Phonon System Research Articles

Ideal topological phononic nodal chain in K2O materials class

Nodal-chain semimetals are characterized by linked nodal rings in Brillouin zone and they have not been reported in the phonon system of atomic crystals yet. Here, based on first-principles calculations and tight-binding model analysis, we propose nearly ideal nodal chains can be realized in the phonon modes of experimentally synthesized ionic crystal K2O materials class. Different from all previous cases, the connection points of the nodal chain in K2O are located at the high symmetry points W and the positions are limited by the symmetries. The nodal rings that forming the nodal chain are symmetrically equivalent and protected by the mirror symmetries. The nontrivial topological properties of nodal chains are validated by the nontrivial Berry phase and surface modes. A general discussion about all symmorphic space groups reveals that, if no more than two inequivalent mirrors exist, Fm m (No. 225) is a unique space group for the appearance of the nodal chain connected at the high symmetry points. Our studies demonstrate that K2O materials class is a wonderful implementable platform to study the nontrivial topological nodal chains in a phonon system.

Progress on nonreciprocity of acoustic metamaterials

Reciprocity is a generic feature in various physical systems because it is directly associated to the symmetry of physical laws under time reversal. The breaking of the reciprocity is vitally important in numerous fields, such as the control of energy flux, imaging technologies and topological insulators. For instance, electrical diodes, as a typical nonreciprocal representative in electronic systems, have already contributed to substantial scientific revolutions in many aspects, including integrated circuits, lighting and signal indication. Motivated by the electrical diodes, thermal diodes exhibiting the rectifying effect on thermal energy are achieved in nonlinear lattices. Similarly, the nonreciprocity in photonic systems can be realized by many mechanisms, such as the nonlinearity of optical medium and the mode conversion. Synchronously, the concept of the nonreciprocity further extends to phononic systems. The main means to achieve acoustic nonreciprocity are based on the nonlinearity of acoustic material, dynamic element, and magnetoelastic interaction. However, the nonlinear approach introduces the inherently low conversion efficiency, the dynamic scheme has difficulty in application at high-speed modulation or on nanoscale, and the method based on magnetoelastic interaction has small bandwidth and high frequency, which have severe limitations for practical application of the nonreciprocity. From the perspectives of principles, history, and problems, this paper reviews in detail the progress of the nonreciprocity based on nonlinearity, dynamic components, and magnetoelastic interactions. Some existing problems with these methods were pointed out. For example, the nonreciprocal solution based on nonlinear media has low energy conversion efficiency, it is difficult to miniaturize the nonreciprocal device based on dynamic components because of itself complexity, and the bandwidth of nonreciprocity based on magnetoelastic interaction is narrow. Correspondingly, improvement of the energy conversion efficiency based on the nonlinear medium, more reasonable design of a dynamic modulation system, and widening broadband of nonreciprocity in the magnetoelastic system, can be researched in the future. For example, in order to reduce the nonreciprocal frequency of magnetoelastic system, it is worth studying the unidirectional transmission of sound waves in the magnetoelastic system under a dynamic magnetic field. For the sake of realizing a nonreciprocal system with no external power source and high conversion efficiency, the nonreciprocity of acoustic waves in a magnetoelastic system under a zero magnetic field may become a focus of future research. In addition, since each scheme has its advantages, the combined effects of multiple schemes may overcome the shortcomings of a single scheme and achieve more significant nonreciprocal effects. So far, the combined effects between nonlinearity and dynamic components have not received much attention. We expect that research of nonreciprocity will be extended to both nonlinear and spatiotemporally modulated systems in the future. The combined effects between nonreciprocity and magnetoelastic interaction may become an important content of future research. Finally, considering practical engineering application, there are still many aspects worthy of further study, such as the miniaturization of nonreciprocal devices, optimal design of nonreciprocity based on optimization theory, and adjustable nonreciprocity based on smart materials or structures. In short, the nonreciprocity of acoustic metamaterials is an important field of scientific research, which has potential applications, such as rectification, vibration and noise reduction, sensing, and bioimaging.

Classification and materials realization of topologically robust nodal ring phonons

Nodal ring phonons with topologically nontrivial properties have triggered much interest in recent years. Unlike fermions inevitably affected by the spin-orbit interaction, nodal ring phonons are topologically robust. In this paper, we investigate the classification of nodal rings in phonon systems based on symmetry arguments and $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ models. We identify that all the nodal ring phonons can be categorized into three types, i.e., in-plane nodal rings protected by mirror symmetry, twisted nodal rings protected by inversion and time-reversal symmetries, and the hybrid type protected by a combination of these symmetries. On the basis of first-principles calculations, we propose that these three types of nodal ring phonons can emerge in two different phases of silver oxide. The calculation results also show clear drumheadlike surface states along high-symmetry paths and nontrivial arc states in the isofrequency surfaces. This work exposes various appearances of nodal rings and also promotes the development of topological phonons.

