Phonon System Research Articles

Enhancement of magnon–photon–phonon entanglement in a cavity magnomechanics with coherent feedback loop

In this paper, we present a coherent feedback loop scheme to enhance the magnon–photon–phonon entanglement in cavity magnomechanics. We provide a proof that the steady state and dynamical state of the system form a genuine tripartite entanglement state. To quantify the entanglement in the bipartite subsystem and the genuine tripartite entanglement, we use the logarithmic negativity and the minimum residual contangle, respectively, in both the steady and dynamical regimes. We demonstrate the feasibility of our proposal by implementing it with experimentally realizable parameters to achieve the tripartite entanglement. We also show that the entanglement can be significantly improved with coherent feedback by appropriately tuning the reflective parameter of the beam splitter and that it is resistant to environmental thermalization. Our findings pave the way for enhancing entanglement in magnon–photon–phonon systems and may have potential applications in quantum information.

Optomechanical Generation of Coherent GHz Vibrations in a Phononic Waveguide.

Nanophononics has the potential for information transfer, in an analogous manner to its photonic and electronic counterparts. The adoption of phononic systems has been limited, due to difficulties associated with the generation, manipulation, and detection of phonons, especially at GHz frequencies. Existing techniques often require piezoelectric materials with an external radiofrequency excitation that are not readily integrated into existing CMOS infrastructures, while nonpiezoelectric demonstrations have been inefficient. In this Letter, we explore the optomechanical generation of coherent phonons in a suspended 2D silicon phononic crystal cavity with a guided mode around 6.8GHz. By incorporating an air-slot into this cavity, we turn the phononic waveguide into an optomechanical platform that exploits localized photonic modes resulting from inherent fabrication imperfections for the transduction of mechanics. Such a platform exhibits very fine control of phonons using light, and is capable of coherent self-sustained phonon generation around 6.8GHz, operating at room temperature. The ability to generate high frequency coherent mechanical vibrations within such a simple 2D CMOS-compatible system could be a first step towards the development of sources in phononic circuitry and the coherent manipulation of other solid-state properties.

Theory of Energy Dispersion of Chiral Phonons

We have developed a microscopic theory on phonon energy dispersion in chiral crystals within a harmonic approximation. One of the main issues is about the splitting of sound velocity of acoustic phonons with opposite ``crystal'' angular momentum. We have shown that the splitting must be zero even in chiral crystals and the difference starts from the order of at least $k^2$ or higher in their energy dispersion. Splitting is evident for chiral optical phonons, and we have derived a formula for their $k$-linear splitting. Another important finding is about possible interactions of atomic displacements in microscopic models. We have found that antisymmetric interactions of $\mathbf{D} _{ij} \cdot (\mathbf{d} _i \times \mathbf{d} _j) $ type are not allowed in microscopic Hamiltonians for chiral phonons in compatible with the stability against the Nambu-Goldstone mode. We have identified that the splitting in both acoustic and optical modes arises from the harmonic potentials with the electric toroidal quadrupole of $G_{u}$-type symmetry. These constraint are important for modeling real materials. Most of our microscopic calculations have been performed for (quasi-)one-dimensional systems with a trigonal crystal symmetry including Te, but these results generally hold also for other chiral phonon systems.

Ultrafast thermalization dynamics in Au/Ni film excited by femtosecond laser double-pulse vortex beam

We theoretically investigated ultrafast thermalization dynamics of spatio-temporal evolutions of temperature fields in typical Au/Ni film excited by femtosecond laser double-pulse vortex beam. It is proposed that the enhanced energy deposition in the layered Au/Ni film can be unprecedentedly facilitated via applying femtosecond laser double-pulse vortex beam, preferentially giving rise to vortical thermalization for the phonon system of bottom Ni layer on picosecond timescale. It can be explained as the intensified dynamics of double-pulse vortex beam interacting with the excited intermediate state of Au/Ni film and the following energy competitive processes of the electron thermal diffusion and the electron-phonon coupling in respective layers. Moreover, the electron-phonon coupling period of Au/Ni film with respect to the crucial laser parameters of pulse separation and vortex beam fluence are explored in details. The results can be basically helpful for understanding the ultrafast dynamics of vortical thermalization for advancing the potential applications of compound-cavity fabrication, stimulated emission depletion (STED) imaging and ultrahigh time-resolved spectroscopy, etc.

