Magnetic skyrmions and their lattices in triplet superconductors

Knigavko, A.; Rosenstein, Baruch; Chen, Y. F.

doi:10.1103/physrevb.60.550

Cited by 35 publications

(63 citation statements)

References 30 publications

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“…Although the later contribution is irrelevant for vortex interaction (in Coulomb gas mapping it plays the same role as the core energy), however the charged mode is important in the following respect: In the regime 0 < β 0 < π/3 the composite vortices (∆α = ±2π, ∆θ = ±2π) have smaller energy than elementary vortices (∆α = ±2π, ∆θ = 0) since the former vortices carry a smaller fraction of magnetic flux quantum and thus have smaller kinetic energy of charged supercurrent. Thus when 0 < β 0 < π/3 there will be a KT transition of the composite vortices (∆α = 2π, ∆θ = 2π) and antivortices (∆α = −2π, ∆θ = −2π) at the temperature (12). This is a rather unique feature, rooted in the nontrivial coupling of phases by vector potential in the triplet superconductor, when a KT transition is governed by topological defects with high topological charge.…”

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confidence: 96%

Fractional-Flux Vortices and Spin Superfluidity in Triplet Superconductors

Babaev

2005

Phys. Rev. Lett.

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We discuss a novel type of fractional flux vortices along with integer flux vortices in KosterlitzThouless transitions in a triplet superconductor. We show that under certain conditions a spintriplet superconductor should exhibit a novel state of spin superfluidity without superconductivity.Superconductors with triplet pairing allow for a rich variety of topological defects and phase transitions [1,2,3,4,5,6]. For example in p-wave superconductors there exist different realizations of fractional vortices such as: the half-quantum vortex (the Alice string), which is a vortex where phase changes by π and spin is reversed when we go around the vortex core, fractional vortices trapped on a grain boundary, fractional flux trapped by twisted wire and other possibilities (for an excellent review see [1,2]). Another subject which was intensively studied is the split phase transitions in triplet systems (e.g. in the presence of disorder or magnetic field) [2,4,5]. There have also been particularly interesting studies of split transitions in a neutral p-wave superfluid in connection with thin films of liquid 3 He [7,8]. Also the related questions of various partial symmetry breakdowns are relevant and were studied in spin-1 Bose condensates in optical traps [9] and bilayer Quantum Hall systems [10]. In this Letter we discuss the effect of flux fractionalization due to spin-orbit coupling, as well as the appearance of neutral vortices in triplet superconductors and discuss its influence on the Kosterlitz-Thouless (KT) transitions. Based on topological arguments we predict the existence of a novel type of ordering in spin-triplet system -the spin-superfluid nonsuperconducting state.We consider a model spin triplet superconductor similar to one considered in [5] with order parameter Ψ a (r) = √ n(x)ζ a (x) where (a = 1, 0, −1) and ζ is a normalized spinor ζ † · ζ = 1. If one neglects mixed gradient terms, the free energy density can be written as [5,6,11,12]:

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confidence: 96%

Fractional-Flux Vortices and Spin Superfluidity in Triplet Superconductors

Babaev

2005

Phys. Rev. Lett.

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“…16, who derived an effective action that allows for skyrmions as saddle-point solutions. The resulting ordinary differential equations (ODEs) describing skyrmions 16 are the starting point for our analytic treatment.…”

Section: Formulation Of the Skyrmion Problemmentioning

confidence: 99%

“…(2.8) the energy per unit length, along the cylinder axis, of a cylindrically symmetric skyrmion in a region of radius R, 16) where E 0 = (Φ 0 /4πλ) 2 . This expression was first obtained in Ref.…”

Section: Skyrmion Solutionmentioning

confidence: 99%

“…We show analytically that the skyrmion-skyrmion interaction, in addition to a leading 1/R-dependence, has a correction proportional to ln R/R 2 that explains a small discrepancy between the numerical results in Ref. 16 and a strict 1/R fit, and we calculate the interaction energy up to O(1/R 2 ). We further show that the melting curve of a skyrmion lattice is qualitatively different from that of a vortex lattice.…”

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confidence: 99%

“…II we review the formulation in Ref. 16 of the skyrmion problem. In particular, we start from the Ginzburg-Landau (GL) model for p-wave superconductors and consider the free energy in a London approximation.…”

