We present a theoretical framework allowing to properly address the nature of surface-like eigenmodes in a hypersonic surface phononic crystal, a composite structure made of periodic metal stripes of nanometer size and periodicity of 1 micron, deposited over a semi-infinite silicon substrate. In surface-based phononic crystals there is no distinction between the eigenmodes of the periodically nanostructured overlayer and the surface acoustic modes of the semi-infinite substrate, the solution of the elastic equation being a pseudo-surface acoustic wave partially localized on the nanostructures and radiating energy into the bulk. This problem is particularly severe in the hypersonic frequency range, where semi-infinite substrate's surface acoustic modes strongly couple to the periodic overlayer, thus preventing any perturbative approach. We solve the problem introducing a surface-likeness coefficient as a tool allowing to find pseudo-surface acoustic waves and to calculate their line shapes. Having accessed the pseudo-surface modes of the composite structure, the same theoretical frame allows reporting on the gap opening in the now well-defined pseudo-SAW frequency spectrum. We show how the filling fraction, mass loading and geometric factors affect both the frequency gap, and how the mechanical energy is scattered out of the surface waveguiding modes.
A phononic crystal formed in a suspended membrane provides full confinement of hypersonic waves and thus realizes a range of chip-scale manipulations. In this letter, we demonstrate the mode-resolved real-space characterization of the mechanical vibration properties in cavities and waveguide systems. Multiple resonant modes are independently characterized in various designed cavities, and wavelength-scale high-$Q$ resonances up to $Q=$ 4200 under atmospheric conditions are confirmed. This also reveals that the waveguide allows us to resolve single-mode wave transmission and thereby drive evane…
The design and fabrication of phononic crystals (PnCs) hold the key to control the propagation of heat and sound at the nanoscale. However, there is a lack of experimental studies addressing the impact of order/disorder on the phononic properties of PnCs. Here, we present a comparative investigation of the influence of disorder on the hypersonic and thermal properties of two-dimensional PnCs. PnCs of ordered and disordered lattices are fabricated of circular holes with equal filling fractions in free-standing Si membranes. Ultrafast pump and probe spectroscopy (asynchronous optical sampling) a…
Radiation pressure within engineered structures has recently been used to couple the motion of nanomechanical objects with high sensitivity to optical and microwave electromagnetic fields. Here, we demonstrate a form of electromechanical crystal for coupling microwave photons and hypersonic phonons by embedding the vacuum-gap capacitor of a superconducting resonator within a phononic crystal acoustic cavity. Utilizing a two-photon resonance condition for efficient microwave pumping and a phononic bandgap shield to eliminate acoustic radiation, we demonstrate large cooperative coupling ($C \app…
We report on the self-consisted semi-analytical theory of magnetoelastic excitation and electrical detection of spin waves and spin currents in hypersonic bulk acoustic waves resonator with ZnO-GGG-YIG/Pt layered structure. Electrical detection of acoustically driven spin waves occurs due to spin pumping from YIG to Pt and inverse spin Hall (ISHE) effect in Pt as well as due to electrical response of ZnO piezotransducer. The frequency-field dependences of the resonator frequencies and ISHE voltage $U_{ISHE}$ are correlated with experimental ones observed previously. Their fitting allows to det…
Phonons at gigahertz frequencies interact with electrons, photons, and atomic systems in solids, and therefore have extensive applications in signal processing, sensing, and quantum technologies. Surface acoustic wave (SAW) resonators that confine surface phonons can play a crucial role in such integrated phononic systems due to small mode size, low dissipation, and efficient electrical transduction. To date, it has been challenging to achieve high quality (Q) factor and small phonon mode size for SAW resonators at gigahertz frequencies. Here, we present a methodology to design compact high-Q …
We report direct visualization of gigahertz-frequency acoustic waves in lithium niobate phononic circuits. Primary propagation parameters, such as the power flow angle (PFA) and propagation loss (PL), are measured by transmission-mode microwave impedance microscopy (TMIM). Using fast Fourier transform, we can separately analyze forward and backward propagating waves and quantitatively evaluate the propagation loss. Our work provides insightful information on the propagation, diffraction, and attenuation in piezoelectric thin films, which is highly desirable for designing and optimizing phononi…
We report direct visualization of gigahertz-frequency Lamb waves propagation in aluminum nitride phononic circuits by transmission-mode microwave impedance microscopy (TMIM). Consistent with the finite-element modeling, the acoustic eigenmodes in both a horn-shaped coupler and a sub-wavelength waveguide are revealed in the TMIM images. Using fast Fourier transform filtering, we quantitatively analyze the acoustic loss of individual Lamb modes along the waveguide and the power coupling coefficient between the waveguide and the parabolic couplers. Our work provides insightful information on the …
We systematically engineer a series of square and rectangular phononic crystals to create experimental realisations of complex topological phononic circuits. The exotic topological transport observed is wholly reliant upon the underlying structure which must belong to either a square or rectangular lattice system and not to any hexagonal-based structure. The phononic system chosen consists of a periodic array of square steel bars which partitions acoustic waves in water over a broadband range of frequencies (~0.5 MHz). An ultrasonic transducer launches an acoustic pulse which propagates along …
