Superfluid vortices in the color-flavor-locked (CFL) phase of dense quark matter are known to be energetically disfavored relative to well-separated triplets of "semi-superfluid" color flux tubes. However, the short-range interaction (metastable versus unstable) has not been established. In this paper we perform numerical calculations using the effective theory of the condensate field, mapping the regions in the parameter space of coupling constants where the vortices are metastable versus unstable. For the case of zero gauge coupling we analytically identify a candidate for the unstable mode, and show that it agrees well with the results of the numerical calculations. We find that in the region of the parameter space that seems likely to correspond to real-world CFL quark matter the vortices are unstable, indicating that if such matter exists in neutron star cores it is very likely to contain semi-superfluid color flux tubes rather than superfluid vortices.
Topological defects arise in a variety of systems, e.g. vortices in superfluid helium to cosmic strings in the early universe. There is an indirect evidence of neutron superfluid vortices from glitches in pulsars. One also expects that topological defects may arise in various high baryon density phases of quantum chromodynamics (QCD), e.g. superfluid topological vortices in the color flavor locked (CFL) phase. Though vastly different in energy/length scales, there are universal features, e.g. in the formation of all these defects. Utilizing this universality, we investigate the possibility of …
Vortices in spin-$0$ superfluids generically carry magnetic fields inside their cores, so that even neutral superfluid vortices may be thought of as magnetic flux tubes. We give a systematic analysis of this `vortex magnetic effect' using effective field theory, clarifying earlier literature on the subject. Our analysis shows that in superfluid Helium-$4$ the vortex magnetic effect may be large enough to be experimentally detectable.
I show that the usual model of the rotational response of a neutron star, which predicts rotation-induced neutronic vortices and no rotation-induced protonic vortices, does not hold (i) beyond a certain threshold of entrainment interaction strength nor (ii) in case of nonzero $Σ^-$ hyperon gap. I demonstrate that in both these cases the rotational response involves creation of phase windings in electrically charged condensate. Lattices of bound states of vortices which are caused these effects can (for a range of parameters) strongly reduce the interaction between rotation-induced vortices wit…
We study, within Ginzburg-Landau theory, the responses of three-flavor superfluid quark-gluon plasmas to external magnetic fields and rotation, in both the color-flavor locked and isoscalar color-antitriplet diquark phases near the critical temperature. Fields are incorporated in the gradient energy arising from long wavelength distortions of the condensate, via covariant derivatives to satisfy local gauge symmetries associated with color and electric charge. Magnetic vortex formation, in response to external magnetic fields, is possible only in the isoscalar phase; in the color-flavor locked …
We discuss quantized vortices in neutron $^3P_2$ superfluids, which are believed to realize in high density neutron matter such as neutron stars. By using the Ginzburg-Landau free energy for $^3P_2$ superfluids, we determine the ground state in the absence and presence of the external magnetic field, and numerically construct $^3P_2$ quantized vortices in the absence and presence of the external magnetic field along the vortex axis (poloidal) or angular direction (toroidal). We find in certain situations the spontaneous magnetization of the vortex core, whose typical magnitude is about $10^{7-…
A rotating ultracold S-wave superfluid Fermi gas is considered, when the population imbalance (or equivalently the mismatch in chemical potentials) corresponds to the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state in the vicinity of the Lifshitz critical point. It is shown that under these conditions the critical angular velocity in two-dimensional systems is an oscillating function of temperature and population imbalance giving rise to reentrant superfluid phases. This leads to vortex lattices with multiple-quantized circulation quanta. The reason for this behavior is the population by Cooper …
${}^{3}P_{2}$ superfluids realized in neutron stars are the largest topological quantum matters in our Universe. We establish the existence and stability of non-Abelian half-quantum vortices (HQVs) in ${}^{3}P_{2}$ superfluids with strong magnetic fields. Using a self-consistent microscopic approach, we find that a singly quantized vortex is energetically destabilized into a pair of two non-Abelian HQVs owing to the strongly spin-orbit-coupled pairing. We find a topologically protected Majorana fermion on each HQV, thereby providing two-fold non-Abelian anyons characterized by both Majorana fe…
Formation of topological defects during symmetry breaking phase transitions via the {\it Kibble mechanism} is extensively used in systems ranging from condensed matter physics to the early stages of the universe. Kibble mechanism uses topological arguments and predicts equal probabilities for the formation of defects and anti-defects. Certain situations, however, require a net bias in the production of defects (or antidefects) during the transition, for example, superfluid transition in a rotating vessel, or flux tubes formation in a superconducting transition in the presence of external magne…
