DOCSLIB.ORG

Skyrmions in Composite Higgs Models in QCD

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Skyrmions in Composite Higgs Models in QCD The skyrmion Skyrmions in Composite Higgs Models in QCD Topology of composite Higgs models Marc Gillioz An example: the littlest Higgs model Relic density August 29, 2011 based on arXiv:1012.5288 and arXiv:1103.5990, in collaboration with Andreas von Manteuffel, Pedro Schwaller and Daniel Wyler 1/18 Marc Gillioz, Zurich PhD seminar 2011 Introduction SM ATLAS Preliminary CLs Limits σ / SM CMS Preliminary, s = 7 TeV The skyrmion σ Observed Observed σ -1 / Combined, L = 1.1-1.7 fb Expected ± 1σ int in QCD Expected σ ∫ Ldt = 1.0-2.3 fb-1 10 Expected ± 2σ 10 ± 1 σ LEP excluded Topology of ± 2 σ s = 7 TeV Tevatron excluded composite Higgs models 95% CL Limit on on Limit CL 95% 1 1 An example: limit on 95% CL the littlest Higgs model -1 Relic density 10 200 300 400 500 600 100 200 300 400 500 600 mH [GeV] Higgs boson mass (GeV/c2) Atlas collaboration (Lepton-Photon 2011) CMS collaboration (Lepton-Photon 2011) LHC data (and indirect evidence from previous experiments) points towards a light Higgs in the mass range 100–150 GeV. 2/18 Marc Gillioz, Zurich PhD seminar 2011 Introduction Any new physics above this scale contributes to The skyrmion in QCD the Higgs mass through radiative corrections. Topology of composite Higgs models need for a symmetry to protect it: An example: ⇒ the littlest Higgs model 1 SUSY: requires the introduction of a superpartner for each Relic density SM field. 2 Composite Higgs: the Higgs is a bound state of fermions from some strongly interacting sector, and it is light since it arises as a pseudo-Goldstone boson technicolor, little Higgs, holographic models, ... → 3/18 Marc Gillioz, Zurich PhD seminar 2011 Introduction The Higgs sector of composite models is described at energies The skyrmion in QCD below the cutoff Λ 4πf by a σ-model, Topology of ∼ composite 2 Higgs models f µ † L = Tr DµΦ D Φ , An example: 4 the littlest Higgs model with two consequences: Relic density 1 The fields described by Φ(x) are much lighter than the symmetry breaking scale f (they are the “pions” of the theory, in analogy with QCD) 2 The model may also contain topological solitons called skyrmions (the “baryons” of the theory) 4/18 Marc Gillioz, Zurich PhD seminar 2011 Outline The skyrmion in QCD 1 The skyrmion in QCD Topology of composite Higgs models An example: 2 Topology of composite Higgs models the littlest Higgs model Relic density 3 An example: the littlest Higgs model 4 Relic density of skyrmions 5/18 Marc Gillioz, Zurich PhD seminar 2011 The chiral effective theory In the limit of massless quarks, QCD has a global SU(Nf )L SU(Nf )R chiral symmetry, broken down to The skyrmion × SU(N ) by a non-zero quark condensate qq = 0. in QCD f V Topology of composite Higgs models The low-energy degrees of freedom of QCD are the pions, An example: described by a σ-model the littlest Higgs model 2 Relic density fπ µ † LχPT = Tr ∂µΦ ∂ Φ , Φ(x) SU(Nf ). 