Nanomechanical systems made from phononic crystals can act as highly coherent microwave-frequency circuits at cryogenic temperatures. However, generating sufficient coupling between these devices and microwave superconducting quantum circuits is challenging due to the vastly different length scales of acoustic and electrical excitations. Here we demonstrate a general recipe for calculating these interactions and show that large piezoelectric coupling rates between microwave superconducting circuits containing Josephson junctions and nanoscale phononic resonances are possible, suggesting a rout…
Phononic crystals and acoustic meta-materials are used to tailor phonon and sound propagation properties by facilitating artificial, periodic structures. Analogous to photonic crystals, phononic band gaps can be created, which influence wave propagation and, more generally, allow engineering of the acoustic properties of a system. Beyond that, nonlinear phenomena in periodic structures have been extensively studied in photonic crystals and atomic Bose-Einstein Condensates in optical lattices. However, creating nonlinear phononic crystals or nonlinear acoustic meta-materials remains challenging…
We present a study of surface acoustic waves (SAW) propagation on a 1D phononic surface (PS) by mean of an heterodyne-detected transient reflecting grating experiment. We excited and detected coherent stationary SAWs characterized by variable wave-vectors. The measured SAW frequencies enables the characterization of the band diagram of this PS sample beyond the first Brillouin zone (BZ). Four different SAW frequencies have been revealed, whose band diagram show articulated dispersion phenomena. In order to address the nature of the investigated SAWs, the experimental results are compared with …
This study investigates the occurrence of acoustic topological edge states in a 2D phononic elastic waveguide due to a phenomenon that is the acoustic analogue of the quantum valley Hall effect. We show that a topological transition takes place between two lattices having broken space inversion symmetry due to the application of a tunable strain field. This condition leads to the formation of gapless edge states at the domain walls, as further illustrated by the analysis of the bulk-edge correspondence and of the associated topological invariants. Although time reversal symmetry is still intac…
We present measurements at millikelvin temperatures of the microwave-frequency acoustic properties of a crystalline silicon nanobeam cavity incorporating a phononic bandgap clamping structure for acoustic confinement. Utilizing pulsed laser light to excite a co-localized optical mode of the nanobeam cavity, we measure the dynamics of cavity acoustic modes with single-phonon sensitivity. Energy ringdown measurements for the fundamental $5$~GHz acoustic mode of the cavity shows an exponential increase in phonon lifetime versus number of periods in the phononic bandgap shield, increasing up to $τ…
We report a new type of phononic crystals with topologically non-trivial bandgaps for both longitudinal and transverse polarizations, resulting in protected one-way elastic edge waves. In our design, gyroscopic inertial effects are used to break the time-reversal symmetry and realize the phononic analogue of the electronic quantum Hall effect. We investigate the response of both hexagonal and square gyroscopic lattices and observe bulk Chern number of 1 and 2, indicating that these structures support single and multi-mode edge elastic waves immune to back-scattering. These robust one-way phono…
The possibility of realizing an electrostatically induced phononic crystal is investigated numerically in an acoustic waveguide based on a graphene sheet that is suspended over periodically arrayed electrodes. The application of dc voltage to these electrodes exerts electrostatic force on the graphene and this results in the periodic formation of stress in the waveguide structure in a non-invasive way, unlike the cases with mass loading and air holes. This non-invasive scheme enables a bandgap, namely a phononic crystal, to be created in the waveguide that can be used to dynamically tune the a…
The rising need for hybrid physical platforms has triggered a renewed interest for the development of agile radio-frequency phononic circuits with complex functionalities. The combination of travelling waves with resonant mechanical elements appears as an appealing means of harnessing elastic vibration. In this work, we demonstrate that this combination can be further enriched by the occurrence of elastic non-linearities induced travelling surface acoustic waves (SAW) interacting with a pair of otherwise linear micron-scale mechanical resonators. Reducing the resonator gap distance and increas…
The engineering of phononic resonances in ferroelectric structures appears as a new knob in the design and realization of novel multifunctional devices. In this work we experimentally study phononic resonators based on insulating (BaTiO3, SrTiO3) and metallic (SrRuO3) oxides. We experimentally demonstrate the confinement of acoustic waves in the 100 GHz frequency range in a phonon nanocavity, the time and spatial beatings resulting from the coupling of two different hybrid nanocavities forming an acoustic molecule, and the direct measurement of Bloch-like oscillations of acoustic phonons in a …
Thanks to the recent discovery on the magic-angle bilayer graphene, twistronics is quickly becom11 ing a burgeoning field in condensed matter physics. This letter expands the realm of twistronics to acoustics by introducing twisted bilayer phononic graphene, which remarkably also harbors the magic angle, evidenced by the associated ultra-flat bands. Beyond mimicking quantum mechanical behaviors of twisted bilayer graphene, we show that their acoustic counterpart offers a considerably more straightforward and robust way to alter the interlayer hopping strength, enabling us to unlock magic angle…
