Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9612074 · Journal of Experimental and Theoretical Physics Letters

Comment on vortex mass and quantum tunneling of vortices

Григорий Ефимович Воловик

Published Jan 1, 1997• 72 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1134/1.567299

Related papers

Fermions on Quantized Vortices in Superfluids and Superconductors

Григорий Ефимович Воловик

The bound states of fermions in cores of quantized vortices in superconductors and Fermi superfluids and their influence on the vortex dynamics are discussed. The role of the spectral flow of the fermions through the gap nodes is emphasized.

arXiv:cond-mat/9603094•TURKISH JOURNAL OF PHYSICS•Jan 1, 1996•6 citations

Transverse force on a vortex and vortex mass: Effects of free bulk and vortex-core bound quasiparticles

Edouard B Sonin

The paper reassesses the old but still controversial problem of the transverse force on a vortex and the vortex mass. The transverse force from free bulk quasiparticles on the vortex, both in the Bose and the Fermi liquids, originates from the Aharonov-Bohm effect. However, in the Fermi liquid, one should take into account peculiarities of the Aharonov-Bohm effect for BCS quasiparticles described by two-component spinor wave functions. There is no connection between the transverse force (either from free bulk quasiparticles or from vortex-core bound quasiparticles) and the spectral flow in the vortex core in superfluid Fermi liquid, in contrast to widely known claims. In fact, there is no steady spectral flow in the core of the moving vortex, and the analogy with the Andreev bound states in the superconductor--normal-metal--superconductor junction, where the spectral flow is really possible, is not valid in this respect. The role of the backflow on the vortex mass is clarified. The backflow is an inevitable consequence of a mismatch between the currents inside and outside the vortex core and restores the conservation of the particle number (charge) violated by this mismatch. In the Fermi liquid, the backflow compensates the current through the core bound states, which is a source of the vortex mass (the Kopnin mass). This results in renormalization of the Kopnin vortex mass by a numerical factor.

arXiv:1301.4554•Physical Review B•Apr 23, 2013•17 citations

Vortex Mass

Григорий Ефимович Воловик

Abstract The mass (inertia) of an object is determined as the response of the momentum of the object to its velocity. This chapter discusses the inertia of an object moving in the quantum vacuum of the Galilean quantum liquid. If it is a foreign object like a 3He atom moving in the quantum vacuum of superfluid 4He, then in addition to its bare mass the object acquires an extra mass, since it involves some part of the superfluid vacuum into motion. If the object is an excitation of the vacuum, like a vortex, all its mass is provided by the liquid. In addition to the associated hydrodynamic mass, which is similar to associated mass of external body moving in the liquid, there are two more contributions to a vortex mass. The ‘relativistic’ mass is the consequence of effective metric in superfluids. It is obtained as vortex energy divided by square of speed of sound, which plays the role of speed of light. In fermionic superfluids the Kopnin mass is added, which results from the fermion zero modes in the vortex core. This mass is related to peculiar phenomenon in quantum field theory. In the limit of smooth core these bound states behave as chiral massless fermions in the presence of magnetic field, and the additional vortex mass results from the non-zero density of states in magnetic field.

•Feb 26, 2009•0 citations

Dynamical signature of vortex mass in Fermi superfluids

Andrea Richaud, Matteo Caldara, Massimo Capone +2 more

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.

arXiv:2410.12417•Physical Review A•Nov 21, 2025•1 citation

Dissipative Dynamics of Quantum Vortices in Fermionic Superfluid

Andrea Barresi, Antoine Boulet, Piotr Magierski +1 more

In a recent article, Kwon et al. [Nature (London) 600, 64 (2021)NATUAS0028-083610.1038/s41586-021-04047-4] revealed nonuniversal dissipative dynamics of quantum vortices in a fermionic superfluid. The enhancement of the dissipative process is pronounced for the Bardeen-Cooper-Schrieffer interaction regime, and it was suggested that the effect is due to the presence of quasiparticles localized inside the vortex core. We test this hypothesis through numerical simulations with time-dependent density-functional theory: a fully microscopic framework with fermionic degrees of freedom. The results of fully microscopic calculations expose the impact of the vortex-bound states on dissipative dynamics in a fermionic superfluid. Their contribution is too weak to explain the experimental measurements, and we identify that thermal effects, giving rise to mutual friction between superfluid and the normal component, dominate the observed dynamics.