4 ∈ In the two-flavour case N = 2, Φ = exp(i π σ/f ) and f · π L 1 π 2 1 π π 2 π2 π 2 χPT = ∂µ + 2 ∂µ ∂µ + ... 2 | | 6fπ | · | − | | 6/18 Marc Gillioz, Zurich PhD seminar 2011 Topological solitons The σ-model also contains topological solitons, the skyrmions: classical static solutions of the field equations, The skyrmion in QCD with finite size and finite energy, Topology of topologically stable, since they cannot be deformed into composite Higgs models the true vacuum by infinitesimal transformation. An example: the littlest Higgs model The presence of skyrmions in a theory depends on the topology Relic density of the vacuum manifold, described by the third homotopy group π3 of the target space. For QCD, π3(SU(Nf )) = Z . Winding number integral: 1 3 † † † Z B(Φ) = 2 ǫijk d x Tr Φ ∂iΦ Φ ∂jΦ Φ ∂kΦ . 24π ∈ 7/18 Marc Gillioz, Zurich PhD seminar 2011 The Skyrme model of baryons B is actually the baryon number of the theory, and the The skyrmion in QCD skyrmions represent baryon states. Witten (1983) Adkins, Nappi, Witten (1983) Topology of composite Higgs models Higher-derivative terms are needed to stabilize the skyrmion. An example: G.H. Derrick (1964) the littlest Higgs model consider the Skyrme Lagrangian: Relic density → 2 2 L fπ µ † 1 † † = Tr ∂µΦ ∂ Φ + 2 Tr Φ ∂µΦ, Φ ∂νΦ 4 32e T.H.R. Skyrme (1961) With e 5, the baryons properties are reproduced with about ∼ 20% precision: mass, radius, magnetic moment, ... 8/18 Marc Gillioz, Zurich PhD seminar 2011 Topology of composite Higgs models The skyrmions in composite Higgs models can be fundamentally different from the QCD ones, because of the The skyrmion in QCD different topology of the vacuum manifold. Topology of Symmetry Models π3 composite Higgs models × “Minimal moose” models Arkani-Hamed et al. (2002) SU(N) SU(N) Z An example: SU(N) – with exact DM parity Freitas, Schwaller, Wyler (2009) the littlest Higgs model SO(N)×SO(N) – with custodial symmetry Chang, Wacker (2004) Z Relic density SO(N) “Bestest LH” Schmaltz, Stolarski, Thaler (2010) SU(2N)/Sp(2N) “Antisymmetric cond.” Low, Skiba, Tucker-Smith (2002) 0 SU(N)/SU(N − 1) LH from a simple group Kaplan, Schmaltz (2003) 0 a SO(N)/SO(N − 1) Min. Composite Higgs Agashe, Contino, Pomarol (2004) 0( ) Littlest Higgs Arkani-Hamed et al. (2002) (b) SU(N)/SO(N) Z2 – with T-parity Cheng, Low (2003) (a) (b) Bryan, Carroll, Pyne (1993) Z for N ≤ 4, Z4 for N = 3. 9/18 Marc Gillioz, Zurich PhD seminar 2011 Topology of composite Higgs models The skyrmion symmetry depends on its winding number: The skyrmion SU(N) SU(N)/SU(N) N. Manton (2011) in QCD × Topology of composite Higgs models An example: ··· the littlest 0 1 2 3 4 Higgs model ± ± ± ± SU(N)/SO(N), N 4 MG, von Manteuffel, Schwaller, Wyler (2010) Relic density ≥ 0 1 SU(3)/SO(3) MG (2011) 10/18 0 1 2 3 Marc Gillioz, Zurich PhD seminar 2011 An example: the littlest Higgs model The littlest Higgs is described by a field