Dirac semimetals, the materials featured with discrete linearly crossing points (called Dirac points) between four bands, are critical states of topologically distinct phases. Such gapless topological states have been accomplished by a band-inversion mechanism, in which the Dirac points can be annihilated pairwise by perturbations without changing the symmetry of the system. Here, we report an experimental observation of Dirac points that are enforced completely by the crystal symmetry, using a nonsymmorphic three-dimensional phononic crystal. Intriguingly, our Dirac phononic crystal hosts fou…
The use of femtosecond laser pulses to impulsively excite thermal and mechanical transients in matter has led, in the last years, to the development of picosecond acoustics. Recently, the pump-probe approach has been applied to nano-engineered materials to optically generate and detect acoustic waves in the GHz-THz frequency range. In this paper, we review the latest advances on ultrafast generation and detection of thermal gradients and pseudo-surface acoustic waves in two-dimensional lattices of metallic nanostructures. Comparing the experimental findings to the numeric analysis of the full …
Acoustically driven spin-wave resonance in a phononic crystal cavity is numerically investigated. The designed cavity enables confinement of gigahertz vibrations in a wavelength-scale point-defect structure and sustains a variety of resonance modes. Inhomogeneous strain distributions in the modes modify the magnetostrictive coupling and the spin-wave excitation susceptible to an external field orientation. In particular, a monopole-like mode in the cavity having a near-symmetrical pattern shows a subwavelength-scale mode volume and can provide a versatile acoustic excitation scheme independent…
There has been great interest in two-dimensional materials, beyond graphene, for both fundamental sciences and technological applications. Silicene, a silicon counterpart of graphene, has been shown to possess some better electronic properties than graphene. However, its thermal transport properties have not been fully studied. In this paper, we apply the first-principles-based phonon Boltzmann transport equation to investigate the thermal conductivity of silicene as well as the phonon scattering mechanisms. Although both graphene and silicene are two-dimensional crystals with similar crystal …
The propagation of intense acoustic waves in a one-dimensional phononic crystal is studied. The medium consists in a structured fluid, formed by a periodic array of fluid layers with alternating linear acoustic properties and quadratic nonlinearity coefficient. The spacing between layers is of the order of the wavelength, therefore Bragg effects such as band-gaps appear. We show that the interplay between strong dispersion and nonlinearity leads to new scenarios of wave propagation. The classical waveform distortion process typical of intense acoustic waves in homogeneous media can be strongly…
This letter investigates a flow-free, pseudospin-based acoustic topological insulator. Zone folding, a strategy originated from photonic crystal, is used to form double Dirac cones in phononic crystal. The lattice symmetry of the phononic crystal is broken by tuning the size of the center "atom" of the unit cell in order to open the nontrivial topological gap. Robust sound one-way propagation is demonstrated both numerically and experimentally. This study provides a flexible approach for realizing acoustic topological insulators, which are promising for applications such as noise control and w…
We have studied acoustic topological edge modes in a honeycomb phononic crystal composed of metallic nano-pillars on a LiNbO$_3$ substrate. Acoustic band calculations show that the topological surface acoustic wave (SAW) mode inhabits the edge of the honeycomb phononic crystal in spite of the hybridization with the internal acoustic modes of the substrate. Pulse-type microwave impedance microscopy realized clear visualization of the gigahertz topological edge mode between two mutually inverted topological phononic crystals. A frequency-dependent image showed that the edge mode evolves as the b…
A design for photoacoustic mass sensors operating above 100 GHz is proposed. The design is based on impulsive optical excitation of a pseudosurface acoustic wave in a surface phononic crystal with nanometric periodic grating, and on time-resolved extreme ultraviolet detection of the pseudosurface acoustic wave frequency shift upon mass loading the device. The present design opens the path to sensors operating in a frequency range currently unaccessible to electro-acoustical transducers, providing enhanced sensitivity, miniaturization and incorporating time-resolving capability while forgoing t…
We present techniques to model and design membrane phononic crystals with low-mass defects, optimized for force sensing. Further, we identify the importance of the phononic crystal mass contrast as it pertains to the size of acoustic bandgaps and to the dissipation properties of defect modes. In particular, we quantify the tradeoff between high mass contrast phononic crystals with their associated robust acoustic isolation, and a reduction of soft clamping of the defect mode. We fabricate a set of phononic crystals with a variety of defect geometries out of high stress stoichiometric silicon n…
A phononic crystal can control the acoustic coupling between a resonator and its support structure. We micromachine a phononic bandgap shield for high Q silicon nitride membranes and study the driven displacement spectra of the membranes and their support structures. We find that inside observed bandgaps the density and amplitude of non-membrane modes are greatly suppressed, and membrane modes are shielded from an external mechanical drive by up to 30 dB.
