinger-Weber potentials for the single-layer MoS2 and black phosphorous. The obtained Stillinger-Weber potentials predict accurate phonon spectrum and mechanical behaviors. We also provide input scripts of these Stillinger-Weber potentials used by publicly available simulation packages including GULP and LAMMPS., Comment: 10 figures, 8 tables

We present an analytic study, based on the tight-binding approximation, of strain effects on the electronic bandgap in single-layer black phosphorus. We obtain an expression for the variation of the bandgap induced by a general strain type that includes both tension in and out of the plane and shear, and use this to determine the most efficient strain direction for different strain types, along which the strongest bandgap manipulation can be achieved. We find that the strain direction that enables the maximum manipulation of the bandgap is not necessarily in the armchair or zigzag direction. Instead, to achieve the strongest bandgap modulation, the direction of the applied mechanical strain is dependent on the type of applied strain., Comment: Physical Review B, accepted

We derive an analytic formula for the Young's modulus in single-layer black phosphorus using the valence force field model. By analyzing the directional dependence for the Young's modulus, we explore the third principle direction with direction angle phi_tp = 0.268pi besides armchair and zigzag directions. The maximum Young's modulus value is in the third principle direction. More specifically, the Young's modulus is 52.2 N/m, 85.4 N/m, and 111.4 N/m in the armchair direction, zigzag direction, and the third principle direction, respectively. This new principle direction is of significance for future discussions of other anisotropic properties in the single-layer black phosphorus., Comment: 5 pages, 3 figs. arXiv admin note: text overlap with arXiv:1410.3545

The topic of this review is the effects of electron-phonon interaction (EPI) on the transport properties of molecular nano-conductors. A nano-conductor connects to two electron leads and two phonon leads, possibly at different temperatures or chemical potentials. The EPI appears only in the nano-conductor. We focus on its effects on charge and energy transport. We introduce three approaches. For weak EPI, we use the nonequilibrium Green's function method to treat it perturbatively. We derive the expressions for the charge and heat currents. For weak system-lead couplings, we use the quantum master equation approach. In both cases, we use a simple single level model to study the effects of EPI on the system's thermoelectric transport properties. It is also interesting to look at the effect of currents on the dynamics of the phonon system. For this, we derive a semi-classical generalized Langevin equation to describe the nano-conductor's atomic dynamics, taking the nonequilibrium electron system, as well as the rest of the atomic degrees of freedom as effective baths. We show simple applications of this approach to the problem of energy transfer between electrons and phonons., Comment: 22 pages,173 refs., AIP Adv.,Special Topic: Phononics and Thermal Energy Control

The Lennard-Jones potential is widely used to describe the interlayer interactions within layered materials like graphene. However, it is also widely known that this potential strongly underestimates the frictional properties for layered materials. Here we propose to supplement the Lennard-Jones potential by a Gaussian-type potential, which enables more accurate calculations of the frictional properties of two-dimensional layered materials. Furthermore, the Gaussian potential is computationally simple as it introduces only one additional potential parameter that is determined by the interlayer shear mode in the layered structure. The resulting Lennard-Jones-Gaussian potential is applied to compute the interlayer cohesive energy and frictional energy for graphene, MoS2, black phosphorus, and their heterostructures., Comment: 9 figures, 3 tables

The interlayer breathing and shear modes in few-layer black phosphorus are investigated for their symmetry and lattice dynamical properties. The symmetry groups for the even-layer and odd-layer few-layer black phosphorus are utilized to determine the irreducible representation and the infrared and Raman activity for the interlayer modes. The valence force field model is applied to calculate the eigenvectorw and frequencies for the interlayer breathing and shear modes, which are explained using the atomic chain model. The anisotropic puckered configuration for black phosphorus leads to a highly anisotropic frequency for the two interlayer shear modes. More specifically, the frequency for the shear mode in the direction perpendicular to the pucker is less than half of the shear mode in the direction parallel with the pucker. We also report a set of interlayer modes having the same frequency for all few-layer black phosphorus with layer number N=3i with integer i, because of their collective vibrational displacements. The optical activity of the collective modes supports possible experimental identification for these modes., Comment: 10 figures, 7 tables

We derive an analytic formula for the elastic bending modulus of single-layer black phosphorus (SLBP) based on the valence force field model. The obtained elastic bending modulus is 4.8028 eV and 7.9905 eV along the armchair and zigzag directions in the SLBP, respectively. These values are obviously larger than the bending modulus of 1.4 eV in graphene due to the intrinsic finite thickness for SLBP. Our derivation analytically illustrates that the elastic bending modulus of the SLBP is proportional to the square of the intrinsic thickness of the SLBP., Comment: analytic approach is applied for the computation of elastic bending modulus

