Accessing general relations for temperature coefficients of Raman shifts in 2D materials.

The temperature coefficient of Raman shifts, which regulates the linear-in-temperature dependence of Raman shifts, plays a vital role in the experimental determinations of thermal conductivities in two-dimensional (2D) materials. Originating from anharmonic phonon effects, however, its connection to the underlying phonon structure remains poorly understood. Here, we explore the possibility of a simple albeit general relation that relates temperature coefficients to frequencies of the associated phonon modes in 2D materials. Remarkably, by resorting to a renormalized phonon picture, we explicitly show that the ratio between the temperature coefficient of Raman shifts and the associated phonon frequency is almost a constant that is varied only among materials. Our general relation fits well to experimental results for typical 2D materials and may have implications for addressing the impact of anharmonic phonon effects on thermal conductivities in 2D materials.

Anomalous energy diffusion in two-dimensional nonlinear lattices.

Heat transport in one-dimensional (1D) momentum-conserved lattices is generally assumed to be anomalous, thus yielding a power-law divergence of thermal conductivity with system length. However, whether heat transport in a two-dimensional (2D) system is anomalous or not is still up for debate because of the difficulties involved in experimental measurements or due to the insufficiently large simulation cell size. Here we simulate energy and momentum diffusion in the 2D nonlinear lattices using the method of fluctuation correlation functions. Our simulations confirm that energy diffusion in the 2D momentum-conserved lattices is anomalous and can be well described by the Lévy-stable distribution. As is expected, we verify that 2D nonlinear lattices with on-site potentials exhibit normal energy diffusion, independent of the dimension. Contrary to the hypothesis of a 1D system, we further clarify that anomalous heat transport in the 2D momentum-conserved system cannot be corroborated by the momentum superdiffusion any longer. Our findings offer some valuable insights into mechanisms of thermal transport in 2D system.

Energy and momentum diffusion in one-dimensional periodic and asymmetric nonlinear lattices with momentum conservation.

The energy diffusion in one-dimensional (1D) momentum conserving nonlinear lattices usually exhibits anomalous superdiffusion, except the coupled rotator lattice with symmetric and periodic interacting potential which has normal energy diffusion corresponding to normal heat conduction. For nonperiodic 1D lattices with momentum conservation, it has been argued that the asymmetric potential can induce normal heat conduction. Later results indicate the observed normal behavior might be the finite size effect and the anomalous behavior will appear in the thermodynamical limit. Here we propose asymmetric and periodic 1D nonlinear lattices with momentum conservation. The energy and momentum diffusion behaviors will be investigated in detail and the same normal diffusion behaviors for both energy and momentum can be observed. These results confirm that the periodicity is the key for normal transport behavior in 1D momentum conserving lattices, whether the potential is symmetric or asymmetric.

Thermal rectification induced by geometrical asymmetry: A two-dimensional multiparticle Lorentz gas model.

We propose a two-dimensional (2D) multiparticle Lorentz gas model by combining the direct simulation Monte Carlo method with the Lorentz gas model, where the normal thermal transport under Fourier's law is confirmed by length-independent thermal conductivity. For this 2D multiparticle Lorentz gas model, the thermal rectification effect is obtained with the asymmetrical setup of a trapezoidal shape, which is a purely geometric effect. Furthermore, we find a scaling behavior between the rectification ratio and the geometrical parameters of the trapezoidal shape, which is verified by numerical simulations.

Effect of boundary chain folding on thermal conductivity of lamellar amorphous polyethylene.

Thermal transport properties of amorphous polymers depend significantly on the chain morphology, and boundary chain folding is a common phenomenon in bulk or lamellar polymer materials. In this work, by using molecular dynamics simulations, we study thermal conductivity of lamellar amorphous polyethylene (LAPE) with varying chain length (L 0). For a short L 0 without boundary chain folding, thermal conductivity of LAPE is homogeneous along the chain length direction. In contrast, boundary chain folding takes place for large L 0, and the local thermal conductivity at the boundary is notably lower than that of the central region, indicating inhomogeneous thermal transport in LAPE. By analysing the chain morphology, we reveal that the boundary chain folding causes the reduction of both the orientation order parameter along the heat flow direction and the radius of gyration, leading to the reduced local thermal conductivity at the boundary. Further vibrational spectrum analysis reveals that the boundary chain folding shifts the vibrational spectrum to the lower frequency, and suppresses the transmission coefficient for both C-C vibration and C-H vibration. Our study suggests that the boundary chain folding is an important factor for polymers to achieve desirable thermal conductivity for plastic heat exchangers and electronic packaging applications.

