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arXiv:2410.12417 · Physical Review A

Dynamical signature of vortex mass in Fermi superfluids

Andrea Richaud, Matteo Caldara, Massimo Capone, Pietro Massignan, Gabriel Wlazłowski

Published Nov 21, 2025• 1 citation
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Abstract

Quantum vortices are commonly described as funnel-like objects around which the superfluid swirls, and their motion is typically modeled in terms of massless particles. Here we show that in Fermi superfluids the normal component confined in the vortex core provides the vortex with a finite inertial mass. This inertia imparts an unambiguous signature to the dynamic behavior of vortices, specifically manifesting as small-amplitude transverse oscillations which remarkably follow the prediction of a simple point-like model supplemented by an effective mass. We demonstrate this phenomenon through large-scale time-dependent simulations of Fermi superfluids across a wide range of interaction parameters, at both zero and finite temperatures, and for various initial conditions. Our findings pave the way for the exploration of inertial effects in superfluid vortex dynamics.

DOI
10.1103/zcb4-dldf

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Quantum vortices are commonly described as funnel-like objects around which the superfluid swirls, and their motion is typically modeled in terms of massless particles. Here we show that in Fermi superfluids the normal component confined in the vortex core provides the vortex with a finite inertial mass. This inertia imparts an unambiguous signature to the dynamic behavior of vortices, specifically manifesting as small-amplitude transverse oscillations which remarkably follow the prediction of a simple point-like model supplemented by an effective mass. We demonstrate this phenomenon through large-scale time-dependent simulations of Fermi superfluids across a wide range of interaction parameters, at both zero and finite temperatures, and for various initial conditions. Our findings pave the way for the exploration of inertial effects in superfluid vortex dynamics.
Vortex mass, which is the inertia of a quantum vortex, has never been observed in superfluids and is a long-standing problem in low-temperature physics. The impact of the mass is considered negligible in typical experiments with superfluid 4He^{4}\mathrm{He}4He. Recent developments of experimental techniques for manipulating quantum vortices in superfluid atomic gases have enabled us to test this problem more accurately. By introducing the vortex mass time and length as universal scales to many-body problems of massive quantum vortices, the theoretical description is formulated in the simplest manner and is universally applicable to different quantum fluids, including fermionic and multicomponent superfluids. There are two branches, the cyclotron and massless branches, for the circular motion of a pair of like-sign vortices. Finding a stable cyclotron branch for the motion of vortices is a clear evidence of vortex mass and superfluid $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{B}$ is the specific example of a system where this phenomena could be observed. The impact of the mass on the massless branch is small but can be enhanced by taking the difference in the two-body dynamics of point vortices with different initial conditions. Our results imply that the vortex mass is a direct cause of the splitting instability of a doubly quantized vortex at absolute zero and that the vortex mass length characterizes the final state after the instability. It is also demonstrated that a pair of massive vortices with opposite circulations has a critical distance characterized by the vortex mass length, below which they are spontaneously annihilated without thermal fluctuations.
Abstract We consider the dynamical properties of quantum vortices with filled massive cores, hence the term “massive vortices”. While the motion of massless vortices is described by first-order motion equations, the inclusion of core mass introduces a second-order time derivative in the motion equations and thus doubles the number of independent dynamical variables needed to describe the vortex. The simplest possible system where this physics is present, i.e. a single massive vortex in a circular domain, is thoroughly discussed. We point out that a massive vortex can exhibit various dynamical regimes, as opposed to its massless counterpart, which can only precess at a constant rate. The predictions of our analytical model are validated by means of numerical simulations of coupled Gross-Pitaevskii equations, which indeed display the signature of the core inertial mass. Eventually, we discuss a nice formal analogy between the motion of massive vortices and that of massive charges in two-dimensional domains pierced by magnetic fields.
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.
Vortex mass in Fermi superfluids and superconductors and its influence on quantum tunneling of vortices are discussed. The vortex mass is essentially enhanced due to the fermion zero modes in the core of the vortex: the bound states of the Bogoliubov quasiparticles localized in the core. These bound states form the normal component, which is nonzero even in the low-temperature limit. In the collisionless regime ω 0 τ≫1 the normal component trapped by the vortex is unbound from the normal component in a bulk superfluid/superconductor and adds to the inertial mass of the moving vortex. In a d-wave superconductor the vortex mass has an additional factor of (B c2/B)1/2 due to the gap nodes.
Excitations in vortex cores in superconductors and other Fermi superfluids are single-particle excitations with a peculiar energy spectrum. These excitations are responsible for many important thermodynamic properties such as specific heat, London penetration length, etc. They also determine the dynamic characteristics of superconductors and superfluids through their interaction with vortices. Flux flow resistance, the Hall effect in type II superconductors and the mutual friction in superfluids are the most important phenomena which strongly depend on vortex core excitations. These phenomena determine the electromagnetic responses of type II superconductors and the hydrodynamic behaviour of superfluids and are of great significance for practical applications of superconducting devices and for understanding the most fundamental properties of correlated electrons and other Fermi particles. In this review we consider the dynamic properties of superconductors and superfluids and outline the basic ideas and results on the vortex dynamics in clean superfluid Fermi systems. The forces acting on moving vortices are discussed including the problem of the transverse force which was a matter of confusion for quite some time. We formulate the equations of the vortex dynamics, which include all the forces and the inertial term associated with excitations bound to the moving vortex.
We explore the experimental implications of a recent theory of the quantum dynamics of vortices in superfluids proximate to Mott insulators (cond-mat/0408329 and cond-mat/0409470). The theory predicts modulations in the local density of states in the regions over which the vortices execute their quantum zero point motion. We use the spatial extent of such modulations in scanning tunnelling microscopy measurements (Hoffman et al., cond-mat/0201348) on the vortex lattice of BSCCO to estimate the inertial mass of a point vortex. We discuss other, more direct, experimental signatures of the vortex dynamics.