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Skyrmion versus vortex flux lattices inp-wave superconductors

Toner

Belitz

2009

Phys. Rev. B

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p-wave superconductors allow for topological defects known as skyrmions, in addition to the usual vortices that are possible in both s-wave and p-wave materials. In strongly type-II superconductors in a magnetic field, a skyrmion flux lattice yields a lower free energy than the Abrikosov flux lattice of vortices, and should thus be realized in p-wave superconductors. We analytically calculate the energy per skyrmion, which agrees very well with numerical results. From this, we obtain the magnetic induction B as a function of the external magnetic field H, and the elastic constants of the skyrmion lattice, near the lower critical field Hc1. Together with the Lindemann criterion, these results suffice to predict the melting curve of the skyrmion lattice. We find a striking difference in the melting curves of vortex lattices and skyrmion lattices: while the former is separated at all temperatures from the Meissner phase by a vortex liquid phase, the skyrmion lattice phase shares a direct boundary with the Meissner phase. That is, skyrmions lattices never melt near Hc1, while vortex lattices always melt sufficiently close to Hc1. This allows for a very simple test for the existence of a skyrmion lattice. Possible µSR experiments to detect skyrmion lattices are also discussed.

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Local Intra-Unit-Cell Order Parameters in Cuprates Beyond Zhang-Rice Model

Moskvin

2016

J Supercond Nov Magn

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Starting with a minimal model with the on-site Hilbert space reduced to only three effective valence centers CuO 7−,6−,5− 4 (nominally Cu 1+,2+,3+ ) we present an unified approach to the description of the variety of the local intra-unit-cell (IUC) order parameters determining a low-energy physics in cuprates. Central point of the model implies the occurrence of unconventional on-site quantum superpositions of the three valent states characterized by different hole occupation: n h =0,1,2 for Cu 1+,2+,3+ centers, respectively, different conventional spin: s=1/2 for Cu 2+ center and s=0 for Cu 1+,3+ centers, and different orbital symmetry:B1g for the ground states of the Cu 2+ center and A1g for the Cu 1+,3+ centers, respectively. The latter does result in a spontaneous orbital symmetry breaking accompanying the formation of the on-site mixed valence superpositions with emergence of the IUC orbital nematic order parameter of the B1g = B1g × A1g (∝ dx2−y2) symmetry. To describe the diagonal and off-diagonal, or quantum local charge order we develop an S=1 pseudospin model with a non-Heisenberg effective Hamiltonian that provides a physically clear description of "the myriad of phases" from a bare parent antiferromagnetic insulating phase to a Fermi liquid in overdoped cuprates. Conventional spin density ρs for mixed valence superpositions can vary inbetween 0 and 1 in accordance with the weight of the Cu 2+ center in the superposition. We show that the superconductivity and spin magnetism are nonsymbiotic phenomena with competing order parameters. Furthermore we argue that instead of a well-isolated Zhang-Rice (ZR) singlet 1 A1g the ground state of the hole Cu 3+ center in cuprates should be described by a complex 1 A1g-1,3 B2g-1,3 Eu multiplet, formed by a competition of conventional hybrid Cu 3d-O 2p b1g(σ) ∝ d x 2 −y 2 state and purely oxygen nonbonding O 2pπ states with a2g(π) and eux,y(π) symmetry. In contrast with inactive ZR singlet we arrive at several novel competing IUC orbital and spin-orbital order parameters, e.g., electric dipole and quadrupole moments, Ising-like net orbital magnetic moment, orbital toroidal moment, intra-plaquette's staggered order of Ising-like oxygen orbital magnetic moments. As a most impressive validation of the non-ZR model we explain fascinating results of recent neutron scattering measurements that revealed novel type of the IUC magnetic ordering in pseudogap phase of several hole-doped cuprates.

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Magnetic skyrmions and their lattices in triplet superconductors

Cited by 35 publications

References 30 publications

Fractional-Flux Vortices and Spin Superfluidity in Triplet Superconductors

Fractional-Flux Vortices and Spin Superfluidity in Triplet Superconductors

Skyrmion versus vortex flux lattices inp-wave superconductors

Local Intra-Unit-Cell Order Parameters in Cuprates Beyond Zhang-Rice Model

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