Σ(x) in the two-index symmetric representation of SU(5), with a vev Σ = 1 The skyrmion breaking the symmetry down to SO(5): in QCD Topology of f 2 1 2 composite L µ † † † Higgs models LH = Tr ∂µΣ ∂ Σ + 2 Tr Σ ∂µΣ, Σ ∂νΣ 4 32e An example: the littlest we add the Skyrme term as in QCD. Higgs model → Relic density The field configuration of minimal energy with B = 1 is obtained using the Cartan embedding Σ(x)=Φ(x)Φ(x)T and a “hedgehog ansatz” σ iσ 0 1 i i Φ(x) = exp[i F (r)x ˆi Ti] , Ti = iσi σi 0 . 4 − 0 0 0 11/18 Marc Gillioz, Zurich PhD seminar 2011 An example: the littlest Higgs model The energy density is a functional of F : ∞ f sin2 F The skyrmion E[F ] = 4π dr˜ r˜2 + 2sin2 F F ′2 + 2˜r2 + sin2 F in QCD e r˜2 Topology of 0 composite Higgs models minimized An example: Π the littlest by solving the Higgs model Euler-Lagrange 120 Relic density equation for F D e 80 f @ ⇓ F Π2 f dE M = 145.8 40 e 1.058 2 0 0 r2 = 0 1 2 3 4 5 fe r @1feD 12/18 Marc Gillioz, Zurich PhD seminar 2011 The effects of gauge fields In the littlest Higgs model, the global SU(5) symmetry is The skyrmion explicitly broken by gauging a [SU(2) U(1)]2 subgroup. in QCD × Topology of composite Higgs models the skyrmion can decay with the help of an instanton. ⇒ An example: D’Hoker, Farhi (1984) the littlest Higgs model Still, the extremely small tunneling probability makes the Relic density skyrmion quasi-stable, with lifetime 2 2 e16π /g τ τ ∼ M ≫ universe Also, the gauge fields lower the mass of the skyrmion, without spoiling its spherical symmetry. 13/18 Marc Gillioz, Zurich PhD seminar 2011 Classical mass of the skyrmion Tends to M∞ = 145.8 f/e at large e Upper bound The skyrmion √ in QCD Me→0 = 16 2 πf/g ∼= 108.9 f Topology of composite Higgs models 200 An example: the littlest Higgs model 150 Relic density f 100 M 50 0 0.5 1 2 5 10 20 e 14/18 Marc Gillioz, Zurich PhD seminar 2011 Relic density of skyrmions The peculiar Z2 topology of the littlest Higgs implies that: skyrmions are produced and annihilated in pairs of The skyrmion in QCD identical particles, Topology of no need to generate an asymmetry to obtain a skyrmion composite Higgs models relic density in the universe. An example: the littlest Higgs model Skyrmion pair-production and annihilation cannot be computed Relic density perturbatively. A naive estimate for the cross-section: π σ π r2 = ∼ ∼ (fe)2 − 2 3·10 27cm3/s The WIMP relic density Ωh ∼= σv ∼= 0.1 is satisfied provided fe 35 TeV Griest, Kamionkowski (1990) ∼ a very natural choice of parameters! → 15/18 Marc Gillioz, Zurich PhD seminar 2011 Relic density of skyrmions Implementing an effective skyrmion-to-matter coupling in microMEGAs: B´elanger et al. (2011) Belyaev et al. (2006) The skyrmion in QCD 100 Topology of 50 composite Higgs models 20 An example: D the littlest 10 Higgs model TeV @ 5 Relic density M EXCLUDED 1 500 1000 1500 2000 2500 f @GeVD Coupling the skyrmion both to the scalar sector and to the fermions yield comparable bounds.
