In everyday life, we’re used to a flexible sheet, like foil, simply bobbing up and down when bent. But in the world of quantum crystals, things are different. Some materials have a remarkable property — the Berry phase, which manifests as Hall viscosity. This means that if you shift layers inside such a crystal, a sideways motion emerges, similar to a car skidding on a slippery road, but without any friction. In a flat membrane, bending sound waves don’t create shear, so Hall viscosity remains ‘invisible’. However, just slightly curving the membrane — giving it the shape of a tiny bowl — makes each vertical deflection imperceptibly twist the material in-plane, like a figure skater pulling their arms in while spinning. This approach essentially turns the curved membrane into a miniature tool for mechanical spectroscopy, allowing the quantum properties of the material to be explored.

Building on the equations of elasticity developed by Lev Landau and the quantum Berry phase, physicists calculated this effect for the magnetic material α-RuCl3. Even an extremely faint sound at a frequency of 10 billion oscillations per second generates a torque of roughly 2×10⁻²² Newton-meters. On an everyday scale, that’s vanishingly small — it would take tens of thousands of years for that torque to rotate a postage stamp by one degree. But for modern interferometric sensors, originally built to hunt for gravitational waves, this signal is already detectable. Moreover, flipping the magnetic field direction changes the rotation sign, allowing it to be reliably picked out from background noise.

This phononic analog of the Einstein–de Haas effect opens the door to ultra-sensitive quantum sensors and microscopic gyroscopes. The work deepens understanding of quantum thermodynamics and paves the way for precise quantum measurements of mechanical angular momentum in two-dimensional materials.