### Abstract

We investigate theoretically the eigenmodes and the stability of one and two arbitrary fractional vortices pinned at one and two κ phase discontinuities in a long Josephson junction. In the particular case of a single κ discontinuity, a vortex is spontaneously created and pinned at the boundary between the 0 and κ regions. In this work we show that only two of four possible vortices are stable. A single vortex has an oscillatory eigenmode with a frequency within the plasma gap. We calculate this eigenfrequency as a function of the fractional flux carried by a vortex. For the case of two vortices, pinned at two κ discontinuities situated at some distance a from each other, splitting of the eigenfrequencies occurs. We calculate this splitting numerically as a function of a for different possible ground states. We also discuss the presence of a critical distance below which two antiferromagnetically ordered vortices form a strongly coupled “vortex molecule��? that behaves as a single object and has only one eigenmode.

Original language | Undefined |
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Pages (from-to) | 104518 |

Number of pages | 8 |

Journal | Physical review B: Condensed matter and materials physics |

Volume | 71 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2005 |

### Keywords

- IR-53369
- EWI-13960
- METIS-226012

## Cite this

Goldobin, E., Susanto, H., Koelle, D., Kleiner, R., & van Gils, S. A. (2005). Oscillatory eigenmodes and stability of one and two arbitrary fractional vortices in long Josephson 0-κ junctions.

*Physical review B: Condensed matter and materials physics*,*71*(10), 104518. https://doi.org/10.1103/PhysRevB.71.104518