Energy and spin diffusion in the one-dimensional classical Heisenberg spin chain at finite and infinite temperatures.

The energy and spin diffusion behaviors in the one-dimensional classical Heisenberg spin chain have been systematically investigated using the equilibrium diffusion method. The spatiotemporal autocorrelation functions for energy and spin are calculated at finite and infinite temperatures. As conserved quantities, the spreading of excess energy and spin can be used to determine their actual diffusion behaviors. At low temperatures, the energy diffusion shows almost ballistic behavior, and spin shows superdiffusion behavior for finite chain size. For energy diffusion, normal diffusion behavior can be obtained when the temperature is higher than 0.75. For spin diffusion, normal diffusion behavior is observed at infinite temperature.

Renormalized vibrations and normal energy transport in 1d FPU-like discrete nonlinear Schrödinger equations.

For one-dimensional (1d) nonlinear atomic lattices, the models with on-site nonlinearities such as the Frenkel-Kontorova (FK) and ϕ4 lattices have normal energy transport while the models with inter-site nonlinearities such as the Fermi-Pasta-Ulam-ß (FPU-ß) lattice exhibit anomalous energy transport. The 1d Discrete Nonlinear Schrödinger (DNLS) equations with on-site nonlinearities has been previously studied and normal energy transport has also been found. Here, we investigate the energy transport of 1d FPU-like DNLS equations with inter-site nonlinearities. Extended from the FPU-ß lattice, the renormalized vibration theory is developed for the FPU-like DNLS models and the predicted renormalized vibrations are verified by direct numerical simulations same as the FPU-ß lattice. However, the energy diffusion processes are explored and normal energy transport is observed for the 1d FPU-like DNLS models, which is different from their atomic lattice counterpart of FPU-ß lattice. The reason might be that, unlike nonlinear atomic lattices where models with on-site nonlinearities have one less conserved quantities than the models with inter-site nonlinearities, the DNLS models with on-site or inter-site nonlinearities have the same number of conserved quantities as the result of gauge transformation.

Novel Two-Dimensional Silicon Dioxide with in-Plane Negative Poisson's Ratio.

Silicon dioxide or silica, normally existing in various bulk crystalline and amorphous forms, was recently found to possess a two-dimensional structure. In this work, we use ab initio calculation and evolutionary algorithm to unveil three new two-dimensional (2D) silica structures whose thermal, dynamical, and mechanical stabilities are compared with many typical bulk silica. In particular, we find that all three of these 2D silica structures have large in-plane negative Poisson's ratios with the largest one being double of penta graphene and three times of borophenes. The negative Poisson's ratio originates from the interplay of lattice symmetry and Si-O tetrahedron symmetry. Slab silica is also an insulating 2D material with the highest electronic band gap (>7 eV) among reported 2D structures. These exotic 2D silica with in-plane negative Poisson's ratios and widest band gaps are expected to have great potential applications in nanomechanics and nanoelectronics.

Stretch diffusion and heat conduction in one-dimensional nonlinear lattices.

For heat conduction in one-dimensional (1D) nonlinear Hamiltonian lattices, it has been known that conserved quantities play an important role in determining the actual heat conduction behavior. In closed or microcanonical Hamiltonian systems, the total energy and stretch are always conserved. Depending on the existence of external on-site potential, the total momentum can be conserved or not. All the momentum-conserving lattices have anomalous heat conduction except the 1D coupled rotator lattice. It was recently claimed that "whenever stretch (momentum) is not conserved in a 1D model, the momentum (stretch) and energy fields exhibit normal diffusion." The stretch in a coupled rotator lattice was also argued to be nonconserved due to the requirement of a finite partition function, which enables the coupled rotator lattice to fulfill this claim. In this work, we will systematically investigate stretch diffusion and heat conduction in terms of energy diffusion for typical 1D nonlinear lattices. Contrary to what was claimed, no clear connection between conserved quantities and heat conduction can be established. The actual situation might be more complicated than what was proposed.

Heat conduction and energy diffusion in momentum-conserving one-dimensional full-lattice ding-a-ling model.

