Models for supercritical motion in a superfluid Fermi liquid

Abstract

We study the drag force on objects moving in a Fermi superfluid at velocities on the order of the Landau velocity vL. The expectation has been that vL is the critical velocity beyond which the drag force starts to increase towards 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 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 vL. 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 vL and the drag force (per cross-sectional area) at 2vL 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 vL. arXiv:1806.02554v2 [cond-mat.supr-con]

Design of a system for controlling a levitating sphere in superfluid 3He at extremely low temperatures

“…Recently, the uniform motion technique was used to discover anomalously long lifetimes of quasiparticles bound to the surfaces of superfluid 3 He-B 7 . This time was found to be about 6 ms, much longer than any other time scales in the system 8 . The discovery of the long lifetime of the quasiparticles also explains another recently observed anomalous phenomenon -exceptionally high apparent thermal conductivity in narrow channels of superfluid 3 He: most likely it is the long-lived surface quasiparticles that carry significant energy along the walls of the channel 9 .…”

Fundamental dissipation due to bound fermions in the zero-temperature limit

“…In particular, it remains an open question how exactly bound-state dynamics should be described in a full two-dimensional model of the wire surface with a flow velocity distribution, a theoretically justifiable bound state spectrum (not fully gapless), diffusion or transport between various parts of the surface etc. Competing theoretical suggestions are sparse, but there have been some discussions related to a layer of vortices covering the wire acting as a buffer and therefore masking the Landau velocity 22 . On the other hand, theoretical work on superflows exceeding the Landau velocity has recently been published studying other systems, such as polaron–polaritons 37 and graphene 38 .…”

“…In terms of dynamics, however, the above picture still lacks rigorous theoretical justification. In particular, its critics have pointed out that thermalisation of the surface-bound states should be so fast, of the order of nanoseconds, that the equilibrium cannot be disturbed by the relatively slow motion (typically milliseconds) of a macroscopic moving object 22 . In this article, we provide experimental evidence to end the controversy.…”

Exceeding the Landau speed limit with topological Bogoliubov Fermi surfaces

“…Remarkably, in the topological superfluid phases of 3 He, superflow may persist when one [1,2], or even both [3][4][5], of those constraints are violated. In particular, topological protection is absent in the chiral superfluid 3 He-A, where the circulation is topologically unstable toward a phase slip with the formation of skyrmions [4,5].…”