Dynamics of Semifluxons in Nb Long Josephson0−πJunctions

Abstract

We propose, implement, and test experimentally long Josephson 0-pi junctions fabricated using conventional Nb-AlOx-Nb technology. We show that by using a pair of current injectors one can create an arbitrary discontinuity of the Josephson phase and, in particular, a pi discontinuity, just as in d-wave/s-wave or in d-wave/d-wave junctions, and study fractional Josephson vortices which spontaneously appear. Moreover, using such junctions, we can investigate the dynamics of the fractional vortices-a domain which is not yet available for natural 0-pi junctions due to their inherently high damping. We observe half-integer zero-field steps which appear on the current-voltage characteristics due to the hopping of semifluxons.

Nonideal artificial phase discontinuity in long Josephson0−κjunctions

“…3 of Ref. 22) the injector current may be distributed in a rather peculiar way across the top electrode. Equation (1) can be rewritten as…”

“…Thus the π-discontinuity of the phase corresponds to (or can be substituted by) an additional current with the density −πδ(x)/x, i.e., by a current dipole of strength π. 22,26,27 Of course, in experiment one cannot pass infinitely large currents via infinitesimal wires, so the real current profile will be an approximation of θ xx (x), e.g., like the one shown in Fig. 2(d).…”

“…9,10,11,12,13 In contrast to an integer Josephson vortex (fluxon), which is a free moving soliton, a semifluxon is like a spin 1 2 particle -it is pinned at a 0-π boundary, has one of two possible polarities ± 1 2 Φ 0 and, the most important, can form the groundstate of the system. Semifluxons are very interesting non-linear objects: they can form a variety of groundstates, 14,15,16,17,18 may flip, 9,11,19 rearrange 15 or get depinned 17,20,21 by a bias current, lead to half-integer zero-field steps 20,21,22 and have a characteristic eigenfrequency. 23 Huge arrays of fractional flux quanta 9,15,16,17 were realized and predicted to have a tunable plasmon band structure 24 which can be thought of as a plasmonic crystal similar to photonic crystals.…”

“…22 This is done by creating a discontinuity of the Josephson phase φ (the difference between φ and µ is explained below) by means of current injectors. Two injectors of width ∆w are attached to one of the junction's electrodes at a distance ∆x from each other, as shown in Fig.…”

Quantum and classical integrable sine-Gordon model with defect

“…Many theoretical studies are dedicated to various models with defects starting from classical and semiclassical to quantum as well as statistical models [1], with several of them devoted exclusively to the sine-Gordon (SG) model with defect (DSG) [2] or inhomogeneity [3], which have enhanced physical importance [4,5]. A specific form of DSG model with a defect at a single point x = 0:…”