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Physical review. B, Condensed matter

Superfluid compressibility and the inertial mass of a moving singularity

Ji-Min Duan

Published Jul 1, 1993• 38 citations
Publisher

Abstract

The concept of finite compressibility of a Fermi superfluid is used to reconsider the problem of inertial mass of vortex lines in both neutral and charged superfluids at T=0. For the charged case, in contrast to previous works where perfect screening was assumed, we take proper account of electromagnetic screening and solve the bulk charge distribution caused by a moving vortex line. A similar problem for a superconducting thin film is also considered.

DOI
10.1103/physrevb.48.333

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The concept of finite compressibility of a Fermi superfluid is used to reconsider the problem of inertial mass of vortex lines in both neutral and charged superfluids at T=0. For the charged case, in contrast to previous works where perfect screening was assumed, we take proper account of electromagnetic screening and solve the bulk charge distribution caused by a moving vortex line. A similar problem for a superconducting thin film is also considered.
We reconsider the problem of the inertial mass of vortex lines in both neutral and charged sss-wave Fermi superfluids at T=0T=0T=0, taking into account the difference between amplitude and phase motion, Fermi-liquid effects, and electromagnetic screening. Our results are consistent with earlier estimates as regards order of magnitude, but differ from them in detail.
Vortex mass is a key concept in the study of superfluid dynamics, referring to the inertia of vortices in a superfluid, which affects their motion and behavior. Despite being an important quantity, the vortex mass has never been observed experimentally, and remains an unresolved issue in this field. As of now, a large body of research assumes that the vortex mass is a local parameter. In contrast, we present a calculation that suggests a logarithmic dependence on the system size, agreeing with some earlier predictions in the context of Bose gases. We analyze the problem using an effective field theory that describes ultracold atomic Fermi gases over the BEC-BCS crossover at both zero and nonzero temperatures. Our study reveals a strong dependence of the vortex mass on the scattering length; in particular, the vortex mass grows rapidly when moving toward the BCS side. Furthermore, we find that the system-size dependence of the vortex mass results in values an order of magnitude larger than those predicted by other models for realistic system sizes. This implies that the vortex mass could be observable in a wider parameter range than was previously expected. This is particularly relevant considering recent advances in experimental techniques that place the observation of vortex mass in superfluid Fermi gases within reach.
We derive a Galilean invariant expression for the electric field induced by a vortex moving through a charged superfluid at T=0T=0T=0, which holds for any superconductor, from the dirty to the superclean limit. The contribution of different areas around the vortex to the average electric field and to the charge distribution is analyzed. The results are extended to a neutral system, where the chemical potential takes over the role of the electrostatic potential in the charged situation. Different contributions to the vortex mass in charged and neutral superfluids are brought together for comparison and discussion.
We consider the inertial mass of a vortex in a superfluid. We obtain a vortex mass that is well defined and is determined microscopically and self-consistently by the elementary excitation energy of the kelvon quasiparticle localized within the vortex core. The obtained result for the vortex mass is found to be consistent with experimental observations on superfluid quantum gases and vortex rings in water. We propose a method to measure the inertial rest mass and Berry phase of a vortex in superfluid Bose and Fermi gases.
An inertial mass of a vortex can be calculated by driving it around in a circle with a steadily revolving pinning potential. We show that in the low-frequency limit this gives precisely the same formula that was used by Baym and Chandler, but find that the result is not unique and depends on the force field used to cause the acceleration. We apply this method to the Gross-Pitaevskii model, and derive a simple formula for the vortex mass. We study both the long-range and short-range properties of the solution. We agree with earlier results that the nonzero compressibility leads to a divergent mass. From the short-range behavior of the solution we find that the mass is sensitive to the form of the pinning potential, and diverges logarithmically when the radius of this potential tends to zero.