Ahmad, Saeed (2012) *Semifluxons in long Josephson junctions with phase shifts.* PhD thesis, University of Nottingham.

## Abstract

A Josephson junction is formed by sandwiching a non-superconducting material between two superconductors. If the phase difference across the superconductors is zero, the junction is called a conventional junction, otherwise it is unconventional junction. Unconventional Josephson junctions are widely used in information process and storage.

First we investigate long Josephson junctions having two p-discontinuity points characterized by a shift of p in phase, that is, a 0-p-0 long Josephson junction, on both infinite and finite domains. The system is described by a modified sine-Gordon equation with an additional shift q(x) in the nonlinearity. Using a perturbation technique, we investigate an instability region where semifluxons are spontaneously generated. We study the dependence of semifluxons on the facet length, and the applied bias current.

We then consider a disk-shaped two-dimensional Josephson junction with concentric regions of 0- and p-phase shifts and investigate the ground state of the system both in finite and infinite domain. This system is described by a (2 + 1) dimensional sine-Gordon equation, which becomes effectively one dimensional in polar coordinates when one considers radially symmetric static solutions. We show that there is a parameter region in which the ground state corresponds to a spontaneously created ringshaped semifluxon. We use a Hamiltonian energy characterization to describe analytically the dependence of the semifluxonlike ground state on the length of the junction and the applied bias current. The existence and stability of excited states bifurcating from a uniform case has been discussed as well.

Finally, we consider 0-k infinitely long Josephson junctions, i.e., junctions having periodic k-jump in the Josephson phase. We discuss the existence and stability of ground states about the periodic solutions and investigate band-gaps structures in the plasma band and its dependence on an applied bias current. We derive an equation governing gap-breathers bifurcating from the edge of the transitional curves.

Item Type: | Thesis (PhD) |
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Supervisors: | Susanto, H. Wattis, J.A.D. |
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Faculties/Schools: | UK Campuses > Faculty of Science > School of Mathematical Sciences |
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ID Code: | 2729 |
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Deposited By: | Dr Saeed Ahmad |
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Deposited On: | 20 Sep 2012 12:25 |
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Last Modified: | 20 Sep 2012 12:25 |
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