The ding-a-ling model is a kind of half lattice and half hard-point-gas (HPG) model. The original ding-a-ling model proposed by Casati et al. does not conserve total momentum and has been found to exhibit normal heat conduction behavior. Recently, a modified ding-a-ling model which conserves total momentum has been studied and normal heat conduction has also been claimed. In this work, we propose a full-lattice ding-a-ling model without hard point collisions where total momentum is also conserved. We investigate the heat conduction and energy diffusion of this full-lattice ding-a-ling model with three different nonlinear inter-particle potential forms. For symmetrical potential lattices, the thermal conductivities diverges with lattice length and their energy diffusions are superdiffusive signaturing anomalous heat conduction. For asymmetrical potential lattices, although the thermal conductivity seems to converge as the length increases, the energy diffusion is definitely deviating from normal diffusion behavior indicating anomalous heat conduction as well. No normal heat conduction behavior can be found for the full-lattice ding-a-ling model.

Renormalized phonons in nonlinear lattices: A variational approach.

We propose a variational approach to study renormalized phonons in momentum-conserving nonlinear lattices with either symmetric or asymmetric potentials. To investigate the influence of pressure for phonon properties, we derive an inequality which provides both the lower and upper bound of the Gibbs free energy as the associated variational principle. This inequality is a direct extension to the Gibbs-Bogoliubov inequality. Taking the symmetry effect into account, the reference system for the variational approach is chosen to be harmonic with an asymmetric quadratic potential which contains variational parameters. We demonstrate the power of this approach by applying it to one-dimensional nonlinear lattices with a symmetric or asymmetric Fermi-Pasta-Ulam-type potential. For a system with a symmetric potential and zero pressure, we recover existing results. For other systems which are beyond the scope of existing theories, including those having symmetric potential and pressure and those having the asymmetric potential with or without pressure, we also obtain accurate sound velocity.

Non-reciprocal geometric wave diode by engineering asymmetric shapes of nonlinear materials.

Unidirectional nonreciprocal transport is at the heart of many fundamental problems and applications in both science and technology. Here we study the novel design of wave diode devices by engineering asymmetric shapes of nonlinear materials to realize the function of non-reciprocal wave propagations. We first show analytical results revealing that both nonlinearity and asymmetry are necessary to induce such non-reciprocal (asymmetric) wave propagations. Detailed numerical simulations are further performed for a more realistic geometric wave diode model with typical asymmetric shape, where good non-reciprocal wave diode effect is demonstrated. Finally, we discuss the scalability of geometric wave diodes. The results open a flexible way for designing wave diodes efficiently simply through shape engineering of nonlinear materials, which may find broad implications in controlling energy, mass and information transports.

Anomalous heat diffusion.

Consider anomalous energy spread in solid phases, i.e., <Δx(2)(t)>E≡∫(x-E)(2)ρE(x,t)dx∝t(ß), as induced by a small initial excess energy perturbation distribution ρE(x,t=0) away from equilibrium. The second derivative of this variance of the nonequilibrium excess energy distribution is shown to rigorously obey the intriguing relation d(2)<Δx(2)(t)>E/dt2=2CJJ(t)/(kBT(2)c), where CJJ(t) equals the thermal equilibrium total heat flux autocorrelation function and c is the specific volumetric heat capacity. Its integral assumes a time-local Helfand-like relation. Given that the averaged nonequilibrium heat flux is governed by an anomalous heat conductivity, the energy diffusion scaling determines a corresponding anomalous thermal conductivity scaling behavior.

Temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with a soft on-site potential.

The temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential (soft-KG) are investigated systematically. Similarly to the previously studied hard-KG lattices, the existence of renormalized phonons is also confirmed in soft-KG lattices. In particular, the temperature dependence of the renormalized phonon frequency predicted by a classical field theory is verified by detailed numerical simulations. However, the thermal conductivities of soft-KG lattices exhibit the opposite trend in temperature dependence in comparison with those of hard-KG lattices. The interesting thing is that the temperature-dependent thermal conductivities of both soft- and hard-KG lattices can be interpreted in the same framework of effective phonon theory. According to the effective phonon theory, the exponents of the power-law dependence of the thermal conductivities as a function of temperature are only determined by the exponents of the soft or hard on-site potentials. These theoretical predictions are consistently verified very well by extensive numerical simulations.

Scaling of temperature-dependent thermal conductivities for one-dimensional nonlinear lattices.

