Physical Review Letters

Landau critical velocity for a macroscopic object moving in superfluid B3 : Evidence for gap suppression at a moving surface

C. A. M. Castelijns, K. F. Coates, A. M. Guénault, S. G. Mussett, G. R. Pickett

Published Jan 6, 1986• 145 citations

Abstract

We have observed that the motion of a vibrating-wire resonator in superfluid $^{3}\mathit{B}$ at temperatures below ${\mathrm{T}}_{\mathrm{c}}$/8 is associated with a sharp critical velocity, ${\mathrm{v}}_{\mathrm{c}}$, above which very high dissipation sets in. We identify this velocity with the Landau critical velocity for pair breaking. That the observed value of ${\mathrm{v}}_{\mathrm{c}}$ is a factor of 2 lower than the critical velocity expected from the BCS value of the gap we take as evidence that the gap is suppressed by about 50% of its bulk value near a moving boundary.

DOI: 10.1103/physrevlett.56.69

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Physical Review Letters

Landau critical velocity for a macroscopic object moving in superfluid B3 : Evidence for gap suppression at a moving surface

C. A. M. Castelijns, K. F. Coates, A. M. Guénault, S. G. Mussett, G. R. Pickett

Published Jan 6, 1986• 145 citations

Publisher

Abstract

We have observed that the motion of a vibrating-wire resonator in superfluid

^{3}\mathit{B}

at temperatures below

{\mathrm{T}}_{\mathrm{c}}

/8 is associated with a sharp critical velocity,

{\mathrm{v}}_{\mathrm{c}}

, above which very high dissipation sets in. We identify this velocity with the Landau critical velocity for pair breaking. That the observed value of

{\mathrm{v}}_{\mathrm{c}}

is a factor of 2 lower than the critical velocity expected from the BCS value of the gap we take as evidence that the gap is suppressed by about 50% of its bulk value near a moving boundary.

DOI: 10.1103/physrevlett.56.69

Related papers

Models for supercritical motion in a superfluid Fermi liquid

J. A. Kuorelahti, Sami Laine, E. V. Thuneberg

We study the drag force on objects moving in a Fermi superfluid at velocities on the order of the Landau velocity ${v}_{L}$ . The expectation has been that ${v}_{L}$ is the critical velocity beyond which the drag force starts to increase toward its normal-state value. This expectation is challenged by a recent experiment measuring the heat generated by a uniformly moving wire immersed in superfluid $^{3}\mathrm{He}$ . We introduce the basis for the calculation of the drag force on a macroscopic object using the Fermi-liquid theory of superfluidity. As a technical tool in the calculations, we propose a boundary condition that describes diffuse reflection of quasiparticles from a surface on a scale that is larger than the superfluid coherence length. We calculate the drag force on steadily moving objects of different sizes. For an object that is small compared to the coherence length, we find a drag force that is in accordance with the expectation. For a macroscopic object, we need to take into account the spatially varying flow field around the object. At low velocities, this arises from ideal flow of the superfluid. At higher velocities, the flow field is modified by excitations that are created when the flow velocity locally exceeds ${v}_{L}$ . The flow field causes Andreev reflection of quasiparticles and thus leads to change in the drag force. We calculate multiple limiting cases for a cylinder-shaped object. In the absence of quasiparticle-quasiparticle collisions, we find that the critical velocity is larger than ${v}_{L}$ and the drag force (per cross-sectional area) at $2{v}_{L}$ is reduced by an order of magnitude compared to the case of a small object. In a collision-dominated limit, the flow shows signs of instability at a velocity below ${v}_{L}$ .We study the drag force on objects moving in a Fermi superfluid at velocities on the order of the Landau velocity ${v}_{L}$. The expectation has been that ${v}_{L}$ is the critical velocity beyond which the drag force starts to increase toward its normal-state value. This expectation is challenged by a recent experiment measuring the heat generated by a uniformly moving wire immersed in superfluid $^{3}\mathrm{He}$. We introduce the basis for the calculation of the drag force on a macroscopic object using the Fermi-liquid theory of superfluidity. As a technical tool in the calculations, we propose a boundary condition that describes diffuse reflection of quasiparticles from a surface on a scale that is larger than the superfluid coherence length. We calculate the drag force on steadily moving objects of different sizes. For an object that is small compared to the coherence length, we find a drag force that is in accordance with the expectation. For a macroscopic object, we need to take into account the spatially varying flow field around the object. At low velocities, this arises from ideal flow of the superfluid. At higher velocities, the flow field is modified by excitations that are created when the flow velocity locally exceeds ${v}_{L}$. The flow field causes Andreev reflection of quasiparticles and thus leads to change in the drag force. We calculate multiple limiting cases for a cylinder-shaped object. In the absence of quasiparticle-quasiparticle collisions, we find that the critical velocity is larger than ${v}_{L}$ and the drag force (per cross-sectional area) at $2{v}_{L}$ is reduced by an order of magnitude compared to the case of a small object. In a collision-dominated limit, the flow shows signs of instability at a velocity below ${v}_{L}$.