arXiv:2207.00870•Physical Review Letters•Jan 26, 2023•17 citations

Dynamic Vortex Mass in Clean Fermi Superfluids and Superconductors

Nikolai B. Kopnin, V. M. Vinokur

We calculate the dynamic vortex mass for clean Fermi superfluids including both $s$- and $d$-wave superconductors as a response to a vortex acceleration. Assuming a finite quasiparticle mean free time, the vortex mass appears to be a tensor with components depending on the quasiparticle relaxation time. The diagonal component dominates in the limit of long mean free time while the off-diagonal mass takes over in the moderately clean regime.

arXiv:cond-mat/9806065•Physical Review Letters•Nov 2, 1998•111 citations
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.
The paper reassesses the old but still controversial problem of the transverse force on a vortex and the vortex mass. The transverse force from free bulk quasiparticles on the vortex, both in the Bose and the Fermi liquids, originates from the Aharonov-Bohm effect. However, in the Fermi liquid, one should take into account peculiarities of the Aharonov-Bohm effect for BCS quasiparticles described by two-component spinor wave functions. There is no connection between the transverse force (either from free bulk quasiparticles or from vortex-core bound quasiparticles) and the spectral flow in the vortex core in superfluid Fermi liquid, in contrast to widely known claims. In fact, there is no steady spectral flow in the core of the moving vortex, and the analogy with the Andreev bound states in the superconductor--normal-metal--superconductor junction, where the spectral flow is really possible, is not valid in this respect. The role of the backflow on the vortex mass is clarified. The backflow is an inevitable consequence of a mismatch between the currents inside and outside the vortex core and restores the conservation of the particle number (charge) violated by this mismatch. In the Fermi liquid, the backflow compensates the current through the core bound states, which is a source of the vortex mass (the Kopnin mass). This results in renormalization of the Kopnin vortex mass by a numerical factor.
Abstract The mass (inertia) of an object is determined as the response of the momentum of the object to its velocity. This chapter discusses the inertia of an object moving in the quantum vacuum of the Galilean quantum liquid. If it is a foreign object like a 3He atom moving in the quantum vacuum of superfluid 4He, then in addition to its bare mass the object acquires an extra mass, since it involves some part of the superfluid vacuum into motion. If the object is an excitation of the vacuum, like a vortex, all its mass is provided by the liquid. In addition to the associated hydrodynamic mass, which is similar to associated mass of external body moving in the liquid, there are two more contributions to a vortex mass. The ‘relativistic’ mass is the consequence of effective metric in superfluids. It is obtained as vortex energy divided by square of speed of sound, which plays the role of speed of light. In fermionic superfluids the Kopnin mass is added, which results from the fermion zero modes in the vortex core. This mass is related to peculiar phenomenon in quantum field theory. In the limit of smooth core these bound states behave as chiral massless fermions in the presence of magnetic field, and the additional vortex mass results from the non-zero density of states in magnetic field.
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.
In a recent article, Kwon et al. [Nature (London) 600, 64 (2021)NATUAS0028-083610.1038/s41586-021-04047-4] revealed nonuniversal dissipative dynamics of quantum vortices in a fermionic superfluid. The enhancement of the dissipative process is pronounced for the Bardeen-Cooper-Schrieffer interaction regime, and it was suggested that the effect is due to the presence of quasiparticles localized inside the vortex core. We test this hypothesis through numerical simulations with time-dependent density-functional theory: a fully microscopic framework with fermionic degrees of freedom. The results of fully microscopic calculations expose the impact of the vortex-bound states on dissipative dynamics in a fermionic superfluid. Their contribution is too weak to explain the experimental measurements, and we identify that thermal effects, giving rise to mutual friction between superfluid and the normal component, dominate the observed dynamics.
We calculate the dynamic vortex mass for clean Fermi superfluids including both sss- and ddd-wave superconductors as a response to a vortex acceleration. Assuming a finite quasiparticle mean free time, the vortex mass appears to be a tensor with components depending on the quasiparticle relaxation time. The diagonal component dominates in the limit of long mean free time while the off-diagonal mass takes over in the moderately clean regime.