Coexistence of phononic sixfold, fourfold, and threefold excitations in the ternary antimonide Zr3Ni3Sb4

Three-, four-, and sixfold excitations have significantly extended the subjects of condensed-matter physics. There is an urgent need for a realistic material that can have coexisting three-, four-, and sixfold excitations. However, these materials are uncommon because these excitations in electronic systems are usually broken by spin-orbit coupling (SOC) and are normally far from the Fermi level. Unlike the case in electronic systems, phonon systems with a negligible SOC effect, not constrained by the Pauli exclusion principle, provide a feasible platform to realize these excitations in a wide frequency range. Hence, in this work, we demonstrate by first-principles calculations and symmetry analysis that perfect three-, four-, sixfold excitations appear in the phonon dispersion rather than the band structures of ${\mathrm{Zr}}_{3}{\mathrm{Ni}}_{3}{\mathrm{Sb}}_{4}$, which is a well-known indirect-gap semiconductor with an ${\mathrm{Y}}_{3}{\mathrm{Au}}_{3}{\mathrm{Sb}}_{4}$-type structure. This material features a threefold-degenerate quadratic contact triple-point phonon, fourfold-degenerate Dirac point phonon, and sixfold degenerate point phonon. Moreover, these nodal point phonons are very robust to uniform strain. Two obvious phonon surface arcs of the (001) plane are extended in the whole Brillouin zone, which will facilitate their detection in future experimental studies. The current work provides an ideal model to investigate rich excitations in a single material.

Atomic-Level, Energy-Conversion Heat Transfer

Abstract Heat is stored in quanta of kinetic and potential energies in matter. The temperature represents the equilibrium and excited occupation (boson) of these energy conditions. Temporal and spatial temperature variations and heat transfer are associated with the kinetics of these equilibrium excitations. During energy-conversion (between electron and phonon systems), the occupancies deviate from equilibria, while holding atomic-scale, inelastic spectral energy transfer kinetics. Heat transfer physics reaches nonequilibrium energy excitations and kinetics among the principal carriers, phonon, electron (and holes and ions), fluid particle, and photon. This allows atomic-level tailoring of energetic materials and energy-conversion processes and their efficiencies. For example, modern thermal-electric harvesters have transformed broad-spectrum, high-entropy heat into a narrow spectrum of low-entropy emissions to efficiently generate thermal electricity. Phonoelectricity, in contrast, intervenes before a low-entropy population of nonequilibrium optical phonons becomes a high-entropy heat. In particular, the suggested phonovoltaic cell generates phonoelectricity by employing the nonequilibrium, low-entropy, and elevated temperature optical-phonon produced population—for example, by relaxing electrons, excited by an electric field. A phonovoltaic material has an ultranarrow electronic bandgap, such that the hot optical-phonon population can relax by producing electron-hole pairs (and power) instead of multiple acoustic phonons (and entropy). Examples of these quanta and spectral heat transfer are reviewed, contemplating a prospect for education and research in this field.

About the Definition of the Local Equilibrium Lattice Temperature in Suspended Monolayer Graphene.

The definition of temperature in non-equilibrium situations is among the most controversial questions in thermodynamics and statistical physics. In this paper, by considering two numerical experiments simulating charge and phonon transport in graphene, two different definitions of local lattice temperature are investigated: one based on the properties of the phonon–phonon collision operator, and the other based on energy Lagrange multipliers. The results indicate that the first one can be interpreted as a measure of how fast the system is trying to approach the local equilibrium, while the second one as the local equilibrium lattice temperature. We also provide the explicit expression of the macroscopic entropy density for the system of phonons, by which we theoretically explain the approach of the system toward equilibrium and characterize the nature of the equilibria, in the spatially homogeneous case.

Hot-Carrier Cooling in High-Quality Graphene Is Intrinsically Limited by Optical Phonons.

