Pinned fluxons in a Josephson junction with a finite-length inhomogeneity

TL;DR

This paper analyzes the existence and stability of pinned fluxons in a Josephson junction with finite-length inhomogeneities, revealing unique stable configurations and their dependence on system parameters.

Contribution

It provides a comprehensive stability analysis of pinned fluxons in inhomogeneous Josephson junctions, including explicit relations and the discovery of non-monotonic stable fluxons.

Findings

Existence of various pinned fluxons depending on inhomogeneity length and current

Only one stable pinned fluxon exists if any are present

Stable pinned fluxons can be non-monotonic in microresistors and microresonators

Abstract

We consider a Josephson junction system installed with a finite length inhomogeneity, either of microresistor or of microresonator type. The system can be modelled by a sine-Gordon equation with a piecewise-constant function to represent the varying Josephson tunneling critical current. The existence of pinned fluxons depends on the length of the inhomogeneity, the variation in the Josephson tunneling critical current and the applied bias current. We establish that a system may either not be able to sustain a pinned fluxon, or - for instance by varying the length of the inhomogeneity - may exhibit various different types of pinned fluxons. Our stability analysis shows that changes of stability can only occur at critical points of the length of the inhomogeneity as a function of the (Hamiltonian) energy density inside the inhomogeneity - a relation we determine explicitly. In combination with continuation arguments and Sturm-Liouville theory, we determine the stability of all constructed pinned fluxons. It follows that if a given system is able to sustain at least one pinned fluxon, there is exactly one stable pinned fluxon, i.e. the system selects one unique stable pinned configuration. Moreover, it is shown that both for microresistors and microresonators this stable pinned configuration may be non-monotonic - something which is not possible in the homogeneous case. Finally, it is shown that results in the literature on localised inhomogeneities can be recovered as limits of our results on microresonators.