Nianbei Li

Colloquium: Phononics: Manipulating heat flow with electronic analogs and beyond

The form of energy termed heat that typically derives from lattice vibrations, i.e., phonons, is usually considered as waste energy and, moreover, deleterious to information processing. However, in this Colloquium, an attempt is made to rebut this common view: By use of tailored models it is demonstrated that phonons can be manipulated similarly to electrons and photons, thus enabling controlled heat transport. Moreover, it is explained that phonons can be put to beneficial use to carry and process information. In the first part ways are presented to control heat transport and to process information for physical systems which are driven by a temperature bias. In particular, a toolkit of familiar electronic analogs for use of phononics is put forward, i.e., phononic devices are described which act as thermal diodes, thermal transistors, thermal logic gates, and thermal memories. These concepts are then put to work to transport, control, and rectify heat in physically realistic nanosystems by devising practical designs of hybrid nanostructures that permit the operation of functional phononic devices; the first experimental realizations are also reported. Next, richer possibilities to manipulate heat flow by use of time-varying thermal bath temperatures or various other external fields are discussed. These give rise to many intriguing phononic nonequilibrium phenomena such as, for example, the directed shuttling of heat, geometrical phase-induced heat pumping, or the phonon Hall effect, which may all find their way into operation with electronic analogs.

Thermal rectification and negative differential thermal resistance in lattices with mass gradient

We study thermal properties of one-dimensional (1D) harmonic and anharmonic lattices with a mass gradient. It is found that a temperature gradient can be built up in the 1D harmonic lattice with a mass gradient due to the existence of gradons. The heat flow is asymmetric in anharmonic lattices with a mass gradient. Moreover, in a certain temperature region, negative differential thermal resistance is observed. Possible applications in constructing thermal rectifiers and thermal transistors by using the graded material are discussed.

Anomalous Heat Diffusion

Consider anomalous energy spread in solid phases, i.e., E≡∫(x-E)(2)ρE(x,t)dx∝t(β), 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)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.

Ratcheting heat flux against a thermal bias

Merely rocking the temperature in one heat bath can direct a steady heat flux from cold to hot against a (time-averaged) non-zero thermal bias in stylized nonlinear lattice junctions that are sandwiched between two heat baths. Likewise, for an average zero-temperature difference between the two contacts a net, ratchet-like heat flux emerges. Computer simulations show that this very heat flux can be manipulated and even reversed by suitably tailoring the frequency (100 MHz) of the alternating-temperature field.

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 Poissons ratios with the largest one being double of penta graphene and three times of borophenes. The negative Poissons 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 Poissons ratios and widest band gaps are expected to have great potential applications in nanomechanics and nanoelectronics.

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.

Thermal conductivities of one-dimensional anharmonic/nonlinear lattices: renormalized phonons and effective phonon theory

Heat transport in low-dimensional systems has attracted enormous attention from both theoretical and experimental aspects due to its significance to the perception of fundamental energy transport theory and its potential applications in the emerging field of phononics: manipulating heat flow with electronic anologs. We consider the heat conduction of one-dimensional nonlinear lattice models. The energy carriers responsible for the heat transport have been identified as the renormalized phonons. Within the framework of renormalized phonons, a phenomenological theory, effective phonon theory, has been developed to explain the heat transport in general one-dimensional nonlinear lattices. With the help of numerical simulations, it has been verified that this effective phonon theory is able to predict the scaling exponents of temperature-dependent thermal conductivities quantitatively and consistently.

1D momentum-conserving systems: the conundrum of anomalous versus normal heat transport

Transport and the spread of heat in Hamiltonian one dimensional momentum conserving nonlinear systems is commonly thought to proceed anomalously. Notable exceptions, however, do exist of which the coupled rotator model is a prominent case. Therefore, the quest arises to identify the origin of manifest anomalous energy and momentum transport in those low dimensional systems. We develop the theory for both, the statistical densities for momentum- and energy-spread and particularly its momentum-/heat-diffusion behavior, as well as its corresponding momentum/heat transport features. We demonstrate that the second temporal derivative of the mean squared deviation of the momentum spread is proportional to the equilibrium correlation of the total momentum flux. Subtracting the part which corresponds to a ballistic momentum spread relates (via this integrated, subleading momentum flux correlation) to an effective viscosity, or equivalently, to the underlying momentum diffusivity. We next put forward the intriguing hypothesis: normal spread of this so adjusted excess momentum density causes normal energy spread and alike normal heat transport (Fourier Law). Its corollary being that an anomalous, superdiffusive broadening of this adjusted excess momentum density in turn implies an anomalous energy spread and correspondingly anomalous, superdiffusive heat transport. This hypothesis is successfully corroborated within extensive molecular dynamics simulations over large extended time scales. Our numerical validation of the hypothesis involves four distinct archetype classes of nonlinear pair-interaction potentials: (i) a globally bounded pair interaction (the noted coupled rotator model), (ii) unbounded interactions acting at large distances (the coupled rotator model amended with harmonic pair interactions), (iii) the case of a hard point gas with unbounded square-well interactions and (iv) a pair interaction potential being unbounded at short distances while displaying an asymptotic free part (Lennard–Jones model). We compare our findings with recent predictions obtained from nonlinear fluctuating hydrodynamics theory.

Temperature dependence of thermal conductivity in 1D nonlinear lattices

We examine the temperature dependence of thermal conductivity of one-dimensional nonlinear (anharmonic) lattices with and without on-site potential. It is found from computer simulation that the heat conductivity depends on temperature via the strength of nonlinearity. Based on this correlation, we make a conjecture in the effective phonon theory that the mean-free-path of the effective phonon is inversely proportional to the strength of nonlinearity. We demonstrate analytically and numerically that the temperature behavior of the heat conductivity κ ∝ 1/T is not universal for 1D harmonic lattices with a small nonlinear perturbation. The computer simulations of temperature dependence of heat conductivity in general 1D nonlinear lattices are in good agreement with our theoretic predictions. Possible experimental tests are discussed.

Localization-delocalization transition in self-dual quasi-periodic lattices

Within the framework of the Aubry-Andre model, one kind of self-dual quasi-periodic lattice, it is known that a sharp transition occurs from all eigenstates being extended to all being localized. The common perception for this type of quasi-periodic lattice is that the self-duality excludes the appearance of a finite critical energy separating localized from extended states. In this work, we propose a multi-chromatic quasi-periodic lattice model retaining the self-duality identical to the Aubry-Andre model. In this model we find numerically a well-defined localization-delocalization transition at the mobility edges in contrast with the Aubry-Andre model. As a result, the diffusion of wave packet exhibits a transition from ballistic to diffusive motion, and back to ballistic motion. We point out that experimental realizations of the predicted transition can be accessed with light waves in photonic lattices and matter waves in optical lattices.