Hierarchical tensile structures with ultralow mechanical dissipation

TL;DR

This paper demonstrates hierarchical silicon nitride nanomechanical resonators with ultralow dissipation, achieving record-high quality factors and force sensitivities, and extends these principles to 2D membranes for advanced sensing and optomechanics.

Contribution

The study introduces a hierarchical design approach for nanomechanical resonators that significantly reduces mechanical dissipation and enhances performance, including extending to 2D membranes.

Findings

Quality factors up to 10^9 at 107 kHz achieved.

Force sensitivities of 740 zN/√Hz at room temperature and 90 zN/√Hz at 6 K.

Hierarchical structures exhibit fractal-like fractional spectral dimensions.

Abstract

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-P\'erot 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.