Pair Of Half-quantum Vortices Research Articles

Half quantum vortices in a nematic superconductor

Motivated by the superconductivity of $M_x$Bi$_2$Se$_3$, we study topological excitations in a nematic superconductor using Ginzburg-Landau theory. An isolated excitation at low field is shown to be either a distorted phase vortex or a tightly-bounded pair of half quantum vortices. Close to upper critical field $H_{c2}$, the vortex lattice is shown to be always hexagonal in the extreme type-II limit. Due to the different symmetries of the vortex lattice states, at least two phase transitions must take place when the external field is lowered from $H_{c2}$.

Mesoscopics of half-quantum vortex pair deconfinement in a trapped spin-one condensate

Motivated by a recent experiment in an antiferromagnetic spin-1 Bose-Einstein condensate of ${}^{23} \textrm{Na}$ atoms, we study the energetical stability of a singly quantum vortex injected into the center of a quasi-two-dimensional gas with zero total spin against dissocation into a pair of half-quantum vortices. We find that the critical dissociation point of this confinement-deconfinement type phase transition can be expressed in terms of the ratio of density-density ($c_0$) and spin-spin ($c_2$) coupling constants. The transition of bound to unbound vortices, in particular, sensitively depends on (1) the ratio of system size ($R$) to density healing length ($\xi_d$), and (2) the trap potential. Specifically, the critical ratio $(c_2 / c_0)_{\textrm{cr}}$ increases when $R / \xi_d$ decreases, and is relatively larger in a harmonic trap than in a box trap. Dissociation is energetically generally favored for $c_2 / c_0 < (c_2 / c_0)_{\textrm{cr}}$, which as a corollary implies that vortex dissociation is observed as well for negative $c_2 < 0$, e.g., in a rubidium spin-1 BEC, whereas in a sodium spin-1 BEC ($c_2>0$) it is energetically blocked above the critical ratio $(c_2 / c_0)_{\textrm{cr}}$. Tuning the coupling ratio $c_2/c_0$ by using microwave control techniques, the dependence of the deconfinement phase transition on coupling parameters, density, and system size we predict, can be verified in experiments with ultracold spinor gases.

Appearance of Magnetization around a Pair of Half-Quantum Vortices in Chiralp-Wave Superconductors

We have investigated quasi-particle excitations around a pair of half-quantum vortices in chiral \(p\)-wave superconductors, using the Bogoliubov–de Gennes equations. We use the elliptic coordinates and the Mathieu function for numerical calculations. We found that the height of peak of a local density of states of the bound states for the half-quantum vortex core is a half of that for a singly quantized vortex core. Also, it was found that a magnetization appears along a pair of half-quantum vortices. Existence of half-quantum vortex might be confirmed by observation of this distribution of the magnetization.

Quasi-particle structures around a pair of half-quantum vortices in chiral p-wave super conductors

Quasi-particle structures around a pair of half-quantum vortices (HQVs) and two singly quantized vortices are investigated, using the Bogoliubov-de Gennes equation. For this purpose, a new numerical method, which incorporates the two phase singularity points, is developed, using elliptic coordinates and the (modified) Mathieu functions. We investigate the local density of states around two singly quantized vortices and a pair of HQVs in chiral p-wave superconductors. As a result, we found that there is a difference between them: Quasiparticle bound states interfere with each other for two singly quantized vortices case and do not for a pair of HQVs case.

Energetically stable singular vortex cores in an atomic spin-1 Bose-Einstein condensate

We analyze the structure and stability of singular singly quantized vortices in a rotating spin-1 Bose-Einstein condensate. We show that the singular vortex can be energetically stable in both the ferromagnetic and polar phases despite the existence of a lower-energy nonsingular coreless vortex in the ferromagnetic phase. The spin-1 system exhibits an energetic hierarchy of length scales resulting from different interaction strengths and we find that the vortex cores deform to a larger size determined by the characteristic length scale of the spin-dependent interaction. We show that in the ferromagnetic phase the resulting stable core structure, despite apparent complexity, can be identified as a single polar core with axially symmetric density profile which is nonvanishing everywhere. In the polar phase, the energetically favored core deformation leads to a splitting of a singly quantized vortex into a pair of half-quantum vortices that preserves the topology of the vortex outside the extended core region, but breaks the axial symmetry of the core. The resulting half-quantum vortices exhibit nonvanishing ferromagnetic cores.