In the Ginzburg-Landau limit, a possible texture without singular cores in a rotating neutron spin-triplet superfluid is studied. It is constructed the lattice of non-singular vortices with a vorticity diffusely distributed over the entire unit cell. The upper limit of the free energy associated with this structure is estimated, and the result shows that non-singular vortices are more preferable in the core of rotating neutron stars than ordinary linear singular vortices. The order parameter of the studied neutron system belongs to the unitary class. This implies that the superfluid under cons…
Alice and Boojums are both representative characters created by Lewis Carroll. We show that they possibly meet in cores of rotating neutron stars. Recent studies of quark-hadron continuity suggest that neutron superfluid matter can connect smoothly to two-flavor symmetric quark matter at high densities. We study how this can be maintained in the presence of the vortices. In the neutron matter, quantized superfluid vortices arise. In the two-flavor dense quark matter, vortices carrying color magnetic fluxes together with fractionally quantized superfluid circulations appear as the most stable c…
Superfluidity and superconductivity are remarkable manifestations of quantum coherence at a macroscopic scale. The dynamics of superfluids has dominated the study of these systems for decades now, but a comprehensive theoretical framework is still lacking. We introduce a local extension of the time-dependent density functional theory to describe the dynamics of fermionic superfluids. Within this approach one can correctly represent vortex quantization, generation, and dynamics, the transition from a superfluid to a normal phase and a number of other large amplitude collective modes which are b…
A microscopic, quantum mechanical model for neutron vortices in the crust of a neutron star is presented. After a brief introduction to the Bogoliubov- de Gennes equations, which form the basis for our calculations, we present results for density distributions, vortex core sizes and vortex energies, both for an isolated neutron vortex and for the case when the vortex core overlaps with a cylindrical nucleus. Earlier results on the vortex core size are confirmed, indicating a much less dramatic variation of the vortex core size with density than predicted by the BCS formula.
We point out that half-quantized non-Abelian vortices exist as the minimum energy states in rotating neutron $^3P_2$ superfluids in the inner cores of magnetars with magnetic field greater than $3 \times 10^{15}$ Gauss, while they do not in ordinary neutron stars with smaller magnetic fields. One integer vortex is split into two half-quantized vortices. The number of vortices is about $10^{19}$ and they are separated at about $μ$m in a vortex lattice for typical parameters, while the vortex core size is about 10-100 fm. They are non-Abelian vortices characterized by non-Abelian first homotopy …
We formulate dissipative magnetohydrodynamic equations for finite-temperature superfluid and superconducting charged relativistic mixtures, taking into account the effects of particle diffusion and possible presence of Feynman-Onsager and/or Abrikosov vortices in the system. The equations depend on a number of phenomenological transport coefficients, which describe, in particular, relative motions of different particle species and their interaction with vortices. We demonstrate how to relate these transport coefficients to the mutual friction parameters and momentum transfer rates arising in t…
We study quantized vortices in ${}^{3}P_{2}$ superfluids using a microscopic theory for the first time. The theory is based on the Eilenberger equation to determine the order parameters and the Bogoliubov-de Gennes (BdG) equation to obtain the eigenenergies and the core magnetization. Within axisymmetric vortex configurations, we find several stable and metastable vortex configurations which depend on the strength of a magnetic field, similar to a $v$ vortex and $o$ vortex in $^3$He superfluids. We demonstrate that the $o$ vortex is the most stable axisymmetric vortex in the presence of a stro…
The core region of a neutron star may feature quark matter in the color-flavor- locked (CFL) phase. The CFL condensate breaks the baryon number symmetry, such that the phenomenon of superfluidity arises. If the core of the star is rotating, vortices will form in the superfluid, carrying the quanta of angular momentum. In a previous study we have solved the question of stability of these vortices, where we found numerical proof of a conjectured instability, according to which superfluid vortices will decay into an arrangement of so-called semi-superfluid fluxtubes. Here we report first results …
We investigate vortex solutions in the Ginzburg-Landau theory for neutron $^3P_2$ superfluids relevant for neutron star cores in which neutron pairs possess the total angular momentum $J=2$ with spin-triplet and $P$ wave, in the presence of the magnetic field parallel to the angular momentum of vortices. The ground state is known to be in the uniaxial nematic (UN) phase in the absence of magnetic field, while it is in the $D_2$ ($D_4$) biaxial nematic (BN) phase in the presence of the magnetic field below (above) the critical value. We find that a singly quantized vortex always splits into two…