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The resistance to motion of a wire in superfluid $^{3}\mathit{B}$ has three contributions: that due to the internal friction of the resonator; that due to pair breaking; and that due to the quasiparticle gas. We have been able to separate quasiparticle contribution and find that it is highly nonlinear with velocity on the scale of the Landau velocity, \ensuremath{\Delta}/ ${\mathrm{p}}_{\mathrm{F}}$ , and falls with increasing velocity. This indicates that the quasiparticle resistance is also governed by the condensate, almost certainly through Andreev reflection in the flow field around the wire.The resistance to motion of a wire in superfluid $^{3}\mathit{B}$ has three contributions: that due to the internal friction of the resonator; that due to pair breaking; and that due to the quasiparticle gas. We have been able to separate quasiparticle contribution and find that it is highly nonlinear with velocity on the scale of the Landau velocity, \ensuremath{\Delta}/${\mathrm{p}}_{\mathrm{F}}$, and falls with increasing velocity. This indicates that the quasiparticle resistance is also governed by the condensate, almost certainly through Andreev reflection in the flow field around the wire.

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arXiv:1610.02347Physical Review LettersFeb 8, 201721 citations

We have observed that the motion of a vibrating-wire resonator in superfluid

^{3}\mathit{B}

at temperatures below

{\mathrm{T}}_{\mathrm{c}}

/8 is associated with a sharp critical velocity,

{\mathrm{v}}_{\mathrm{c}}

, above which very high dissipation sets in. We identify this velocity with the Landau critical velocity for pair breaking. That the observed value of

{\mathrm{v}}_{\mathrm{c}}

is a factor of 2 lower than the critical velocity expected from the BCS value of the gap we take as evidence that the gap is suppressed by about 50% of its bulk value near a moving boundary.

We study the drag force on objects moving in a Fermi superfluid at velocities on the order of the Landau velocity

{v}_{L}

. The expectation has been that

{v}_{L}

is the critical velocity beyond which the drag force starts to increase toward its normal-state value. This expectation is challenged by a recent experiment measuring the heat generated by a uniformly moving wire immersed in superfluid

^{3}\mathrm{He}

. We introduce the basis for the calculation of the drag force on a macroscopic object using the Fermi-liquid theory of superfluidity. As a technical tool in the calculations, we propose a boundary condition that describes diffuse reflection of quasiparticles from a surface on a scale that is larger than the superfluid coherence length. We calculate the drag force on steadily moving objects of different sizes. For an object that is small compared to the coherence length, we find a drag force that is in accordance with the expectation. For a macroscopic object, we need to take into account the spatially varying flow field around the object. At low velocities, this arises from ideal flow of the superfluid. At higher velocities, the flow field is modified by excitations that are created when the flow velocity locally exceeds

{v}_{L}

. The flow field causes Andreev reflection of quasiparticles and thus leads to change in the drag force. We calculate multiple limiting cases for a cylinder-shaped object. In the absence of quasiparticle-quasiparticle collisions, we find that the critical velocity is larger than

{v}_{L}

and the drag force (per cross-sectional area) at

2{v}_{L}

is reduced by an order of magnitude compared to the case of a small object. In a collision-dominated limit, the flow shows signs of instability at a velocity below

{v}_{L}

We have observed the distortion of the gap and associated excitation spectrum in superfluid

^{3}\mathit{B}

with increasing magnetic field up to the first-order transition to the A phase at a temperature of

{\mathit{T}}_{\mathit{c}}

/T of about 7 (\ensuremath{\le}140 \ensuremath{\mu}K at P=0). The pair-breaking critical velocity of a vibrating-wire resonator is monitored as a function of field. By plotting the critical velocity we can follow changes in the B-phase excitation spectrum with increasing magnetic field, which are in excellent agreement with the calculations of Ashida and Nagai. The sudden transition to the A phase at the critical field is clearly seen.

The resistance to motion of a wire in superfluid

^{3}\mathit{B}

has three contributions: that due to the internal friction of the resonator; that due to pair breaking; and that due to the quasiparticle gas. We have been able to separate quasiparticle contribution and find that it is highly nonlinear with velocity on the scale of the Landau velocity, \ensuremath{\Delta}/

{\mathrm{p}}_{\mathrm{F}}

, and falls with increasing velocity. This indicates that the quasiparticle resistance is also governed by the condensate, almost certainly through Andreev reflection in the flow field around the wire.