# Frequency-dependent Study of Solid Helium-4 Contained in a Rigid Double-torus Torsional Oscillator

## TL;DR

This study used a rigid double-torus torsional oscillator to investigate solid helium-4, finding that observed responses are due to elastic effects rather than supersolidity, with dissipation significantly reduced.

## Contribution

It demonstrates that elastic effects dominate the response in a rigid TO, challenging previous interpretations of supersolid signatures in solid helium-4.

## Key findings

- Response magnitude scales with frequency squared
- Dissipation is greatly suppressed in the rigid TO
- No evidence of frequency-independent supersolid response

## Abstract

The rigid double-torus torsional oscillator (TO) is constructed to reduce any elastic effects in-herent to complicate TO structures, allowing explicit probing for a genuine supersolid signature. We investigated the frequency- and temperature-dependent response of the rigid double-torus TO containing solid 4He with 0.6 ppb 3He and 300 ppb 3He. We did not find evidence to support the frequency-independent contribution proposed to be a property of supersolid helium. The frequency-dependent contribution which comes from the simple elastic effect of solid helium coupled to TO is essentially responsible for the entire response. The magnitude of the period drop is linearly proportional to ${f}^{2}$, indicating that the responses observed in this TO are mostly caused by the overshoot of `soft' solid helium against the wall of the torus. Dissipation of the rigid TO is vastly suppressed compared to those of non-rigid TOs.