Unwinding in Hopfion vortex bunches

Jäykkä, Juha; Hietarinta, Jarmo

doi:10.1103/physrevd.79.125027

Cited by 22 publications

(33 citation statements)

References 13 publications

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“…These maps were first classified by Pontrjagin 79 and have also appeared in other physical contexts. 53,80,81 Without losing generality, we can reduce the torus T 2 to a sphere S 2 so the mappings are S 2 ϫ S 1 → S 2 . When for fixed d ͑k x , k y , ͒ has an S 2 winding number of Ϯp, the topological classification is Z 2p .…”

Section: ͑423͒mentioning

confidence: 99%

Topological defects and gapless modes in insulators and superconductors

2010

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We develop a unified framework to classify topological defects in insulators and superconductors described by spatially modulated Bloch and Bogoliubov de Gennes Hamiltonians.We consider Hamiltonians H(k,r) that vary slowly with adiabatic parameters r surrounding the defect and belong to any of the ten symmetry classes defined by time-reversal symmetry and particle-hole symmetry. The topological classes for such defects are identified and explicit formulas for the topological invariants are presented. We introduce a generalization of the bulk-boundary correspondence that relates the topological classes to defect Hamiltonians to the presence of protected gapless modes at the defect. Many examples of line and point defects in three-dimensional systems will be discussed. These can host one dimensional chiral Dirac fermions, helical Dirac fermions, chiral Majorana fermions, and helical Majorana fermions, as well as zero-dimensional chiral and Majorana zero modes. This approach can also be used to classify temporal pumping cycles, such as the Thouless charge pump, as well as a fermion parity pump, which is related to the Ising non-Abelian statistics of defects that support Majorana zero modes. We develop a unified framework to classify topological defects in insulators and superconductors described by spatially modulated Bloch and Bogoliubov de Gennes Hamiltonians. We consider Hamiltonians H͑k , r͒ that vary slowly with adiabatic parameters r surrounding the defect and belong to any of the ten symmetry classes defined by time-reversal symmetry and particle-hole symmetry. The topological classes for such defects are identified and explicit formulas for the topological invariants are presented. We introduce a generalization of the bulk-boundary correspondence that relates the topological classes to defect Hamiltonians to the presence of protected gapless modes at the defect. Many examples of line and point defects in three-dimensional systems will be discussed. These can host one dimensional chiral Dirac fermions, helical Dirac fermions, chiral Majorana fermions, and helical Majorana fermions, as well as zero-dimensional chiral and Majorana zero modes. This approach can also be used to classify temporal pumping cycles, such as the Thouless charge pump, as well as a fermion parity pump, which is related to the Ising non-Abelian statistics of defects that support Majorana zero modes. Disciplines Physical Sciences and Mathematics | Physics

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Section: ͑423͒mentioning

confidence: 99%

Topological defects and gapless modes in insulators and superconductors

2010

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“…Solitons in this model resemble knotted rods; so it seems a good idea to investigate basic properties of these rods, such as their response to stretching and twisting. There have been some studies concerning the Skyrme-Faddeev model on R 2 × S 1 in the literature (Kundu & Rybakov 1981;Hietarinta et al 2004;Jäykkä & Hietarinta 2009;Ferreira et al 2012), but, surprisingly, the simple buckling effects described here have not previously been investigated. The Skyrme-Faddeev model has been proposed as a model of glueballs (Faddeev & Niemi 1999).…”

Section: Introductionmentioning

confidence: 99%

“…Skyrme-Faddeev solitons with D > 1 have been investigated in Jäykkä & Hietarinta (2009), and these correspond to elastic rods with D strands.…”

Section: Solitons Wrapping a Circlementioning

confidence: 99%

Helical buckling of Skyrme–Faddeev solitons

Foster

Harland

2012

Proc. R. Soc. A.

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“…Topological objects are often interesting topics in various fields of physics ranging from the condensed matter physics [1,2] to the particle physics and the modern universe [3,4]. Although many works have been done, much less attention is paid to their mathematical existence [5][6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Stable knots in the trapped Bose-Einstein condensates

Liu

Feng

Yang

2014

EPL

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The knot of spin texture is studied within the two-component Bose-Einstein condensates which are described by the nonlinear Gross-Pitaevskii equations. We start from the non-interacting equations including an axisymmetric harmonic trap to obtain an exact solution, which exhibits a non-trivial topological structure. The spin-texture is a knot with an integral Hopf invariant. The stability of the knot is verified by numerically evolving the nonlinear Gross-Pitaevskii equations along imaginary time.

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Unwinding in Hopfion vortex bunches

Cited by 22 publications

References 13 publications

Topological defects and gapless modes in insulators and superconductors

Topological defects and gapless modes in insulators and superconductors

Helical buckling of Skyrme–Faddeev solitons

Stable knots in the trapped Bose-Einstein condensates

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