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arXiv:cond-mat/0411298 · Physical Review B

Vortex matter in the charged Bose liquid at absolute zero

V. V. Kabanov, A. S. Alexandrov

Published Apr 28, 2005• 9 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.71.132511

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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∞B=\ensuremath{\infty}B=\ensuremath∞ and no indication of a phase transition. The size of each vortex core decreases at about B\ensuremath−1∕2{B}^{\ensuremath{-}1∕2}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 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.
We theoretically investigate vortex-lattice phases of rotating spinor Bose-Einstein condensates (BEC's) with a ferromagnetic spin interaction by numerically solving the Gross-Pitaevskii equation. The spinor BEC under slow rotation can sustain a rich variety of exotic vortices due to the multicomponent order parameters, such as Mermin-Ho and Anderson-Toulouse coreless vortices (the two-dimensional Skyrmion and meron) and nonaxisymmetric vortices with shifting vortex cores. Here, we present the spin texture of various vortex-lattice states at higher rotation rates and in the presence of an external magnetic field. In addition, the vortex phase diagram is constructed in the plane of the total magnetization MMM and the external rotation frequency $\ensuremath{\Omega}$ by comparing the free energies of possible vortices. It is shown that the vortex phase diagrams in the $M\text{\ensuremath{-}}\ensuremath{\Omega}$ plane may be divided into two categories: (i) the coreless vortex lattice formed by the several types of Mermin-Ho vortices and (ii) the vortex lattice filling in the cores with the pure polar (antiferromagnetic) state. In particular, it is found that the type-(ii) state forms composite lattices of coreless and polar-core vortices. The difference between type (i) and type (ii) results from the existence of the singularity of the spin textures, which may be experimentally confirmed by the spin imaging within polarized light recently proposed by Carusotto and Mueller. We also discuss the stability of triangular and square lattice states for rapidly rotating condensates.
The phase diagram of lowest-energy vortices in the polar phase of spin-1 Bose-Einstein condensates is investigated theoretically. Singly quantized vortices are categorized by the local ordered state in the vortex core and three types of vortices are found as lowest-energy vortices, which are elliptic AF-core vortices, axisymmetric F-core vortices, and N-core vortices. These vortices are named after the local ordered state, ferromagnetic (F), antiferromagnetic (AF), broken-axisymmetry (BA), and normal (N) states apart from the bulk polar (P) state. The N-core vortex is a conventional vortex, in the core of which the superfluid order parameter vanishes. The other two types of vortices are stabilized when the quadratic Zeeman energy is smaller than a critical value. The axisymmetric F-core vortex is the lowest-energy vortex for ferromagnetic interaction, and it has an F core surrounded by a BA skin that forms a ferromagnetic-spin texture, as exemplified by the localized Mermin-Ho texture. The elliptic AF-core vortex is stabilized for antiferromagnetic interaction; the vortex core has both nematic-spin and ferromagnetic orders locally and is composed of the AF-core soliton spanned between two BA edges. The phase transition from the N-core vortex to the other two vortices is continuous, whereas that between the AF-core and F-core vortices is discontinuous. The critical point of the continuous vortex-core transition is computed by the perturbation analysis of the Bogoliubov theory and the Ginzburg-Landau formalism describes the critical behavior. The influence of trapping potential on the core structure is also investigated.
Fermions localized within vortex cores can form one-dimensional Fermi liquids. The nonzero density of states in these Fermi-liquids can lead to instability of the symmetric structure of the vortex core. We consider a symmetry breaking which is obtained due to spontaneous admixture of the spin-triplet p-wave component of the order parameter in conventional s-wave vortex in the presence of magnetic field. This occurs at low enough temperature and leads to an asymmetric shape of the vortex core. Similar phenomenon of the symmetry breaking induced by the core fermions occurs in electroweak ZZZ-strings (S.G. Naculich, Phys. Rev. Lett., 75 (1995), 998).
We study ultracold neutral fermion superfluids in the presence of fictitious magnetic fields, as well as charged fermion superfluids in the presence of real magnetic fields. Charged fermion superfluids undergo a phase transition from type-I to type-II superfluidity, where the magnetic properties of the superfluid change from being a perfect diamagnet without vortices to a partial diamagnet with the emergence of the Abrikosov vortex lattice. The transition from type-I to type-II superfluidity is tuned by changing the scattering parameter (interaction) for fixed density. We also find that neutral fermion superfluids such as 6Li^{6}\mathrm{Li}6Li and 40K^{40}\mathrm{K}40K are extreme type-II superfluids and are more robust to the penetration of a fictitious magnetic field in the BCS-BEC crossover region near unitarity, where the critical fictitious magnetic field reaches a maximum as a function of the scattering parameter (interaction).