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Physical review. B, Condensed matter

Vortex in the charged Bose liquid

A. S. Alexandrov

Published Dec 1, 1999• 8 citations
Publisher

Abstract

Equations describing a single vortex in the charged Bose liquid at zero temperature are derived. The zero-temperature coherence length, magnetic-field penetration depth, vortex structure and energy, and lower critical field are calculated. The vortex differs from that in type-II BCS superconductors or in neutral superfluids. Its core is charged, and there is an electric field inside the core.

DOI
10.1103/physrevb.60.14573

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Equations describing a single vortex in the charged Bose liquid at zero temperature are derived. The zero-temperature coherence length, magnetic-field penetration depth, vortex structure and energy, and lower critical field are calculated. The vortex differs from that in type-II BCS superconductors or in neutral superfluids. Its core is charged, and there is an electric field inside the core.
The Gross-Pitaevskii-type equation is solved for the charge Bose liquid in an external magnetic field at zero temperature. There is a vortex lattice with locally broken charge neutrality. Remarkably, there is no upper critical field at zero temperature, so the density of single flux-quantum vortices monotonously increases with the magnetic field up to $B=\ensuremath{\infty}$ and no indication of a phase transition. The size of each vortex core decreases at about ${B}^{\ensuremath{-}1∕2}$ keeping the system globally charge neutral. If bosons are composed of two fermions, a phase transition to a spin-polarized Fermi liquid at some magnetic field larger than the pair-breaking field is predicted.
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 a single vortex in a superfluid Fermi gas in the BCS-BEC crossover regime near a Feshbach resonance. The effect of the molecular Bose-Einstein condensate upon the vortex structure is discussed within the mean field approximation at zero temperature. Using the self-consistent Bogoliubov-de Gennes equation of the fermion-boson coupled model, we calculate density distributions of atoms and molecules. As the number of the molecules increases, both atomic and molecular density changes from BCS-like distribution to BEC-like. We also study the change of the vortex core size in the crossover regime.
We investigate the vortex structures and dynamics in two-dimensional uniform Bose quantum liquids, accounting for quantum fluctuation effects via solving the extended Gross-Pitaevskii equation with Lee-Huang-Yang corrections. Using effective potential field analysis and the finite difference method, we establish the conditions for the existence of vortex excitations in such systems. Our results show that vortex excitations require a minimum background density, which is lower than the equilibrium density. As the vortex topological charge increases, this minimum density approaches the equilibrium density. At the critical density, the condensate's healing length remains finite, but the vortex core size diverges---a phenomenon highlighting the distinct properties of quantum liquids compared to gaseous Bose-Einstein condensates. Furthermore, stability analysis reveals that vortex stability depends on the liquid density, confirmed by dynamical evolution under perturbations.
Adiabatic effective action for vortices in neutral and charged superfluids at zero temperature are calculated using the topological Landau-Ginzburg theory recently proposed by Hatsuda, Yahikozawa, Ao and Thouless, and vortex dynamics are examined. The Berry phase term arising in the effective action naturally yields the Magnus force in both neutral and charged superfluids. It is shown that in neutral superfluid there is only one degree of freedom, namely the center of vorticities, and the vortex energy is proportional to the sum of all vorticities so that it is finite only for the vanishing total vorticity of the system. On the other hand the effective mass and the vortex energy for a vortex in charged superfluids are defined individually as expected. The effects of the vortex core on these quantities are also estimated. The possible depinning scenario which is governed by the Magnus force and the inertial mass is also discussed.