Load more

Recommended publications
  • Chiral Magnetism: a Geometric Perspective
    SciPost Phys. 10, 078 (2021) Chiral magnetism: a geometric perspective Daniel Hill1, Valeriy Slastikov2 and Oleg Tchernyshyov1? 1 Department of Physics and Astronomy and Institute for Quantum Matter, Johns Hopkins University, Baltimore, MD 21218, USA 2 School of Mathematics, University of Bristol, Bristol BS8 1TW, UK ? [email protected] Abstract We discuss a geometric perspective on chiral ferromagnetism. Much like gravity be- comes the effect of spacetime curvature in theory of relativity, the Dzyaloshinski-Moriya interaction arises in a Heisenberg model with nontrivial spin parallel transport. The Dzyaloshinskii-Moriya vectors serve as a background SO(3) gauge field. In 2 spatial di- mensions, the model is partly solvable when an applied magnetic field matches the gauge curvature. At this special point, solutions to the Bogomolny equation are exact excited states of the model. We construct a variational ground state in the form of a skyrmion crystal and confirm its viability by Monte Carlo simulations. The geometric perspective offers insights into important problems in magnetism, e.g., conservation of spin current in the presence of chiral interactions. Copyright D. Hill et al. Received 15-01-2021 This work is licensed under the Creative Commons Accepted 25-03-2021 Check for Attribution 4.0 International License. Published 29-03-2021 updates Published by the SciPost Foundation. doi:10.21468/SciPostPhys.10.3.078 Contents 1 Introduction2 1.1 The specific problem: the skyrmion crystal2 1.2 The broader impact: geometrization of chiral magnetism3 2 Chiral magnetism: a geometric perspective4 2.1 Spin vectors4 2.2 Local rotations and the SO(3) gauge field5 2.3 Spin parallel transport and curvature5 2.4 Gauged Heisenberg model6 2.5 Spin conservation7 2.5.1 Pure Heisenberg model7 2.5.2 Gauged Heisenberg model8 2.6 Historical note9 3 Skyrmion crystal in a two-dimensional chiral ferromagnet9 3.1 Bogomolny states in the pure Heisenberg model 10 3.2 Bogomolny states in the gauged Heisenberg model 11 3.2.1 False vacuum 12 1 SciPost Phys.
    [Show full text]
  • A Simple Mass-Splitting Mechanism in the Skyrme Model
    A simple mass-splitting mechanism in the Skyrme model J.M. Speight∗ School of Mathematics, University of Leeds Leeds LS2 9JT, England April 2, 2018 Abstract It is shown that the addition of a single chiral symmetry breaking term to the standard !-meson variant of the nuclear Skyrme model can reproduce the proton-neutron mass difference. 1 Introduction The Skyrme model [9] is a nonlinear sigma model whose perturbative quanta are interpreted as pions and whose topological solitons are interpreted as nucleons. At the classical level, there is no difference between protons and neutrons in this model; the distinction only emerges after quantization of the internal rotational degrees of freedom enjoyed by the static soliton, and is determined, roughly speaking, by the sense (clockwise or anticlockwise) of internal rotation. It is clear, therefore, that in order to account for the slight mass difference between the neutron and the proton (mn = 939:56563 MeV, mp = 938:27231 MeV), the model's action must contain a small term which breaks time reversal symmetry, so that \clockwise" and \anticlockwise" internal rotation are dynamically inequivalent. Devising such a term, while maintaining Lorentz and parity invariance, does not seem to be possible in any version of the model containing only pion fields. It should be noted that adding electromagnetic effects to arXiv:1803.11216v1 [hep-th] 29 Mar 2018 the usual Skyrme model has precisely the opposite effect to the one desired: unsurprisingly, Coulomb repulsion renders the proton heavier than the neutron [3]. As has been long known, the proton-neutron mass splitting can be accommodated if one extends the model to include coupled vector mesons [5].
    [Show full text]
  • Recent Progress on Dense Nuclear Matter in Skyrmion Approaches Yong-Liang Ma, Mannque Rho
    Recent progress on dense nuclear matter in skyrmion approaches Yong-Liang Ma, Mannque Rho To cite this version: Yong-Liang Ma, Mannque Rho. Recent progress on dense nuclear matter in skyrmion approaches. SCIENCE CHINA Physics, Mechanics & Astronomy, 2017, 60, pp.032001. 10.1007/s11433-016-0497- 2. cea-01491871 HAL Id: cea-01491871 https://hal-cea.archives-ouvertes.fr/cea-01491871 Submitted on 17 Mar 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. SCIENCE CHINA Physics, Mechanics & Astronomy . Invited Review . Month 2016 Vol. *** No. ***: ****** doi: ******** Recent progress on dense nuclear matter in skyrmion approaches Yong-Liang Ma1 & Mannque Rho2 1Center of Theoretical Physics and College of Physics, Jilin University, Changchun, 130012, China; Email:[email protected] 2Institut de Physique Th´eorique, CEA Saclay, 91191 Gif-sur-Yvette c´edex, France; Email:[email protected] The Skyrme model provides a novel unified approach to nuclear physics. In this approach, single baryon, baryonic matter and medium-modified hadron properties are treated on the same footing. Intrinsic density dependence (IDD) reflecting the change of vacuum by compressed baryonic matter figures naturally in the approach. In this article, we review the recent progress on accessing dense nuclear matter by putting baryons treated as solitons, namely, skyrmions, on crystal lattice with accents on the implications in compact stars.