In quantum optomechanics, finding materials and strategies to limit losses has been crucial to the progress of the field. Recently, superfluid 4He was proposed as a promising mechanical element for quantum optomechanics. This quantum fluid shows highly desirable properties (e.g. extremely low acoustic loss) for a quantum optomechanical system. In current implementations, superfluid optomechanical systems suffer from external sources of loss, which spoils the quality factor of resonators. In this work, we propose a new implementation, exploiting nanofluidic confinement. Our approach, based on a…
We demonstrate that the parity-time symmetry for sound is realized in the laser-pumped multiple-quantum-well structure. Breaking of the parity-time symmetry for the phonons with wave vectors corresponding to the Bragg condition makes the structure a highly-selective acoustic wave amplifier. Single-mode distributed feedback phonon lasing is predicted for structures with realistic parameters.
Spin-1 Weyl point is formed by three bands touching at a single point in the three dimensional (3D) momentum space, with two of which show cone-like dispersion while the third band is flat. Such a triply degenerate point carries higher topological charge $\pm2$2 and can be described by a three-band Hamiltonian. We first propose a tight-binding model of a 3D Lieb lattice with chiral interlayer coupling to form the Spin-1 Weyl point. Then we design a chiral phononic crystal that carries these spin-1 Weyl points and special straight-type acoustic Fermi arcs. We also computationally demonstrate th…
We present a tunable phononic crystal which undergoes a phase transition from mechanically insulating to mechanically transmissive (metallic). Specifically, in our simulations for a phononic lattice under biaxial tension ($σ_{xx} =σ_{yy}$ = 0.01 N$/$m), we find a bandgap for out-of-plane phonons in the range of 48.8 - 56.4 MHz, which we can close by increasing the degree of tension uniaxiality ($σ_{xx} / σ_{yy}$) to 1.7. To manipulate the tension distribution, we design a realistic device of finite size, where $σ_{xx} / σ_{yy}$ is tuned by applying a gate voltage to a phononic crystal made fro…
We present here precise measurement of the resonance frequency, lifetime and shape of confined acoustic modes in the tens of GHz regime in GaAs/AlAs superlattice planar and micropillar cavities at low temperature ($\sim 20\,\textrm{K}$). The subharmonic resonant pump-probe technique, where the repetition rate of the pump laser is tuned to a subharmonic of the cavity resonance to maximize the amplitude of the acoustic resonance, in combination with a Sagnac interferometer technique for high sensitivity ($\sim 10 \,\textrm{fm}$) to the surface displacement, has been used. The cavity fundamental …
The ability to manipulate phonon waveforms in continuous media has attracted significant research interest and is crucial for practical applications ranging from biological imaging to material characterization. Although several spatial focusing techniques have been developed, these systems require sophisticated artificial structures, which limit their practical applications. This is because the spatial control of acoustic phonon waves is not as straightforward as photonics so there is a strong demand for an alternative approach. Here we demonstrate a phononic time lens in a dispersive one-dime…
Topological insulators, first observed in electronic systems, have inspired many analogues in photonic and phononic crystals in which remarkable one-way propagation edge states are supported by topologically nontrivial bandgaps. Such bandgaps can be achieved by breaking the time-reversal symmetry to lift the degeneracy associated with Dirac cones at the corners of the Brillouin zone. Here, we report on our construction of a phononic crystal exhibiting a Dirac-like cone in the Brillouin zone center. We demonstrate that simultaneously breaking the time-reversal symmetry and altering the geometri…
Topological phases, including the conventional first-order and higher-order topological insulators and semimetals, have emerged as a thriving topic in the fields of condensed-matter physics and material science. Usually, a topological insulator is characterized by a fixed order topological invariant and exhibits associated bulk-boundary correspondence. Here, we realize a new type of topological insulator in a bilayer phononic crystal, which hosts simultaneously the first-order and second-order topologies, referred here as the hybrid-order topological insulator. The one-dimensional gapless heli…
