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Register a new userStrained crystalline nanomechanical resonators with ultralow dissipation
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In strained mechanical resonators, the concurrence of tensile stress and geometric nonlinearity dramatically reduces dissipation. This phenomenon, dissipation dilution, is employed in mirror suspensions of gravitational wave interferometers and at the nanoscale, where soft-clamping and strain engineering have allowed extremely high quality factors. However, these techniques have so far only been applied in amorphous materials, specifically silicon nitride. Crystalline materials exhibit significantly lower intrinsic damping at cryogenic temperatures, due to the absence of two level systems in the bulk, as exploited in Weber bars and silicon optomechanical cavities. Applying dissipation dilution engineering to strained crystalline materials could therefore enable extremely low loss nanomechanical resonators, due to the combination of reduced internal friction, high intrinsic strain, and high yield strength. Pioneering work has not yet fully exploited this potential. Here, we demonstrate that single crystal strained silicon, a material developed for high mobility transistors, can be used to realize mechanical resonators with ultralow dissipation. We observe that high aspect ratio ($>10^5$) strained silicon nanostrings support MHz mechanical modes with quality factors exceeding $10^{10}$ at 7 K, a tenfold improvement over values reported in silicon nitride. At 7 K, the thermal noise-limited force sensitivity is approximately $45 mathrm{{zN}/{sqrt{Hz}}}$ - approaching that of carbon nanotubes - and the heating rate is only 60 quanta-per-second. Our nanomechanical resonators exhibit lower dissipation than the most pristine macroscopic oscillators and their low mass makes them particularly promising for quantum sensing and transduction.
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Structural hierarchy is found in myriad biological systems and has improved man-made structures ranging from the Eiffel tower to optical cavities. Hierarchical metamaterials utilize structure at multiple size scales to realize new and highly desirable properties which can be strikingly different from those of the constituent materials. In mechanical resonators whose rigidity is provided by static tension, structural hierarchy can reduce the dissipation of the fundamental mode to ultralow levels due to an unconventional form of soft clamping. Here, we apply hierarchical design to silicon nitride nanomechanical resonators and realize binary tree-shaped resonators with quality factors as high as $10^9$ at 107 kHz frequency, reaching the parameter regime of levitated particles. The resonators thermal-noise-limited force sensitivities reach $740 mathrm{zN/sqrt{Hz}}$ at room temperature and $mathrm{90 zN/sqrt{Hz}}$ at 6 K, surpassing state-of-the-art cantilevers currently used for force microscopy. We also find that the self-similar structure of binary tree resonators results in fractional spectral dimensions, which is characteristic of fractal geometries. Moreover, we show that the hierarchical design principles can be extended to 2D trampoline membranes, and we fabricate ultralow dissipation membranes suitable for interferometric position measurements in Fabry-Perot cavities. Hierarchical nanomechanical resonators open new avenues in force sensing, signal transduction and quantum optomechanics, where low dissipation is paramount and operation with the fundamental mode is often advantageous.
We have studied damping in polycrystalline Al nanomechanical resonators by measuring the temperature dependence of their resonance frequency and quality factor over a temperature range of 0.1 - 4 K. Two regimes are clearly distinguished with a crossover temperature of 1 K. Below 1 K we observe a logarithmic temperature dependence of the frequency and linear dependence of damping that cannot be explained by the existing standard models. We attribute these phenomena to the effect of the two-level systems characterized by the unexpectedly long (at least two orders of magnitude longer) relaxation times and discuss possible microscopic models for such systems. We conclude that the dynamics of the two-level systems is dominated by their interaction with one-dimensional phonon modes of the resonators.
State of the art nanomechanical resonators present quality factors Q ~ 10^3 - 10^5, which are much lower than those that can be naively extrapolated from the behavior of micromechanical resonators. We analyze the dissipation mechanism that arises in nanomechanical beam-structures due to the tunneling of mesoscopic phonons between the beam and its supports (known as clamping losses). We derive the environmental force spectral density that determines the quantum Brownian motion of a given resonance. Our treatment is valid for low frequencies and provides the leading contribution in the aspect ratio. This yields fundamental limits for the Q-values which are described by simple scaling laws and are relevant for state of the art experimental structures. In this context, for resonant frequencies in the 0.1-1GHz range, while this dissipation mechanism can limit flexural resonators it is found to be negligible for torsional ones. In the case of structureless 3D supports the corresponding environmental spectral densities are Ohmic for flexural resonators and super-Ohmic for torsional ones, while for 2D slab supports they yield 1/f noise. Furthermore analogous results are established for the case of suspended semiconducting single-walled carbon nanotubes. Finally, we provide a general expression for the spectral density that allows to extend our treatment to other geometries and illustrate its use by applying it to a microtoroid. Our analysis is relevant for applications in high precision measurements and for the prospects of probing quantum effects in a macroscopic mechanical degree of freedom.
The measurement of micron-sized mechanical resonators by electrical techniques is difficult, because of the combination of a high frequency and a small mechanical displacement which together suppress the electromechanical coupling. The only electromagnetic technique proven up to the range of several hundred MHz requires the usage of heavy magnetic fields and cryogenic conditions. Here we show how, without the need of either of them, to fully electrically detect the vibrations of conductive nanomechanical resonators up to the microwave regime. We use the electrically actuated vibrations to modulate an LC tank circuit which blocks the stray capacitance, and detect the created sideband voltage by a microwave analyzer. We show the novel technique up to mechanical frequencies of 200 MHz. Finally, we estimate how one could approach the quantum limit of mechanical systems.
Heterostructures play significant roles in modern semiconductor devices and micro/nanosystems in a plethora of applications in electronics, optoelectronics, and transducers. While state-of-the-art heterostructures often involve stacks of crystalline epi-layers each down to a few nanometers thick, the intriguing limit would be heterto-atomic-layer structures. Here we report the first experimental demonstration of freestanding van der Waals heterostructures and their functional nanomechanical devices. By stacking single-layer (1L) MoS2 on top of suspended single-, bi-, tri- and four-layer (1L to 4L) graphene sheets, we realize array of MoS2-graphene heterostructures with varying thickness and size. These heterostructures all exhibit robust nanomechanical resonances in the very high frequency (VHF) band (up to ~100 MHz). We observe that fundamental-mode resonance frequencies of the heterostructure devices fall between the values of graphene and MoS2 devices. Quality (Q) factors of heterostructure resonators are lower than those of graphene but comparable to those of MoS2 devices, suggesting interface damping related to interlayer interactions in the van der Waals heterostructures. This study validates suspended atomic layer heterostructures as an effective device platform and opens opportunities for exploiting mechanically coupled effects and interlayer interactions in such devices.
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