    [Show full text]
  • Skyrmion Flow Near Room Temperature in an Ultralow Current Density
    ARTICLE Received 16 Apr 2012 | Accepted 5 Jul 2012 | Published 7 Aug 2012 DOI: 10.1038/ncomms1990 Skyrmion flow near room temperature in an ultralow current density X.Z. Yu1, N. Kanazawa2, W.Z. Zhang3, T. Nagai3, T. Hara3, K. Kimoto3, Y. Matsui3, Y. Onose2,4 & Y. Tokura1,2,4 The manipulation of spin textures with electric currents is an important challenge in the field of spintronics. Many attempts have been made to electrically drive magnetic domain walls in ferromagnets, yet the necessary current density remains quite high (~107 A cm − 2). A recent neutron study combining Hall effect measurements has shown that an ultralow current density of J~102 A cm − 2 can trigger the rotational and translational motion of the skyrmion lattice in MnSi, a helimagnet, within a narrow temperature range. Raising the temperature range in which skyrmions are stable and reducing the current required to drive them are therefore desirable objectives. Here we demonstrate near-room-temperature motion of skyrmions driven by electrical currents in a microdevice composed of the helimagnet FeGe, by using in-situ Lorentz transmission electron microscopy. The rotational and translational motions of skyrmion crystal begin under critical current densities far below 100 A cm − 2. 1 Correlated Electron Research Group (CERG) and Cross-Correlated Materials Research Group (CMRG), RIKEN-ASI, Wako 351-0198, Japan. 2 Department of Applied Physics and Quantum-Phase Electronics Center (QPEC), University of Tokyo, Tokyo 113-8656, Japan. 3 National Institute for Materials Science, Tsukuba 305-0044, Japan. 4 Multiferroics Project, Exploratory Research for Advanced Technology (ERATO), Japan Science and Technology Agency, Tokyo 113-8656, Japan.
    [Show full text]
  • Mesons, Baryons and Waves in the Baby Skyrmion Model 1. Introduction
    DTP-96/17 November 28, 1996 Mesons, Baryons and Waves in the Baby Skyrmion Mo del 1 A. Kudryavtsev B. Piette, and W.J. Zakrzewski Department of Mathematical Sciences University of Durham, Durham DH1 3LE, England 1 also at ITEP, Moscow, Russia E-Mail: [email protected] [email protected] [email protected] ABSTRACT We study various classical solutions of the baby-Skyrmion mo del in (2 + 1) dimen- sions. We p oint out the existence of higher energy states interpret them as resonances of Skyrmions and anti-Skyrmions and study their decays. Most of the discussion in- volves a highly exited Skyrmion-like state with winding numb er one which decays into an ordinary Skyrmion and a Skyrmion-anti-Skyrmion pair. We also study wave-like solutions of the mo del and show that some of such solutions can b e constructed from the solutions of the sine-Gordon equation. We also show that the baby-Skyrmion has non-top ological stationary solutions. We study their interactions with Skyrmions. 1. Intro duction. In previous pap ers bytwo of us (BP and WJZ) [1-3] some hedgehog-like solutions of the so called baby-Skyrmion mo del were studied. It was shown there that the mo del has soliton-like top ologically stable static solutions (called baby-Skyrmions) and that these solitons can form b ound states. The interaction b etween the solitons was studied in detail and it was shown that the long distance force between 2 baby-Skyrmions dep ends on their relative orientation.