Many promising optoelectronic devices, such as broadband photodetectors, nonlinear frequency converters, and building blocks for data communication systems, exploit photoexcited charge carriers in graphene. For these systems, it is essential to understand the relaxation dynamics after photoexcitation. These dynamics contain a sub-100 fs thermalization phase, which occurs through carrier–carrier scattering and leads to a carrier distribution with an elevated temperature. This is followed by a picosecond cooling phase, where different phonon systems play a role: graphene acoustic and optical phonons, and substrate phonons. Here, we address the cooling pathway of two technologically relevant systems, both consisting of high-quality graphene with a mobility >10 000 cm2 V–1 s–1 and environments that do not efficiently take up electronic heat from graphene: WSe2-encapsulated graphene and suspended graphene. We study the cooling dynamics using ultrafast pump–probe spectroscopy at room temperature. Cooling via disorder-assisted acoustic phonon scattering and out-of-plane heat transfer to substrate phonons is relatively inefficient in these systems, suggesting a cooling time of tens of picoseconds. However, we observe much faster cooling, on a time scale of a few picoseconds. We attribute this to an intrinsic cooling mechanism, where carriers in the high-energy tail of the hot-carrier distribution emit optical phonons. This creates a permanent heat sink, as carriers efficiently rethermalize. We develop a macroscopic model that explains the observed dynamics, where cooling is eventually limited by optical-to-acoustic phonon coupling. These fundamental insights will guide the development of graphene-based optoelectronic devices.

Higher-order band topology

A conventional topological insulator (TI) has gapped bulk states but gapless edge states. The emergence of the gapless edge states is dictated by the bulk topological invariant of the insulator and the preservation of relevant symmetries. Over the past four years, a new type of TI has been found, which hosts gapless hinge or corner states, rather than edge states. These unconventional TIs, termed higher-order TIs (HOTIs), are common among crystalline and quasi-crystalline materials. Higher-order band topology expands our previous understanding of topological phases and provides unprecedented lower-dimensional boundary states for devices. Here, we review the principles, theories and experimental realizations of HOTIs for both electrons and classical waves. There is an emphasis on the development of HOTIs in photonic, phononic and circuit systems owing to their special contributions to these fields. From these discussions, we remark on trends and challenges in the field and the impact of higher-order band topology on other scientific disciplines.

Topological cavities in phononic plates for robust energy harvesting

Piezoelectric energy harvesting has attracted tremendous interest for designing sustainable self-powered devices/systems targeted to special environment such as wireless or wearable applications. The traditional cavity (e.g., phononic cavity mode) excitation is highly applicable in terms of sufficient power generation, nevertheless, has to endure the drawback of extremely poor robustness intrinsic to the trivial cavity modes. We propose to use phononic thin plate systems for robust energy harvesting application relying on zero-dimensional cavities confined by the Kekulé distorted topological vortices. The harvesting power induced by topological cavities is about 30 times that of the bare plate. Further studies on the effects of deliberately introduced defects on the output power show that the proposed energy harvesting system is highly robust against symmetry-preserving defects, and is less influenced even for symmetry-breaking defects at moderate perturbation level. Beyond the reported energy harvesting application, we foresee that our work may open avenues for robust operations in the realm of wireless sensing and structural health monitoring.

Three-Dimensional Dirac Phonons with Inversion Symmetry.

Dirac semimetals associated with bulk Dirac fermions are well known in topological electronic systems. In sharp contrast, three-dimensional (3D) Dirac phonons in crystalline solids are still unavailable. Here we perform symmetry arguments and first-principles calculations to systematically investigate 3D Dirac phonons in all space groups with inversion symmetry. The results show that there are two categories of 3D Dirac phonons depending on their protection mechanisms and positions in momentum space. The first category originates from the four-dimensional irreducible representations at the high symmetry points. The second category arises from the phonon branch inversion, and the symmetry guarantees Dirac points to be located along the high symmetry lines. Furthermore, we reveal that nonsymmorphic symmetries and the combination of inversion and time-reversal symmetries play essential roles in the emergence of 3D Dirac phonons. Our work not only offers a comprehensive understanding of 3D Dirac phonons but also provides significant guidance for exploring Dirac bosons in both phononic and photonic systems.

Границы применимости теории Элиашберга и ограничения на температуру сверхпроводящего перехода

The discovery of record - breaking values of superconducting transition temperature $T_c$ in quite a number of hydrides under high pressure was an impressive demonstration of capabilities of electron - phonon mechanism of Cooper pairing. This lead to an increased interest to foundations and limitations of Eliashberg - McMillan theory as the main theory describing superconductivity in a system of electrons and phonons. Below we shall consider both elementary basics of this theory and a number of new results derived only recently. We shall discuss limitations on the value of the coupling constant related to lattice instability and a phase transition to another phase (CDW, bipolarons). Within the stable metallic phase the effective pairing constant may acquire arbitrary values. We consider extensions beyond the traditional adiabatic approximation. It is shown that Eliasberg - McMillan theory is also applicable in the strong antiadiabatic limit. The limit of very strong coupling, being most relevant for the physics of hydrides, is analyzed in details. We also discuss the bounds for $T_c$ appearing in this limit.