Vortex configuration and vortex–vortex interaction in nano-structured superconductors

We study the vortex structures and quasi-particle structures in nano-structured superconductors. We used the Bogoliubov–de Gennes equation and the finite element method and obtained stable magnetic flux structures and the quasi-particle states. We found the vortex configurations are affected by the interference of the quasi-particle bound states around the vortices. In order to clarify the interference between the quasi-particle wave-functions around two vortices we have developed a numerical method using the elliptic coordinates and the Mathieu functions. We apply this method to two singly quantized vortex state in a conventional s-wave superconductor and a pair of half-quantum vortices in a chiral p-wave superconductor.

Dissociation dynamics of singly charged vortices into half-quantum vortex pairs

The quest for identification and understanding of fractional vorticity is a major subject of research in the quantum fluids domain, ranging from superconductors, superfluid Helium-3 to cold atoms. In a two-dimensional Bose degenerate gas with a spin degree of freedom, the fundamental topological excitations are fractional vortical entities, called half-quantum vortices. Convincing evidence for the existence of half-quantum vortices was recently provided in spinor polariton condensates. The half-quantum vortices can be regarded as the fundamental structural components of singly charged vortices but, so far, no experimental evidence of this relation has been provided. Here we report on the direct and time-resolved observation of the dynamical process of the dissociation of a singly charged vortex into its primary components, a pair of half-quantum vortices. The physical origin of the observed phenomenology is found in a spatially inhomogeneous static potential that couples the two spin components of the condensate.

Entropy-driven formation of a half-quantum vortex lattice

Half-quantum vortices (HQVs) can exist in a superconductor or superfluid with an exact or approximate U(1) \times U(1) symmetry, for instance in spinor condensates, 3He-A, Sr2RuO4, and possibly cuprate superconductors with stripe order. In this paper, we show that a lattice of HQVs can be stabilized at finite temperature even when it does not have lower energy than the lattice of full vortices at T = 0 since there is a gain in configurational entropy when a full vortex fractionalizes into a pair of HQVs. Specifically, the lattice of HQVs has an optical branch of phonon modes absent in the lattice of full vortices. Moreover, the HQV lattice at T > 0 can have a different structure than the HQV lattice at T = 0.

Quasi-particle excitations around a pair of half-quantum vortices in p- wave superconductors

Triplet superconductors such as Sr2RuO4 and NaxCoO2⋅yH2O are now found to be p-wave (px±ipy) or f-wave ((px±ipy) coscpz) superconductors. It was phenomenologically suggested that in these p-wave or f-wave superconductors, a pair of half-quantum vortices (HQVs) becomes stable. Using the Bogoliubov-de Gennes equation, previously we have analyzed quasi-particle excitations around an HQV at one end of a d-soliton for simplicity. In next study, we will investigate the stability of the pair of HQV’s, which are connected by the d-soliton. For this purpose, we have developed a new numerical method to solve the Bogoliubov-de Gennes equation for two vortices state, using Mathieu functions.

Singular and Half-Quantum Vortices and Associated Majorana Particles in Superfluid3He-A between Parallel Plates

Motivated by a recent experiment on superfluid 3 He-A confined in narrow parallel plates using a rotating cryostat, we explore possible vortices that are stable under a magnetic field applied to an arbitrary angle relative to the plates in order to seek vortices that can accommodate the Majorana zero mode in the core. After proving that the singular vortex with the unit winding number provides the Majorana mode in a spinful situation, we establish the phase diagram in the plane; the rotation frequency Ω vs the system size R by finding possible order parameter textures within the Ginzburg–Landau framework. We also analyze the stability for a single and a pair of half-quantum vortices, which possess the Majorana mode in their core. It is concluded from the above-mentioned results that the Majorana zero mode can be found in the present on-going experiment performed at ISSP, University of Tokyo.

