We discuss computational analysis of phononic thermal conduction in the suspended membrane geometry, in the experimentally commonly appearing case where heat can flow out radially in two dimensions from a central source. As we are mostly interested in the low-temperature behavior where bulk scattering of phonons becomes irrelevant, we study the limit where all phonon scattering takes place at the membrane surfaces. Moreover, we limit the discussion here to the case where this surface scattering is fully diffusive, the so called Casimir limit. Our analysis shows that in the two-dimensional case, no analytic results are available, in contrast to the well known 1D Casimir limit. Numerical solutions are presented for the temperature profiles in the membrane radial direction, for several different membrane thicknesses. Our results can be applied, for example, in the design of membrane-supported bolometric radiation detectors.
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.
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…
In a previous publication, we discussed the formalism and some computational results for phononic thermal conduction in the suspended membrane geometry for radial heat flow from a central source, which is a common geometry for some low-temperature detectors, for example. We studied the case where only diffusive surface scattering is present, the so called Casimir limit, which can be experimentally relevant at temperatures below $\sim$ 10 K in typical materials, and even higher for ultrathin samples. Here, we extend our studies to much thinner membranes, obtaining numerical results for geometri…
Dielectric membranes with exceptional mechanical and optical properties present one of the most promising platforms in quantum opto-mechanics. The performance of stressed silicon nitride nanomembranes as mechanical resonators notoriously depends on how their frame is clamped to the sample mount, which in practice usually necessitates delicate, and difficult-to-reproduce mounting solutions. Here, we demonstrate that a phononic bandgap shield integrated in the membrane's silicon frame eliminates this dependence, by suppressing dissipation through phonon tunneling. We dry-etch the membrane's fram…
By calculating a Casimir energy for the acoustic phonons of Graphene, we find some temperature-dependent corrections for the pretension of a Graphene sheet suspended on a trench. We obtain values of the order of few mN/m for these corrections in fully as well as doubly clamped Graphene on a narrow trench with one nanometer width, at room temperature. These values are considerable compared to the experimental values, and can increase the fundamental resonance frequency of the Graphene. The values of these corrections increase by increasing the temperature, and so they can be utilized for tuning…
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…
Coherent control of thermal transport with pillar-based phononic crystals
Nanoscience Center, Department of Physics, University of Jyvaskyla（于韦斯屈莱大学物理系纳米科学中心）；Faculty of Physics and Astronomy, Adam Mickiewicz University（亚当·密茨凯维奇大学物理与天文学学院）
Nanoelectromechanical systems (NEMS), utilising localised mechanical vibrations, were pioneered for sensors, signal processors and to study macroscopic quantum mechanics. Increasingly the concept of integrating multiple mechanical elements via electrical/optical means has emerged as a challenge towards NEMS circuits. Here we develop phononic crystal waveguides (PnC WGs), using a 1-dimensional array of suspended membranes, that offer purely mechanical means to integrate isolated NEMS resonators. In the first steps to this objective, we demonstrate the PnC WG can support and guide mechanical vib…
The impact of lattice type, period, porosity and thickness of two-dimensional silicon phononic crystals on the reduction of thermal conductance by coherent modification of phonon dispersion is investigated using the theory of elasticity and finite element method. Increase in the period and porosity of the phononic crystal affects the group velocity and phonon density of states and, as a consequence, reduces the in-plane thermal conductance of the structure as compared to unpatterned membrane. This reduction does not depend significantly on the lattice type and thickness of phononic crystals. M…
The phonon propagation dynamics in a phononic crystal waveguide, realized via a suspended one-dimensional membrane array with periodic air holes, is investigated as function of its geometry. The bandstructure of the phononic crystal can be engineered by modifying the characteristics of the phonon standing waves in the waveguide by varying the waveguide width and the pitch of the air holes. This enables the phonon transmission bands, the bandgaps, the velocity and the nonlinear dispersion in the phononic crystal to be controlled. Indeed the engineered bandstructure can also be tuned to sustain …
We find the Casimir energy, at finite temperature, for acoustic phonons in a Graphene sheet suspended over a rectangular trench, and the corresponding Casimir forces are interpreted as correction terms to the built-in tensions of the Graphene. We show that these corrections generally break the tensional isotropy of the membrane, and can increase or decrease the membrane tension. We demonstrate that for a narrow rectangular trench with side-lengths in the order of few nanometers and few micrometers, these temperature corrections are expected to be noticeable ($\sim 10^{-4} N/m$) at the room tem…
Casimir forces on suspended thin dielectric membranes covered with graphene
The Hong Kong University of Science and Technology（香港科技大学）；Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier（夏尔·库隆实验室（L2C），CNRS-蒙彼利埃大学联合研究单位5221）
Development of broadband thermal sensors for the detection of, among others, radiation, single nanoparticles, or single molecules is of great interest. In recent years, photothermal spectroscopy based on the shift of the resonance frequency of stressed nanomechanical resonators has been successfully demonstrated. Here, we show the application of soft-clamped phononic crystal membranes made of silicon nitride as thermal sensors. It is experimentally demonstrated how a quasi-bandgap remains even at very low tensile stress, in agreement with finite element method simulations. An increase of the r…
Role of the Casimir force in the capacitive radio-frequency microelectromechanical switches
Central Astronomical Observatory at Pulkovo of the Russian Academy of Sciences（俄罗斯科学院普尔科沃中央天文台）；Peter the Great Saint Petersburg Polytechnic University（彼得大帝圣彼得堡理工大学）
As one of the basic components of phononics, thermal diodes transmit heat current asymmetrically similar to electronic rectifiers and diodes in microelectronics. Heat can be conducted through them easily in one direction while being blocked in the other direction. In this work, we report an easily-fabricated mesoscale chemical vapor deposited (CVD) diamond thermal diode without sharp temperature change driven by the gradient grain structure of CVD diamond membranes. We build a spectral model of diamond thermal conductivity with complete phonon dispersion relation to show significant thermal re…
We discuss the possibility to create hybrid quantum systems that combine ultracold atoms with graphene membranes. We investigate a setup in which a cold atom cloud is placed close to a free-standing sheet of graphene at distances on the order of a few hundred nanometers. The atoms then couple to the graphene membrane via Casimir-Polder forces. Temporal changes in the atomic state of the atomic cloud changes the Casimir-Polder interaction, thereby leading to the creation of a backaction force in the graphene sheet. This setup provides a controllable way to engineer ripples in a graphene sheet.
