Pinned states in Josephson arrays: A general stability theorem

Details Pinned states in Josephson arrays: A general stability theorem Pinned states in Josephson arrays: A general stability theorem

1998-05-29

arxiv.org/abs/cond-mat/9805405v1

Physics

Condensed Matter

Superconductivity

To appear in Phys. Rev. B

Scientific paper

10.1103/PhysRevB.58.5215

Using the lumped circuit equations, we derive a stability criterion for superconducting pinned states in two-dimensional arrays of Josephson junctions. The analysis neglects quantum, thermal, and inductive effects, but allows disordered junctions, arbitrary network connectivity, and arbitrary spatial patterns of applied magnetic flux and DC current injection. We prove that a pinned state is linearly stable if and only if its corresponding stiffness matrix is positive definite. This algebraic condition can be used to predict the critical current and frustration at which depinning occurs.

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