    [Show full text]
  • Skyrmion Deformation in Finite Nuclei
    Section I. Particles and Nuclei optimization of the basis) results in more high precision at essentially less dimensions of the basis in comparison with the known calculations [1] in traditional approach In addition to the energies and r.m.s radii, the density distributions, formfactors, pair correlation functions and momentum distributions are analyzed for three and four nucleons with a number of commonly used interaction potentials (Minnesota, Afnan-Tang. F.ikemeier-Haekenbroich etc.) as well as with our version of potential K2 [2] with small repulsion at short distances. Comparison of the results is carried out, and the convergence with the basis dimension increase is analyzed in the cases of spinless approximation [2,3] for the nuclear interaction potential, isospin representation with spin-dependent potentials, and the approach without use of the isospin quantum number. We find the hierarchy of configurations for symmetric and asymmetric (with respect to permutation o\" identical particles) wave function components with the increase of the basis dimension, and it is shown for the optimal choice of the basis functions that each of the involved asymmetric Gaussian component needs a few (about 3) symmetric ones to be involved into consideration because of their dominant role Due to the essential deer ase of the number of equations in comparison with that in traditional approaches, precise study of nuclei containing up to six nucleons with central exchange NN-potentials becoues possible. The minimum number of equations in our approach as well as the optimization schemes for constructing the optimal basis gives a possibility to present the results of precise calculations in the form of a short list of parameters of the explicit wave function (in Gaussian representation) which can be directly used by other researches for studying the processes with the nuclei *H, 'He and ''He involved References 1.
    [Show full text]
  • A New Large Nc Relation As a Probe of Skyrmions and Their Holographic
    Tests of Universality of Baryon Form Factors In Holographic QCD A. Cherman, T.D. Cohen, M. Nielsen, PRL103(09) Univ. of Maryland and Univ. of Sao Paulo Low x Meeting, September 2009 QCD: strong-coupled theory AdS/QCD models: successful at reproducing low energy hadronic observables • two classes of AdS/QCD models Top-down models: Botton-up models: arise from sting theory QCD large Nc dual to a classical 5D theory D4/D8 system gauge theory confining as QCD field content 5D matched AdS/CFT requires large Nc to low energy chiral and ´t Hooft coupling symmetry of QCD Both cases: large Nc is required QCD is a weakly-interacting theory of long -lived mesons in the • ‘t Hooft, 1973 large Nc limit. • In the large Nc limit, baryons are ‘soliton -like’ configurations of meson fields. Witten, 1979 1 • Baryon masses scale as Nc (composed of Nc quarks), 1/2 interactions with mesons scale as Nc . • Unlike mesons, baryons are not narrow at large Nc. • Nucleons, deltas, become degenerate. Mass splitting -1 scales as Nc . • In contrast to the pure meson sector, meson loops make leading order contributions to baryon properties at large Nc. • Variety of baryon models (Skyrme models) use large Nc properties of baryons for inspiration. Skyrme, 1961 • Baryons modeled as quantum states of slowly rotating Adkins, Nappi, hedgehog Skyrmions of meson fields. Witten, 1983 Dashen, Manohar, Jenkins,1993-95 Model-independent relations for baryons valid at large Nc • Goldberger-Treiman relation: • Relation is model-indepedent, and follows from chiral symmetry. • Nucleon and delta couplings with pions are related by • • This relation follows just from the large Nc limit • New model-independent relation: • Ratio of nucleon form factors in position space, evaluated at large distances: • Relation depends on both the large Nc and chiral limits.