Weyl points (WPs) are isolated degeneracies carrying quantized topological charges, and are therefore robust against Hermitian perturbations. WPs are predicted to spread to the Weyl exceptional rings (WERs) in the presence of non-Hermiticity. Here, we use a one-dimensional (1D) Aubry-Andre-Harper (AAH) model to construct a Weyl semimetal in a 3D parameter space comprised of one reciprocal dimension and two synthetic dimensions. The inclusion of non-Hermiticity in the form of gain and loss produces a WER. The topology of the WER is characterized by both its topological charge and non-Hermitian …
Hexagonal boron nitride (h-BN), one of the hallmark van der Waals (vdW) layered crystals with an ensemble of attractive physical properties, is playing increasingly important roles in exploring two-dimensional (2D) electronics, photonics, mechanics, and emerging quantum engineering. Here, we report on the demonstration of h-BN phononic crystal waveguides with designed pass and stop bands in the radio frequency (RF) range and controllable wave propagation and transmission, by harnessing arrays of coupled h-BN nanomechanical resonators with engineerable coupling strength. Experimental measuremen…
The interaction of optical and mechanical modes in nanoscale optomechanical systems has been widely studied for applications ranging from sensing to quantum information science. Here, we develop a platform for cavity optomechanical circuits in which localized and interacting 1550 nm photons and 2.4 GHz phonons are combined with photonic and phononic waveguides. Working in GaAs facilitates manipulation of the localized mechanical mode either with a radio frequency field through the piezo-electric effect, or optically through the strong photoelastic effect. We use this to demonstrate a novel aco…
Dissipative acousto-mechanical parametric interface between high-overtone acoustics and flexural phonons
Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Aalto University（阿尔托大学）；Tsinghua University（清华大学）
Quantum acoustodynamics (QAD) is a rapidly developing field of research, offering possibilities to realize and study macroscopic quantum-mechanical systems in a new range of frequencies, and implement transducers and new types of memories for hybrid quantum devices. Here we propose a novel design for a versatile diamond QAD cavity operating at GHz frequencies, exhibiting effective mode volumes of about $10^{-4}λ^3$. Our phononic crystal waveguide cavity implements a non-resonant analogue of the optical lightning-rod effect to localize the energy of an acoustic mode into a deeply-subwavelength …
We report the results of Brillouin-Mandelstam spectroscopy and Mueller matrix spectroscopic ellipsometry of the nanoscale "pillar with the hat" periodic silicon structures, revealing intriguing phononic and photonic properties. It has been theoretically shown that periodic structures with properly tuned dimensions can act simultaneously as phononic and photonic - phoxonic - crystals, strongly affecting the light-matter interactions. Acoustic phonon states can be tuned by external boundaries, either as a result of phonon confinement effects in individual nanostructures, or as a result of artifi…
We numerically and experimentally investigate the phononic loss for superconducting resonators fabricated on a piezoelectric substrate. With the help of finite element method simulations, we calculate the energy loss due to electromechanical conversion into bulk and surface acoustic waves. This sets an upper limit for the resonator internal quality factor $Q_i$. To validate the simulation, we fabricate quarter wavelength coplanar waveguide resonators on GaAs and measure $Q_i$ as function of frequency, power and temperature. We observe a linear increase of $Q_i$ with frequency, as predicted by …
We theoretically show how to strongly couple the center-of-mass motion of a micromagnet in a harmonic potential to one of its acoustic phononic modes. The coupling is induced by a combination of an oscillating magnetic field gradient and a static homogeneous magnetic field. The former parametrically couples the center-of-mass motion to a magnonic mode while the latter tunes the magnonic mode in resonance with a given acoustic phononic mode. The magnetic fields can be adjusted to either cool the center-of-mass motion to the ground state, or to enter into the strong quantum coupling regime. The …
Topological phononics offers numerous opportunities in manipulating elastic waves that can propagate in solids without being backscattered. Due to the lack of nanoscale imaging tools that aid the system design, however, acoustic topological metamaterials have been mostly demonstrated in macroscale systems operating at low (kilohertz to megahertz) frequencies. Here, we report the realization of gigahertz topological valley Hall effect in nanoelectromechanical AlN membranes. Propagation of elastic wave through phononic crystals is directly visualized by microwave microscopy with unprecedented se…