Charge-four Weyl phonons

By using ab initio calculations and symmetry analysis, we define a class of Weyl phonons: charge-four Weyl phonons (CFWPs) characterized by Chern number $\ifmmode\pm\else\textpm\fi{}4$ in their acoustic phonon spectra due to chiral point-group symmetries. Some high-symmetry points in the chiral space groups (SGs) of phononic systems behaving as quadratic Weyl points tend to form CFWPs. As enumerated in this paper, the CFWPs are located at the boundaries or the center of the three-dimensional Brillouin zone and are protected by the time-reversal symmetry $\mathcal{T}$ and the corresponding point-group symmetries. Moreover, in a realistic chiral crystal example of BiIrSe in SG 198, a monopole CFWP is confirmed at point $\mathrm{\ensuremath{\Gamma}}$ with quadratic twofold degeneracies, and in another example of ${\mathrm{Li}}_{3}{\mathrm{CuS}}_{2}$ in SG 214, the CFWPs are found at the high-symmetry points $\mathrm{\ensuremath{\Gamma}}$ and $H$. Our theoretical results not only uncover a class of Weyl phonons but also put forward an effective way to search for CFWPs in spinless systems.

Effect of spin–phonon coupling on quantum correlation in the spin-1 XY model

The XY model coupled with an external system as a phonon system may be studied in terms of its own variables only. Hence, the effect of phonons external in such system can be included in a general class of functionals of the coordinates of the system only. The specific form of this influence functional representing the effect of definite and random forces of a linear dissipative system and combination of these are analyzed in detail. Thus the effect of the spin–phonon interaction on entanglement is investigated where we obtain a small effect of the spin–phonon coupling on von Neumann entropy.

Real spin angular momentum and acoustic spin torque in a topological phononic crystal

The topological one-way waveguide mode of the acoustic wave has recently been demonstrated in various meta-structure systems. Here, we show that in a topological phononic crystal with a symmetry-broken acoustic unit cell, the topological state possesses not just a “spin-like” pseudospin mode but also real spin angular momentum. By rotating the double-square units, the band of the phononic crystal will become inverse and induce both topological phase transition and spin angular momentum reversal. As such, by putting two topologically different systems together, the spin angular momentum dependent one-way interface modes can be selectively excited by acoustic spin sources, exhibiting robust transport protected by tight spin-momentum locking. The spin angular momentum density distribution in the unit cell and edge states shows that in addition to the pseudospin, there is a strong correlation between the real spin angular momentum and topological properties in this acoustic system, producing the topologically selective acoustic torque. Revealing the real spin angular momentum and associated acoustic spin torque properties of these topological phononic and acoustic systems will give people a more general understanding about symmetric breaking wave systems and help people to explore more potential applications of acoustic spins in various topological systems.

Photonic crystals with a touch of topology

Topological Materials Manmade photonic crystals offer a flexible platform for controlling the propagation and flow of light. Such control can be extended across the electromagnetic spectrum by correctly engineering the bandgap. Limitations in the fabrication process, however, can result in structural imperfections that allow the light or energy to leak out. Wang et al. add magnetism to the mix to form heterostructures of magnetic photonic crystals. They demonstrate that, for microwaves, this magnetic addition provides a topological aspect to the band structure, resulting in the propagation of the microwaves in one direction that is robust to defects. The ability to controllably route and collimate electromagnetic waves also could be applied to electronic and phononic waveguide systems. Phys. Rev. Lett. 126 , 067401 (2021).

Computation and data driven discovery of topological phononic materials

The discovery of topological quantum states marks a new chapter in both condensed matter physics and materials sciences. By analogy to spin electronic system, topological concepts have been extended into phonons, boosting the birth of topological phononics (TPs). Here, we present a high-throughput screening and data-driven approach to compute and evaluate TPs among over 10,000 real materials. We have discovered 5014 TP materials and grouped them into two main classes of Weyl and nodal-line (ring) TPs. We have clarified the physical mechanism for the occurrence of single Weyl, high degenerate Weyl, individual nodal-line (ring), nodal-link, nodal-chain, and nodal-net TPs in various materials and their mutual correlations. Among the phononic systems, we have predicted the hourglass nodal net TPs in TeO3, as well as the clean and single type-I Weyl TPs between the acoustic and optical branches in half-Heusler LiCaAs. In addition, we found that different types of TPs can coexist in many materials (such as ScZn). Their potential applications and experimental detections have been discussed. This work substantially increases the amount of TP materials, which enables an in-depth investigation of their structure-property relations and opens new avenues for future device design related to TPs.