    [Show full text]
  • Nucleon-Antinucleon Interaction from the Skyrme Model: II
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server Nucleon-Antinucleon Interaction from the Skyrme Model: II Yang Lu, Pavlos Protopapas and R. D. Amado Department of Physics and Astronomy University of Pennsylvania, Philadelphia, Pennsylvania 19104 September 13, 1997 Abstract We calculate the full static interaction of a Skyrmion and an anti-Skyrmion as a function of separation and relative grooming. From this, using projection methods and Born-Oppenheimer mixing, we obtain the nucleon antinucleon interaction. We find agreement with the major features of the empirical interaction including the strong central attraction and the sharp onset of annihilation at about 1 fm. 1 Introduction Making a theory of low energy nucleon-antinucleon annihilation from the entrance channel through to the annihilation products presents a daunting challenge. An exact QCD based calculation of the process is beyond our present analytical understanding and our computational resources. We are left then with either abandoning the problem or using some approximate or effective theory. Such a theory must include an account of the nature of the nucleon and the antinucleon, in order to describe annihilation, as well as containing a description of their interaction. The theory should also have its roots in QCD. The only such effective theory of annihilation that contains the requisite ingredients and gives hope of being tractable is based on the Skyrme model [1]. This models QCD in the classical or large number of colors (NC ) limit and at long distances or low momentum [2, 3]. Sommermann et al.
    [Show full text]
  • Defect Characterization and Testing of Skyrmion-Based Logic Circuits Ziqi Zhou, Ujjwal Guin, Peng Li, and Vishwani D
    Defect Characterization and Testing of Skyrmion-Based Logic Circuits Ziqi Zhou, Ujjwal Guin, Peng Li, and Vishwani D. Agrawal Department of Electrical and Computer Engineering Auburn University, AL, USA fziqi.zhou, ujjwal.guin, peng.li, [email protected] Abstract—Magnetic skyrmion is an emerging digital technology didate for a beyond CMOS technology. We believe a significant that provides ultra-high integration density and requires ultra- amount of work is still necessary to make these devices feasible low energy. Skyrmion is a magnetic pattern behaving like a stable for commercial applications. To the best of our knowledge, little pseudoparticle, created by a transverse current injection in ferro- magnetic thin film. The state of a logic signal is represented by the is available on their testing [25]. In manufacturing, a wide variety presence (logic-1) or absence (logic-0) of a single skyrmion. Pat- of defects may occur, and finding tests for them is often imprac- terns on ferromagnetic and metal films form interconnects, called tical. Thus, modeled faults serve as the basis for tests, and their nanotracks, through which electric currents move skyrmions. coverage measures the effectiveness of tests in detecting the manu- Because skyrmion-based logic gates (e.g., AND, OR, inverter, and facturing defects. Main contributions of this paper are as follows: fanout) operate through skyrmion-to-skyrmion interaction, their logic circuit implementation and manufacturing defects differ • Defect characterization: As technology-specific defects, we from those of CMOS circuits. We examine breaks and bridges examine breaks, extra material, etching blemishes, bridges in nanotrack interconnects, and 19 technology-specific defects in among interconnects, and a set of 19 physical defects in skyrmion gate structures.
    [Show full text]
  • Skyrmion Crystals in Centrosymmetric Itinerant Magnets Without Horizontal Mirror Plane Ryota Yambe1,2* & Satoru Hayami2
    www.nature.com/scientificreports OPEN Skyrmion crystals in centrosymmetric itinerant magnets without horizontal mirror plane Ryota Yambe1,2* & Satoru Hayami2 We theoretically investigate a new stabilization mechanism of a skyrmion crystal (SkX) in centrosymmetric itinerant magnets with magnetic anisotropy. By considering a trigonal crystal system without the horizontal mirror plane, we derive an efective spin model with an anisotropic Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction for a multi-band periodic Anderson model. We fnd that the anisotropic RKKY interaction gives rise to two distinct SkXs with diferent skyrmion numbers of one and two depending on a magnetic feld. We also clarify that a phase arising from the multiple-Q spin density waves becomes a control parameter for a feld-induced topological phase transition between the SkXs. The mechanism will be useful not only for understanding the SkXs, such as that in Gd2PdSi3 , but also for exploring further skyrmion-hosting materials in trigonal itinerant magnets. A magnetic skyrmion, which is characterized by a topologically nontrivial spin texture1–3, has been extensively studied in condensed matter physics since the discovery of the skyrmion crystal (SkX) in chiral magnets 4–6. Te SkX exhibits a nonzero topological winding number called the skyrmion number Nsk , which is defned as Nsk R �R/4π , where R is a skyrmion density related to the solid angle consisting of three spins Si , Sj , = 7 and S on the triangle R: tan (�R/2) Si (Sj S )/(1 Si Sj Sj S S Si) . Te study of the SkX has k = · × k + · + · k + k · attracted much attention, as the swirling topological magnetic texture owing to nonzero Nsk gives rise to an emergent electromagnetic feld through the spin Berry phase and results in intriguing transport phenomena and dynamics8–12, such as the topological Hall efect13,14 and the skyrmion Hall efect15,16.