We report on fabrication and characterization of ultra-thin suspended single crystalline flat silicon membranes with thickness down to 6 nm. We have developed a method to control the strain in the membranes by adding a strain compensating frame on the silicon membrane perimeter to avoid buckling of the released membranes. We show that by changing the properties of the frame the strain of the membrane can be tuned in controlled manner. Consequently, both the mechanical properties and the band structure can be engineered and the resulting membranes provide a unique laboratory to study low-dimens…
We calculate the operating parameters of a transition edge sensor that is mounted on a thin dielectric membrane with the assumption that the phononic heat transport in the membrane is ballistic. Our treatment uses the correct phonon modes from elasticity theory (Lamb-modes), and spans the transition from 3D to 2D behavior. The phonon cooling power and conductance have a global minimum as function of membrane thickness, which leads to an optimal value for the membrane thickness with respect to noise equivalent power at a fixed operating temperature. The energy resolution of a calorimeter will n…
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…
We report on low mechanical loss in a high-stress silicon nitride (Si_{3}N_{4}) membrane at temperatures below 100 mK. We isolate a membrane via a phononic shield formed within a supporting silicon frame, and measure the mechanical quality factor of a number of high-tension membrane modes as we vary our dilution refrigerator base temperature between 35 mK and 5 K. At the lowest temperatures, we obtain a maximum quality factor (Q) of 2.3\times10^{8}, corresponding to a Q-frequency product (QFP) of 3.7\times10^{14} Hz. These measurements complement the recent observation of improved quality fact…
In this study, we use the transient thermal grating optical technique \textemdash a non-contact, laser-based thermal metrology technique with intrinsically high accuracy \textemdash to investigate room-temperature phonon-mediated thermal transport in two nanoporous holey silicon membranes with limiting dimensions of 100 nm and 250 nm respectively. We compare the experimental results to ab initio calculations of phonon-mediated thermal transport according to the phonon Boltzmann transport equation (BTE) using two different computational techniques. We find that the calculations conducted within…
The Casimir force was predicted in 1948 as a force arising between macroscopic bodies from the zero-point energy. At finite temperatures it has been shown that a thermal Casimir force exists due to thermal rather than zero-point energy and there are a growing number of experiments that characterise the effect at a range of temperatures and distances. Additionally, in the rapidly evolving field of cavity optomechanics there is an endeavor to manipulate phonons and enhance coherence. We demonstrate a new way to achieve this through the first observation of Casimir spring and dilution in macrosco…
The thermal correction to the energy of Casimir-Polder interaction of atoms with a suspended graphene membrane described by the Dirac model is investigated. We show that a major impact on the thermal correction is made by the size of the gap in the energy spectrum of graphene quasiparticles. Specifically, if the temperature is much smaller than the gap parameter (alternatively, larger or of the order of the gap parameter), the thermal correction is shown to be relatively small (alternatively, large). We have calculated the free energy of the thermal Casimir-Polder interaction of atoms of He, N…
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）
The discovery of nanostructures and the development of growth and fabrication techniques of one- and two-dimensional materials provide the possibility to probe experimentally heat transport in low-dimensional systems. Nevertheless measuring the thermal conductivity of these systems is extremely challenging and subject to large uncertainties, thus hindering the chance for a direct comparison between experiments and statistical physics models. Atomistic simulations of realistic nanostructures provide the ideal bridge between abstract models and experiments. After briefly introducing the state of…
In recent times the possibility of non-reciprocity in heat transfer between two bodies has been extensively studied. In particular the role of strong magnetic fields has been investigated. A much simpler approach with considerable flexibility would be to consider heat transfer in synthetic electric and magnetic fields which are easily applied. We demonstrate the breakdown of detailed balance for the heat transfer function $\mathcal{T} (ω)$, i.e. the spectrum of heat transfer between two objects due to the presence of synthetic electric and magnetic fields. The spectral measurements carry lot m…