Underlying mechanism of the driving force for generating spin currents thermally in a ferrimagnetic insulator due to a temperature gradient

We previously proposed the idea that the effective thermal-energy transfer from the phonon system to the spin system in liquid phase epitaxial (LPE) films of Bi-substituted yttrium iron garnet (Bi:YIG), a ferrimagnetic insulator, takes place through enhanced spin-orbit coupling (SOC) with local 3d-electron spins in Fe3+ ions, and that the spin-thermoelectric (STE) generation in a paramagnetic platinum (Pt) layer is raised by increased spin pumping to the Pt layer from the Bi:YIG film. However, we could not specifically relate the underlying mechanism to the driving force for the generation of spin currents due to nonequilibrium dynamics of magnons driven by the temperature gradient ∇T in a magnetic insulator. In this paper, we discuss the origin of the driving force for generating spin currents, which are increased through enhanced SOC in LPE yttrium iron garnet films.

P T symmetry in a superconducting hybrid quantum system with longitudinal coupling.

We propose a scheme consisting of coupled nanomechanical cantilever resonators and superconducting flux qubits to engineer a parity-time- (P T-) symmetric phononic system formed by active and passive modes. The effective gain (loss) of the phonon mode is achieved by the longitudinal coupling of the resonator and the fast dissipative superconducting qubit with a blue-sideband driving (red-sideband driving). A P T-symmetric to broken-P T-symmetric phase transition can be observed in both balanced gain-to-loss and unbalanced gain-to-loss cases. Applying a resonant weak probe field to the dissipative resonator, we find that (i) for balanced gain and loss, the acoustic signal absorption to amplification can be tuned by changing the coupling strength between resonators; (ii) for unbalanced gain and loss, both acoustically induced transparency and anomalous dispersion can be observed around Δ = 0, where the maximum group delay is also located at this point. Our work provides an experimentally feasible scheme to design P T-symmetric phononic systems and a powerful platform for controllable acoustic signal transmission in a hybrid quantum system.

A LINDBLADIAN OPERATOR FOR OPEN SYSTEM THERMALIZATION, WITH APPLICATIONS

A general phenomenological expression is provided, within the frame of the Gorini-Kossakowski-Sudarshan-Lindblad formalism, for the time (t) development of the density operator ρ(t) during thermalization, namely the process such that an open system with arbitrary initial states, when coupled to a thermal bath, ρ (t -> ∞) takes up a Gibbsian form. The theory is applied to a molecular vibrating system, to a semi-classical vibronic entity, and may be applied to the excitation probabilities in a condensed state’s phonon system and to arbitrarily large-scale systems (reaching as far as global warming). A sideline is to an entropy-decreasing Maxwell-demon type quantum state transition. While the prescription may not be unique, it gives rise to an experimentally testable non-monotonicity in the system’s information entropy. The calculated entropy maximum found for an electronic doublet is interpreted as a “transient democratization” of the states and, though lacking a formal proof, a conjecture is proposed for the occurrence of maxima in general instances.

Experimental realization of an additively manufactured monatomic lattice for studying wave propagation

Increasing interest in wave propagation in phononic systems and metamaterials motivates the development of experimental designs, measurement techniques, and fabrication methods for use in basic research and classroom demonstrations. The simplest phononic system, the monatomic chain, exhibits rich physics such as dispersion and frequency-domain filtering. However, a limited number of experimental studies showcase monatomic chains for macroscale observation of phonons. Herein, we discuss the design, fabrication, and testing of monatomic lattices as enabled by three-dimensional (3D) printing. Using this widely available technology, we provide design guidelines for realization of a monatomic chain composed of 3D printed serpentine springs and press-fitted cylindrical masses. We also present measurement techniques that record propagating waves and algorithms for the experimental determination of dispersion behavior.

Dirac phonons in two-dimensional materials

Phonons are an ideal platform for realizing stable spinless two-dimensional (2D) Dirac points because they have a bosonic nature and hard-to-break time-reversal symmetry. It should be noted that the twofold degenerate nodal points in the phonon dispersions of almost all reported 2D materials are misclassified as ``Dirac points'' owing to a historical issue. The correct name for these twofold degenerate nodal points should be ``Weyl'' because 2D phononic systems are essentially spinless and because each twofold degenerate point is described by a Weyl model in two dimensions. To date, reports of fourfold degenerate Dirac point phonons in 2D materials are lacking. In this paper, we searched through all 80 layer groups (LGs) and discovered that Dirac phonons can be realized in 7 of the 80 LGs. Moreover, the Dirac points in the phonon dispersions of 2D materials can be divided into essential and accidental degenerate points, which appear at high-symmetry points and on high-symmetry lines, respectively. Guided by symmetry analysis, we identified the presence of Dirac phonons in several 2D material candidates with six LGs. This work offers a method for identifying Dirac phonons in 2D and proposes 2D material candidates for realizing Dirac phonons.