QUINTET PAIRING AND NON-ABELIAN VORTEX STRING IN SPIN-3/2 COLD ATOMIC SYSTEMS

We study the s-wave quintet Cooper pairing phase (S pair = 2) in spin-3/2 cold atomic systems and identify various novel features which do not appear in spin-1/2 pairing systems. A single quantum vortex is shown to be energetically less stable than a pair of half-quantum vortices. The half-quantum vortex exhibits the global analogue of the non-Abelian Alice string and SO(4) Cheshire charge in gauge theories. The non-Abelian half-quantum vortex loop enables topological generation of quantum entanglement.

Triplet Superconductivity in a Nutshell

The triplet superconductors have been around us since 1980, when Jerome et al. discovered the Bechgaard salts (TMTSF)2PF6 and (TMTSF)2ClO4. Now there are more than 20 or so triplet superconductors discovered. Recently we found that most of them with the known gap symmetries can be mapped to the superfluid phase of 3He-A and 3He-A1. Further, in most of them, $\hat{l}$ (the chiral vector, i.e. the quantization axis of the pair angular momentum) is fixed parallel to one of the crystal axes and all the topological defects are considered in terms of $\hat{d}$ -textures, where $\hat{d}$ is the spin vector. Then Sr2RuO4, UPt3, PrOs4Sb12 and (TMTSF)2ClO4 belong to type-A, which is an analog of superfluid 3He-A. In these superconductors, a vortex splits into a pair of half quantum vortices (HQVs) at low temperatures. On the other hand, CePt3Si, CeIrSi3, CeRhSi3, UIr and Li2Pt3B (those in non-centrosymmetric crystals) belong to type-A1, which is an analog of superfluid 3He-A1. In all of these triplet superconductors, vortices harbor the zero mode or the Majorana fermions, the implications of which deserves further exploration.

Vortex phases of an unconventional superconductor with two components order parameter

We examined the single vortex structure of superconductor with the order parameter of two components by numerical calculation. Under certain conditions in the case of time-reversal preserving phase a single vortex dissociates into a pair of half-quantum vortices. We determine the phase diagram for these vortices in the space of parameters of the Ginzburg–Landau functional. A novel characteristic length which is longer than the coherence length ξ and shorter than the magnetic penetration length λ London is introduced.

Dissociation of Flux Line in Unconventional Superconductor

Besides usual flux lines the topology of the “real” vector phase in a multicomponent superconductor admits an existence of half-quantum vortices in the bulk. These vortices have a divergent energy near H c 1 . However, the possibility of their existence reveals itself in an instability of a usual singular one-quantum vortex towards dissociation into the nonsingular bound pair of half-quantum vortices. Considering an example of the multicomponent Ginzburg-Landau functional we found analytically critical values of phenomenological parameters corresponding to this instability, as well as the symmetry group of the vortex pair.

Satellite magnetic resonances of a bound pair of half-quantum vortices in rotating superfluid 3He-A.

The transverse magnetic resonance satellite frequency and intensity associated with a bound pair of half quantum vortices in a thin slab of $^{3}\mathit{A}$, rotating about the slab normal and subject to a magnetic field applied at an angle \ensuremath{\theta} with the slab normal, is recalculated in a variational approach. This approach takes properly into account the azimuthal symmetry of the spin wave function and therefore corrects a previous prediction by Salomaa and Volovik. The corresponding quantities for the longitudinal resonance are also calculated. In addition, a general criterion is given for determining the physical transverse-resonance wave function in a large magnetic field in the presence of any distribution of spin disgyrations of any kinds, whether with integer or fractional Frank indices.