Oscillatory eigenmodes and stability of one and two arbitrary fractional vortices in long Josephson 0−κ junctions

E. Goldobin; H. Susanto; D. Koelle; R. Kleiner; S. A. van Gils

doi:10.1103/PhysRevB.71.104518

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Oscillatory eigenmodes and stability of one and two arbitrary fractional vortices in long Josephson 0−κ junctions

E. Goldobin, H. Susanto, D. Koelle, R. Kleiner, S. A. van Gils

DOI 10.1103/PhysRevB.71.104518 · Physical Review B

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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.