Magnon-Phonon-Interaction-Induced Electromagnetic Wave Radiation in the Strong-Coupling Region

We theoretically study the electromagnetic wave radiation of magnons driven by acoustic phonons in systems with strong magnon-phonon interaction. We evaluate the field dependence of radiation intensity spectra that exhibits the avoided crossing, a characteristic of strongly coupled systems. At the crossover where the magnon and phonon eigenstates are hybridized, we demonstrate the existence of two resonant radiation frequencies with circular polarization and the enhancement of antenna radiation efficiency by over 100 times. We can also reconfigure the ellipticity of the antenna polarization by changing the applied out-of-plane magnetic field. Our results open up possibilities of developing ultracompact antennas by using the hybridized magnon-phonon mode.

Multiple Open and Closed Nodal‐Line Phonons in Solids with a 1 Space Group

AbstractUnlike electron systems, the phonon system has its own advantages (such as no limitations regarding Fermi energy and the effect of spin‐orbit coupling) and, therefore, can be viewed as a unique platform to predict spinless nodal‐line states. Nodal‐line phonons can be divided into open and closed nodal‐line phonons from a mathematical point of view. In this work, using first‐principle calculations, we select Ba(AgS)2 and Ca(ZnP)2, with the space group 1, as examples of realistic materials to investigate the difference between the open and closed nodal‐line phonons. Two phonon band‐crossing points (PBCPs) along the K–Γ and H–A paths are present in their phonon spectra, and they correspond to closed nodal lines in Ba(AgS)2 and open nodal lines in Ca(ZnP)2, respectively. The difference between these two types nodal‐line phonons is explained through symmetry analysis. All the nodal‐line phonons are topologically nontrivial, with the prominent phonon surface states well separated from the bulk states, favorable for experimental detection. This work offers a deep understanding of the open and closed nodal‐line phonons. It also proposes ideal candidates with multiple open and closed nodal‐line phonons for follow‐up experimental confirmation.

Symmetry-enforced planar nodal chain phonons in non-symmorphic materials

Nodal chains in which two nodal rings connect at one point were recently discovered in non-symmorphic electronic systems and then generalized to symmorphic phononic systems. In this work, we identify a new class of planar nodal chains in non-symmorphic phononic systems, where the connecting rings lie in the same plane. The constituting nodal rings are protected by mirror symmetry, and their intersection is guaranteed by the combination of time-reversal and non-symmorphic twofold screw symmetry. The connecting points are fourfold degenerate while those in previous works are twofold degenerate. We found 8 out of 230 space groups that can host the proposed planar nodal chain phonons. Taking wurtzite GaN (space group No. 186) as an example, the planar nodal chain is confirmed by first-principles calculations. The planar nodal chains result in two distinct classes of drumhead surface states on the [10(–1)0] and the [0001] surface Brillouin zones. Our finding reveals a class of planar nodal chains in non-symmorphic phononic systems, expanding the catalog of topological nodal chains and enriching the family of topological surface states.

Non-reciprocal frequency conversion in a two-dimensional waveguide incorporating a local nonlinear gate

We study non-reciprocal frequency conversion in a linear two-dimensional (2D) acoustic waveguide consisting of coupled oscillators incorporating a local asymmetric gate of nonlinearly coupled oscillators. The 2D waveguide supports an acoustic and an optical frequency band. We consider a monochromatic harmonic excitation at the acoustic band that initiates a propagating wave in the linear waveguide. As the wave scatters across the nonlinear gate, its frequency is converted to a higher (triple) harmonic in the optical band. This frequency conversion is due to a local 1:3 internal resonance at the nonlinear gate. The efficacy and robustness of the frequency conversion are validated by direct numerical simulations. A large portion of the energy of the wave is transmitted across the nonlinear gate with converted frequency and this frequency conversion is realized robustly over a range of excitation frequencies and magnitudes. In addition, owing to the nonlinearity, the frequency conversion is tunable to frequency and energy. The transmissibility (i.e., transmitted over reflected energy at the gate) is sensitive to the excitation parameters indicative of bifurcations of the nonlinear acoustics. Lastly, frequency conversion induces strong non-reciprocity in the acoustics since the energy transfer with frequency conversion is only realizable in a preferred direction of wave propagation and prohibited in the reverse direction. The methodology and results of the present nonlinear frequency converter are applicable to various fields including targeted energy transfer in phononic systems and acoustic computing.

