A novel way to realize a π Josephson junction is proposed, based on a weak link in an unconventional d-wave superconductor with appropriately chosen boundary geometry. The critical current of such a junction is calculated from a fully self-consistent solution of microscopic Eilenberger theory of superconductivity. The results clearly show that a transition to a π Josephson junction occurs for both low temperatures and small sizes of the geometry.
Figure 1: Interleaved simulation snapshots and magnetic field renderings. A toy magnet, carrying small permanent magnets in its ends, is moved towards a sphere into which it induces a magnetization. As the magnet approaches the sphere, the induced field and thus the attracting forces increase until they exceed the gravitational force and pull the sphere towards the magnet.
AbstractWe introduce magnetic interaction for rigid body simulation. Our approach is based on an equivalent dipole method and as such it is discrete from the ground up. Our approach is symmetric as we base both field and force computations on dipole interactions. Enriching rigid body simulation with magnetism allows for many new and interesting possibilities in computer animation and special effects. Our method also allows the accurate computation of magnetic fields for arbitrarily shaped objects, which is especially interesting for pedagogy as it allows the user to visually discover properties of magnetism which would otherwise be difficult to grasp. We demonstrate our method on a variety of problems and our results reflect intuitive as well as surprising effects. Our method is fast and can be coupled with any rigid body solver to simulate dozens of magnetic objects at interactive rates.
Self-consistent solutions of microscopic Eilenberger theory are presented for a two-dimensional model of a superconducting channel with a geometric constriction. Magnetic fields, external ones as well as those caused by the supercurrents, are included and the relevant equations are solved numerically without further assumptions. Results concerning the influence of temperature, geometric parameters, of κ = λL/ξ0 and of external magnetic fields on the Andreev bound states in the weak link and on the current-phase relation are presented. We find that the Andreev bound states within the junction obtain peculiar substructure when a finite supercurrent flows. As long as the London penetration depth is comparable to or bigger than the extension of the constriction, the Josephson effect is independent of κ. Furthermore, the weak link is very insensitive to external magnetic fields. Features restricted to a self-consistent calculation are discussed.
We show that a constriction-type Josephson junction realized by an epitactic thin film of a d-wave superconductor with an appropriate boundary geometry exhibits intrinsic phase differences between 0 and depending on geometric parameters and temperature. Based on microscopic Eilenberger theory, we provide a general derivation of the relation between the change in the free energy of the junction and the current-phase relation. From the change in the free energy, we calculate phase diagrams and discuss transitions driven by geometric parameters and temperature.
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