    [Show full text]
  • Optical Skyrmions in Evanescent Electromagnetic Fields S
    Optical skyrmions in evanescent electromagnetic fields S. Tsesses1, E. Ostrovsky1, K. Cohen1, B. Gjonaj2, N. Lindner3, G. Bartal1* 1 Andrew and Erna Viterbi Department of Electrical Engineering, Technion – Israel Institute of Technology, 3200003 Haifa, Israel. 2 Faculty of Medical Sciences, Albanian University, Durrës st., Tirana 1000, Albania. 3 Physics Department, Technion – Israel Institute of Technology, 3200003 Haifa, Israel. *Correspondence to: [email protected] Abstract: Topological defects play a key role in a variety of physical systems, ranging from high- energy to solid state physics. They yield fascinating emergent phenomena and serve as a bridge between the microspic and macroscopic world. A skyrmion is a unique type of topological defect, showing great promise for applications in the fields of magnetic storage and spintronics. Here, we discover and observe optical skyrmion lattices that can be easily created and controlled, while illustrating their robustness to imperfections. Optical skyrmions are experimentally demonstrated by interfering surface plasmon polaritons and are measured via phase-resolved near-field optical microscopy. This discovery could give rise to new physical phenomena involving skyrmions and exclusive to photonic systems; open up new possibilities for inducing skyrmions in material systems through light-matter interactions; and enable applications in optical information processing, transfer and storage. One Sentence Summary: An optical skyrmion lattice is theoretically discovered and experimentally observed. Topological defects are field configurations which cannot be deformed to a standard, smooth shape. They are at the core of many fascinating phenomena in hydrodynamics (1), aerodynamics (2), exotic phases of matter (3–5), cosmology (6) and optics (7) and, in many cases, are of importance to practical applications.
    [Show full text]
  • Filming the Formation and Fluctuation of Skyrmion Domains by Cryo-Lorentz Transmission Electron Microscopy
    Filming the formation and fluctuation of skyrmion domains by cryo-Lorentz transmission electron microscopy Jayaraman Rajeswaria,1, Ping Huangb,1, Giulia Fulvia Mancinia, Yoshie Murookaa, Tatiana Latychevskaiac, Damien McGroutherd, Marco Cantonie, Edoardo Baldinia, Jonathan Stuart Whitef, Arnaud Magrezg, Thierry Giamarchih, Henrik Moodysson Rønnowb, and Fabrizio Carbonea,2 aLaboratory for Ultrafast Microscopy and Electron Scattering, Institute of Condensed Matter Physics, Lausanne Center for Ultrafast Science (LACUS), École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland; bLaboratory for Quantum Magnetism, Institute of Condensed Matter Physics, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland; cPhysics Department, University of Zurich, CH-8057 Zürich, Switzerland; dScottish Universities Physics Alliance, School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom; eCentre Interdisciplinaire de Microscopie Electronique, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland; fLaboratory for Neutron Scattering and Imaging, Paul Scherrer Institut, CH-5232 Villigen, Switzerland; gCompetence in Research of Electronically Advanced Materials, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland; and hDepartment of Quantum Matter Physics, University of Geneva, CH-1211 Geneva, Switzerland Edited by Margaret M. Murnane, University of Colorado at Boulder, Boulder, CO, and approved October 6, 2015 (received for review July 7, 2015) Magnetic skyrmions
    [Show full text]