Hierarchical tensile structures with ultralow dissipation*

Self-similar structures occur naturally and have been employed to engineer exotic physical properties. We report nanofabricated resonators with exceptionally low mechanical dissipation rates enabled by an unconventional type of “soft-clamping" which emerges in branched systems of tensioned strings. We fabricate self-similar binary trees of high-stress Si₃N₄ with fundamental mode quality factors as high as 500 million at 150 kHz mode frequencies, corresponding to thermal-noise-limited force sensitivities below 1 aN/rtHz. Intriguingly, the hierarchical organization of branches in binary tree resonators results in high-order acoustic mode densities consistent with non-integer spectral dimensions, characteristic of fractal geometries. Finally, exploiting the same design principles we create trampoline membranes with quality factors up to 250 million at 100 kHz mode frequencies. Our results open new avenues in nanoscale sensing and quantum experiments with mechanical resonators.