Phase retrapping in a pointlike φ Josephson junction: the butterfly effect.

We consider a φ Josephson junction, which has a bistable zero-voltage state with the stationary phases ψ = ±φ. In the nonzero voltage state the phase "moves" viscously along a tilted periodic double-well potential. When the tilting is reduced quasistatically, the phase is retrapped in one of the potential wells. We study the viscous phase dynamics to determine in which well (-φ or +φ) the phase is retrapped for a given damping, when the junction returns from the finite-voltage state back to the zero-voltage state. In the limit of low damping, the φ Josephson junction exhibits a butterfly effect-extreme sensitivity of the destination well on damping. This leads to an impossibility to predict the destination well.

Experimental evidence of a φ Josephson junction.

We demonstrate experimentally the existence of Josephson junctions having a doubly degenerate ground state with an average Josephson phase ψ=±φ. The value of φ can be chosen by design in the interval 0<φ<π. The junctions used in our experiments are fabricated as 0-π Josephson junctions of moderate normalized length with asymmetric 0 and π regions. We show that (a) these φ Josephson junctions have two critical currents, corresponding to the escape of the phase ψ from -φ and +φ states, (b) the phase ψ can be set to a particular state by tuning an external magnetic field, or (c) by using a proper bias current sweep sequence. The experimental observations are in agreement with previous theoretical predictions.

Josephson junction with a magnetic-field tunable ground state.

We consider an asymmetric 0-π Josephson junction consisting of 0 and π regions of different lengths L(0) and L(π). As predicted earlier this system can be described by an effective sine-Gordon equation for the spatially averaged phase ψ so that the effective current-phase relation of this system includes a negative second harmonic ∝sin(2ψ). If its amplitude is large enough, the ground state of the junction is doubly degenerate ψ=±φ, where φ depends on the amplitudes of the first and second harmonics. We study the behavior of such a junction in an applied magnetic field H and demonstrate that H induces an additional term ∝Hcosψ in the effective current-phase relation. This results in a nontrivial ground state tunable by magnetic field. The dependence of the critical current on H allows for revealing the ground state experimentally.

New Andreev-type states in superconducting nanowires.

Superconducting nanowires can exhibit a spatially inhomogeneous pair condensate that leads to the formation of new Andreev-type states. Such states are mainly located beyond the regions where the order parameter is enhanced, and no normal-superconducting contact or external magnetic field is needed for their formation. Our numerical self-consistent solutions of the Bogoliubov-de Gennes equations for cylindrical nanowires, in the clean limit, demonstrate that these new Andreev-type states decrease the ratio of the energy gap to the critical temperature as compared to its bulk value. The low-lying excitations in a clean superconducting nanowire are these new Andreev-type states induced by quantum confinement of the electrons in the transverse direction.

Observation of splintered Josephson vortices at grain boundaries in YBa(2)Cu(3)O(7-delta).

We have directly observed well-separated Josephson vortex splinters with unquantized magnetic flux at asymmetric 45 degrees grain boundaries in YBa(2)Cu(3)O(7-delta) films by imaging magnetic flux with scanning SQUID microscopy. The existence of these splinter vortices has been predicted and is well described by a model based on dx(2)(-y(2)) pairing symmetry and facetting of the grain boundary on a length scale shorter than the Josephson penetration depth.