Phononic Stiefel-Whitney topology with corner vibrational modes in two-dimensional Xenes and ligand-functionalized derivatives

Two-dimensional (2D) Stiefel-Whitney (SW) insulator is a fragile topological state characterized by the second SW class in the presence of space-time inversion symmetry. So far, SWIs have been proposed in several electronic materials but seldom in phononic systems. Here we recognize that a large class of 2D buckled honeycomb crystals termed Xenes and their ligand-functionalized derivatives realize the nontrivial phononic SW topology. The phononic SWIs are identified by a nonzero second SW number $w_2=1$, associated with gaped edge states and robust topological corner modes. Despite the versatility of electronic topological properties in these materials, the nontrivial phononic SW topology is mainly attributed to the double band inversion between in-plane acoustic and out-of-plane optical bands with opposite parities due to the structural buckling of the honeycomb lattice. Our findings not only reveal an overlooked phononic topological property of 2D Xene-related materials, but also afford abundant readily synthesizable material candidates with simple phononic spectra for further experimental studies of phononic SW topology physics.

Single pair of multi-Weyl points in nonmagnetic crystals

Topological semimetal states having the minimal number, i.e., only a single pair, of Weyl points are desirable for the study of effects associated with chiral topological charges. So far, the search for such states is focused on magnetic spinful systems. Here, we find that nonmagnetic spinless systems can host a class of single-pair-Weyl-point (SP-WP) states, where the two Weyl points are located at two high-symmetry time-reversal-invariant momenta. We identify 32 candidate space groups that host such states, and we show that the chiral charge of each Weyl point in the SP-WP state must be an even integer. Besides achieving the minimal number, Weyl points in SP-WP states are far separated in momentum space, making the physics of each individual point better exposed. The large separation combined with the even topological charge lead to extended surface Fermi loops with a non-contractible winding topology on the surface Brillouin zone torus, distinct from conventional Weyl semimetals. We confirm our proposal in the phonon spectra of two concrete materials TlBO$_2$ and KNiIO$_6$. Our finding applies to a wide range of systems, including electronic, phononic, and various artificial systems. It offers a new direction for the search of ideal platforms to study chiral particles.

Physics of phonons in systems with approximate screw symmetry

Properties of systems with exact n-fold screw symmetry (n=2, 3, 4, 6) have been well studied because they can be understood in terms of space groups. On the other hand, existence of materials with approximate screw symmetries, such as 7-fold and 10-fold screw symmetries, has been predicted. In this paper, we study properties of phonons in crystals with approximate screw symmetries, which will lead to unique and new physical phenomena. In a crystal with an approximate screw symmetry, we propose a method to extract information of pseudoangular momentum of phonons, which is a quantum number characterizing the properties of phonon modes under screw symmetry, based on the fact that the information of the quantum numbers defined under exact screw symmetry partially remains in the eigenvectors of approximate screw symmetric systems. As a preparation, we study a one-dimensional crystal with partially broken translation symmetry to have an enlarged unit cell, and we show how to extract information of a quantum number corresponding to the pseudoangular momentum, by studying a relative phase between neighboring atoms. We also extend this method to systems with an approximate screw symmetry, and discuss properties of the pseudoangular momentum. We apply this method to results of our first-principle calculations on candidate materials with an approximate translational symmetry or with an approximate screw symmetry, and show how this approximate symmetry is reflected in the phonon wavefunctions.

Non-equilibrium phonon distribution caused by an electrical current

In an attempt to explain flash sintering experiments, it had been proposed that the electron–phonon coupling leads to a proliferation of short wave-length lattice vibrations in an electric field. In this paper we investigate this by solving two coupled Boltzmann equations, describing a free electron gas in an electric field scattering from a crystal lattice coupled to a heat bath. The electric field imposes cylindrical symmetry and drives the electrons and the phonons into a non-equilibrium steady state. We find that the phonon distribution shows a strong excess population at the Brillouin zone edge in the direction of the electric field. We argue analytically, that this can be traced back to the shifted Fermi sphere for the electrons. Furthermore, not only energy but also momentum is exchanged in the electron–phonon system, which defies any attempt at describing the system by a two-temperature model.