Gigahertz Phononic Integrated Circuits on Thin-Film Lithium Niobate on Sapphire

Acoustic devices play an important role in classical information processing. The slower speed and lower losses of mechanical waves enable compact and efficient elements for delaying, filtering, and storing of electric signals at radio and microwave frequencies. Discovering ways of better controlling the propagation of phonons on a chip is an important step towards enabling larger scale phononic circuits and systems. We present a platform, inspired by decades of advances in integrated photonics, that utilizes the strong piezoelectric effect in a thin film of lithium niobate on sapphire to excite guided acoustic waves immune from leakage into the bulk due to the phononic analogue of index-guiding. We demonstrate an efficient transducer matched to 50 ohm and guiding within a 1-micron wide mechanical waveguide as key building blocks of this platform. Putting these components together, we realize acoustic delay lines, racetrack resonators, and meander line waveguides for sensing applications. To evaluate the promise of this platform for emerging quantum technologies, we characterize losses at low temperature and measure quality factors on the order of 50,000 at 4 kelvin. Finally, we demonstrate phononic four-wave mixing in these circuits and measure the nonlinear coefficients to provide estimates of the power needed for relevant parametric processes.

Spin-lattice dynamics model with angular momentum transfer for canonical and microcanonical ensembles

A unified model of molecular and atomistic spin dynamics is presented enabling simulations both in microcanonical and canonical ensembles without the necessity of additional phenomenological spin damping. Transfer of energy and angular momentum between the lattice and the spin systems is achieved by a coupling term based upon the spin-orbit interaction. The characteristic spectra of the spin and phonon systems are analyzed for different coupling strength and temperatures. The spin spectral density shows magnon modes together with the uncorrelated noise induced by the coupling to the lattice. The effective damping parameter is investigated showing an increase with both coupling strength and temperature. The model paves the way to understanding magnetic relaxation processes beyond the phenomenological approach of the Gilbert damping and the dynamics of the energy transfer between lattice and spins.

“Fuzzy Band Gaps”: A Physically Motivated Indicator of Bloch Wave Evanescence in Phononic Systems

Phononic crystals (PCs) have been widely reported to exhibit band gaps, which for non-dissipative systems are well defined from the dispersion relation as a frequency range in which no propagating (i.e., non-decaying) wave modes exist. However, the notion of a band gap is less clear in dissipative systems, as all wave modes exhibit attenuation. Various measures have been proposed to quantify the “evanescence” of frequency ranges and/or wave propagation directions, but these measures are not based on measurable physical quantities. Furthermore, in finite systems created by truncating a PC, wave propagation is strongly attenuated but not completely forbidden, and a quantitative measure that predicts wave transmission in a finite PC from the infinite dispersion relation is elusive. In this paper, we propose an “evanescence indicator” for PCs with 1D periodicity that relates the decay component of the Bloch wavevector to the transmitted wave amplitude through a finite PC. When plotted over a frequency range of interest, this indicator reveals frequency regions of strongly attenuated wave propagation, which are dubbed “fuzzy band gaps” due to the smooth (rather than abrupt) transition between evanescent and propagating wave characteristics. The indicator is capable of identifying polarized fuzzy band gaps, including fuzzy band gaps which exists with respect to “hybrid” polarizations which consist of multiple simultaneous polarizations. We validate the indicator using simulations and experiments of wave transmission through highly viscoelastic and finite phononic crystals.

Quantum dynamics of electric-dipole coupled defect centers in solids

We investigate the quantum dynamics of two defect centers in solids, which are coupled by vacuum-induced dipole–dipole interactions. When the interaction between defects and phonons is taken into account, the two coupled electron–phonon systems make up two equivalent multilevel atoms. By making Born–Markov and rotating wave approximations, we derive a master equation describing the dynamics of the coupled multilevel atoms. The results indicate the concepts of subradiant and superradiant states can be applied to these systems and the population transfer process presents different behaviors from those of the two dipolar-coupled two-level atoms due to the participation of phonons.