The distinguishing structural feature of single-layer black phosphorus is its puckered structure, which leads to many novel physical properties. In this work, we first present a new parameterization of the Stillinger-Weber potential for single-layer black phosphorus. In doing so, we reveal the importance of a cross-pucker interaction term in capturing its unique mechanical properties, such as a negative Poisson's ratio. In particular, we show that the cross-pucker interaction enables the pucker to act as a re-entrant hinge, which expands in the lateral direction when it is stretched in the longitudinal direction. As a consequence, single-layer black phosphorus has a negative Poisson's ratio in the direction perpendicular to the atomic plane. As an additional demonstration of the impact of the cross-pucker interaction, we show that it is also the key factor that enables capturing of the edge stress-induced bending of single-layer black phosphorus that has been reported in ab initio calculations., Comment: Nanoscale, published

The single-layer black phosphorus is characteristic for its puckered structure, which has leaded to highly anisotropy in its optical, electronic, and mechanical properties. We report, using the non-equilibrium Green's function approach and the first-principles method, that the anisotropy in the thermal conduction is very weak in the single-layer black phosphorus -- the difference between two in-plane directions is less than 4%. Our phonon calculations disclose that the two in-plane acoustic phonon branches have lower group velocities in the direction perpendicular to the pucker, as the black phosphorus is softer in this direction, leading to a weakening effect for the thermal conductance in the perpendicular direction. However, the out-of-plane acoustic phonon branch behaviors abnormally; i.e., the group velocity of this phonon branch is higher in the perpendicular direction, although the single-layer black phosphorus is softer in this direction. The abnormal behavior of the out-of-plane phonon branch is closely related to the highly anisotropic Poisson's ratio in the single-layer black phosphorus. As a result of the counteraction between the in-plane phonon modes and the out-of-plane phonon mode, the thermal conductance in the perpendicular direction is weaker than the parallel direction, but the anisotropy is pretty small., Comment: Nanotechnology, published

Single-layer graphene is so flexible that its flexural mode (also called the ZA mode, bending mode, or out-of-plane transverse acoustic mode) is important for its thermal and mechanical properties. Accordingly, this review focuses on exploring the relationship between the flexural mode and thermal and mechanical properties of graphene. We first survey the lattice dynamic properties of the flexural mode, where the rigid translational and rotational invariances play a crucial role. After that, we outline contributions from the flexural mode in four different physical properties or phenomena of graphene -- its thermal conductivity, thermal expansion, Young's modulus, and nanomechanical resonance. We explain how graphene's superior thermal conductivity is mainly due to its three acoustic phonon modes at room temperature, including the flexural mode. Its coefficient of thermal expansion is negative in a wide temperature range resulting from the particular vibration morphology of the flexural mode. We then describe how the Young's modulus of graphene can be extracted from its thermal fluctuations, which are dominated by the flexural mode. Finally, we discuss the effects of the flexural mode on graphene nanomechanical resonators, while also discussing how the essential properties of the resonators, including mass sensitivity and quality factor, can be enhanced., Comment: Journal of Physics: Condensed Matter, topical review, published

The Euler buckling theorem states that the buckling critical strain is an inverse square function of the length for a thin plate in the static compression process. However, the suitability of this theorem in the dynamical process is unclear, so we perform molecular dynamics simulations to examine the applicability of the Euler buckling theorem in case of a fast compression of the single-layer MoS2. We find that the Euler buckling theorem is not applicable in such dynamical process, as the buckling critical strain becomes a length-independent constant in the buckled system with many ripples. However, the Euler buckling theorem can be resumed in this dynamical process after restricting the theorem to an individual ripple in the buckled structure., Comment: 4 pages, 4 figures

Molecular dynamics simulations are performed to investigate the buckling of single-layer MoS2 under uniaxial compression. The strain rate is found to play an important role on the critical buckling strain, where higher strain rate leads to larger critical strain. The critical strain is almost temperature-independent for T<50 K, and it increases with increasing temperature for T>50 K owning to the thermal vibration assisted healing mechanism on the buckling deformation. The length-dependence of the critical strain from our simulations is in good agreement with the prediction of the Euler buckling theory., Comment: Nanotechnology, accepted

Graphene and MoS2 are two well-known quasi two-dimensional materials. This review is a comparative survey of the complementary lattice dynamical and mechanical properties of graphene and MoS2. This comparison facilitates the study of graphene/MoS2 heterostructures, which is expected to mitigate the negative properties of each individual constituent., Comment: Frontiers of Physics, published, Focus Review