Dirac point phonons at high-symmetry points: Towards materials realization

Dirac point semimetals and related Fermi arc surface states are extremely important in topological electronic systems. In 2021, Chen et al. [Phy. Rev. Lett. 126, 185301 (2021)] proposed that Dirac points can appear on high-symmetry lines (HSLs) or at high-symmetry points (HSPs) in three-dimensional (3D) phonon systems as an extension from Dirac points in electronic systems. Inspired by this work, we present an exhaustive list of Dirac point phonons (DPPs) at HSPs in 230 space groups (SGs) by checking the encyclopedia of emergent particles in 3D crystals. The DPPs are divided into four categories: charge-zero (C-0) DPPs, charge-two (C-2) DPPs, quadratic DPPs (QDPPs), and cubic crossing DPPs (CCDPPs). 29 SGs, 6 SGs, 19 SGs, and 5 SGs are identified as candidate SGs for obtaining C-0 DPPs, C-2 DPPs, QDPPs, and CCDPPs at HSPs, respectively. Importantly, herein we contribute to the realization of materials with DPPs at HSPs and through the following: (i) we propose five realistic materials, namely, $Pna{2}_{1}$-type ${\mathrm{Li}}_{3}{\mathrm{AsS}}_{3}, P{2}_{1}$-type NiSbS, $P\overline{4}{2}_{1}c$-type ${\mathrm{NaBH}}_{4}$, and $Pm\overline{3}n$-type ${\mathrm{Ti}}_{3}\mathrm{Au}$ and ${\mathrm{Ta}}_{3}\mathrm{Sn}$ as materials with C-0 DPPs, C-2 DPPs, QDPPs, and CCDPPs at HSPs, respectively, based on the first-principles calculations. The surface states for these five materials are also examined in this work. (ii) We present 626 candidates with C-0 DPPs, 183 candidates with C-2 DPPs, 433 candidates with QDPPs, and 102 candidates with CCDPPs at HSPs, which were discovered by checking the phonon dispersions of 10 037 materials listed in the phonon database at Kyoto University. (iii) Due to the materials with SGs 103, 104, 106, 158, 184, 222, 223, 226, and 228 are not included in the phonon database at Kyoto University, we propose 18 candidates with C-0 DPPs, 5 candidates with QDPPs, and 8 candidates with CCDPPs at HSPs with above-mentioned SGs by screening the Inorganic Crystal Structure Database (ICSD). Therefore, our findings can be used to guide research into Dirac points at HSPs in 3D phonon systems.

Ideal phononic charge-two nodal point and long nontrivial surface arcs in Na2Zn2O3

Recently, there has been significant interest in exploring the chiral quasiparticles in phonons, which describe the atomic lattice vibrations in solids. In this work, using first-principle calculation, we select a realistic material Na2Zn2O3 as an example to demonstrate that it is an ideal candidate with charge-two Dirac point phonons and charge-two Weyl point phonons at high-symmetry points A and Γ, respectively. The phononic charge-two nodal points in Na2Zn2O3 are visible and almost ideal. That is, there are no other phonon bands nearby. Moreover, nontrivial phononic surface arcs span the whole surface Brillouin zone. Such clean and long nontrivial arc-shaped phononic surface states benefit the experimental detection. The current work is hoped to guide the investigations of chiral nodal points in phononic systems.

Elastic topological interface states and voltage feeder by breaking inversion symmetry on thin plates

The rapid progress in the engineering of topological edge/interface states has attracted considerable interest in both photonic and phononic systems originating from their electronic equivalent systems. However, most classical wave types, such as electromagnetic/acoustic waves in topological engineering, are described by two-dimensional (2D) partial differential equations (PDEs), which are not suitable for thin plate motions. We present a 1D elastic topological interface state induced by symmetry breaking to bridge a knowledge gap in 4D PDE, particularly for flexural waves on thin-plate frameworks. We also leverage the localized state at the interface for energy harvesting, which can provide a sufficiently high voltage feeder by piezoelectric effects.