Bistable Fourth Sound Resonance in Superfluid $^3$He-B due to Gap Suppression

TL;DR

This study demonstrates the excitation of a fourth-sound resonance in superfluid helium-3 confined in nanofluidic channels, revealing non-linear effects linked to gap suppression and critical velocities consistent with theoretical models.

Contribution

The paper introduces nanofluidic resonators capable of probing superfluid gap suppression and critical velocities in superfluid helium-3 with unprecedented confinement.

Findings

Observation of non-linear softening of resonance due to flow-induced gap suppression

Calibration of resonance amplitude into superfluid velocity showing critical behavior

Agreement between measured critical velocities and Ginzburg-Landau predictions

Abstract

Superfluidity in $^3$He exhibits many unique properties that are of interest to modern condensed matter research, including multiple superfluid phase transitions, topological defects, and exotic classes of excitations like Majorana and Weyl fermions. Many of the most interesting theoretical proposals, which remain underexplored, are realized in highly confined geometries, where surface effects play a dominant role in the thermodynamic and hydrodynamic properties. We have developed nanofluidic resonators capable of exciting a fourth-sound acoustic mode in thin channels with a highly confined dimension ($750-1800$ nm) that is only $1-2$ orders of magnitude larger than the superfluid coherence length. When a sufficiently large drive force is applied, we observe a non-linear softening of the resonance that we interpret as due to the flow suppression of the superfluid gap. We have developed a model of the device that allows the resonance amplitude to be calibrated into a superfluid velocity, which exhibits critical behavior at particular velocities. We identify one of the observed critical velocities as being the velocity at which the gap component parallel to the flow is suppressed to zero. We compare the calibrated velocity to the prediction of a Ginzburg-Landau model, and find reasonable agreement. This measurement represents an ongoing effort to link the hydrodynamic measurements of these nanofluidic devices to theoretical predictions regarding surface gap suppression and surface-bound states.