Dynamics of pinned quantized vortices in superfluid ${}^4$He in a microelectromechanical oscillator

Abstract

We numerically studied the vortex dynamics at zero temperature in superfluid ${}^4$He confined between two parallel rough solid boundaries, one of which oscillates in a shear mode. This study was motivated by the experimental work by Barquist $et$ $al.$ which employed a microelectromechanical systems (MEMS) oscillator operating in superfluid ${}^4$He at a near-zero temperature. Their experiments suggest that the motion of the MEMS oscillator is damped by quantized vortices. In our study, we postulated that this damping effect was closely associated with vortex pinning phenomena and developed pinning models. Our primary objective is to understand the vortex dynamics in the presence of pinning and to provide insight into the experimental observations regarding the damping mechanism. We confirmed that Kelvin waves were excited in the pinned vortices when the oscillation frequency of the solid boundary matched with the mode frequency of the Kelvin wave. Additionally, we examined the formation and evolution of vortex tangles between the boundaries. The vortex tangle was suppressed in the presence of pinning, while the absence of pinning allowed to form well developed vortex tangle resulting in turbulence. Finally, by evaluating the tension of pinned vortices we extracted the damping force acting on the solid boundaries.

11 pages + supplement, 17 figures

References in corpus (7)

• Mesoscopic physics of nanomechanical systems
• Drag force on an oscillating object in quantum turbulence
• Intrinsic vortex pinning in superconducting quasicrystals
• Nanoscale Real-Time Detection of Quantum Vortices at Millikelvin Temperatures
• Critical Velocity in the Presence of Surface Bound States in Superfluid ${}^3$He-B
• Damping of a micro-electromechanical oscillator in turbulent superfluid ${}^4$He: A novel probe of quantized vorticity in the ultra-low temperature regime
• Superfluid ${}^4$He as a rigorous test bench for different damping models in nanoelectromechanical resonators

Cited by in corpus (2)

• Decay of two-dimensional superfluid turbulence over pinning surface
• Modelling turbulent flow of superfluid ${}^4$He past a rough solid wall in the $T=0$ limit