In general nonlinear lattices, the existence of renormalized phonons due to the nonlinear interactions has been independently discovered by many research groups. Regarding these renormalized phonons as the energy carriers responsible for the heat transport, the scaling laws of temperature-dependent thermal conductivities of one-dimensional nonlinear lattices can be derived from the phenomenological effective phonon approach. For the paradigmatic nonlinear φ(4) lattice, κ(T)[proportionality]T(-1.35), which was numerically obtained more than a decade ago, can be well explained by the current approach. Most importantly, this approach is able to predict the scaling laws of temperature-dependent thermal conductivities of generalized nonlinear Klein-Gordon lattices. These theoretical predictions are compared by numerical simulations, and perfect agreements have been found.

Energy carriers in the Fermi-Pasta-Ulam ß lattice: solitons or phonons?

We investigate anomalous energy transport processes in the Fermi-Pasta-Ulam ß lattice, in particular, the maximum sound velocity of the relevant weakly damped energy carriers. That velocity is numerically resolved by measuring the propagating fronts of the correlation functions of energy-momentum fluctuations at different times. We use fixed boundary conditions and stochastic heat baths. The numerical results are compared with the theoretical predictions of the sound velocities for solitons and effective (renormalized) phonons, respectively. Excellent agreement has been found for the prediction of effective long wavelength phonons, giving strong evidence that the energy carriers should be effective phonons rather than solitons.

Shuttling heat across one-dimensional homogenous nonlinear lattices with a Brownian heat motor.

We investigate directed thermal heat flux across one-dimensional homogenous nonlinear lattices when no net thermal bias is present on average. A nonlinear lattice of Fermi-Pasta-Ulam-type or Lennard-Jones-type system is connected at both ends to thermal baths which are held at the same temperature on temporal average. We study two different modulations of the heat bath temperatures, namely: (i) a symmetric, harmonic ac driving of temperature of one heat bath only and (ii) a harmonic mixing drive of temperature acting on both heat baths. While for case (i) an adiabatic result for the net heat transport can be derived in terms of the temperature-dependent heat conductivity of the nonlinear lattice a similar such transport approach fails for the harmonic mixing case (ii). Then, for case (ii), not even the sign of the resulting Brownian motion induced heat flux can be predicted a priori. A nonvanishing heat flux (including a nonadiabatic reversal of flux) is detected which is the result of an induced dynamical symmetry breaking mechanism in conjunction with the nonlinearity of the lattice dynamics. Computer simulations demonstrate that the heat flux is robust against an increase of lattice sizes. The observed ratchet effect for such directed heat currents is quite sizable for our studied class of homogenous nonlinear lattice structures, thereby making this setup accessible for experimental implementation and verification.

Molecular wires acting as quantum heat ratchets.

We explore heat transfer in molecular junctions between two leads in the absence of a finite net thermal bias. The application of an unbiased time-periodic temperature modulation of the leads entails a dynamical breaking of reflection symmetry, such that a directed heat current may emerge (ratchet effect). In particular, we consider two cases of adiabatically slow driving, namely, (i) periodic temperature modulation of only one lead and (ii) temperature modulation of both leads with an ac driving that contains a second harmonic, thus, generating harmonic mixing. Both scenarios yield sizable directed heat currents, which should be detectable with present techniques. Adding a static thermal bias allows one to compute the heat current-thermal load characteristics, which includes the ratchet effect of negative thermal bias with positive-valued heat flow against the thermal bias, up to the thermal stop load. The ratchet heat flow in turn generates also an electric current. An applied electric stop voltage, yielding effective zero electric current flow, then mimics a solely heat-ratchet-induced thermopower ("ratchet Seebeck effect"), although no net thermal bias is acting. Moreover, we find that the relative phase between the two harmonics in scenario (ii) enables steering the net heat current into a direction of choice.

Parameter-dependent thermal conductivity of one-dimensional phi4 lattice.

We examine the thermal conductivity of a one-dimensional phi4 lattice with strong on-site harmonic potential. The expression for the thermal conductivity in terms of different parameters is derived from the effective phonon theory. Numerical calculations using nonequilibrium molecular dynamics are compared with the predictions of the effective phonon theory and the theory of the Peierls-Boltzmann transport equation. It is found that the numerical results are consistent with the prediction of the effective phonon theory in the intermediate parameter range and approach the predictions of Peierls-Boltzmann transport theory in the strongly pinned limit.