Exact analytical solution of the problem of current-carrying states of the Josephson junction in external magnetic fields
- B. I. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Avenue, 61103 Kharkov (Ukraine)
The classical problem of the Josephson junction of arbitrary length W in the presence of externally applied magnetic fields (H) and transport currents (J) is reconsidered from the point of view of stability theory. In particular, we derive the complete infinite set of exact analytical solutions for the phase difference that describe the current-carrying states of the junction with arbitrary W and an arbitrary mode of the injection of J. These solutions are parametrized by two natural parameters: the constants of integration. The boundaries of their stability regions in the parametric plane are determined by a corresponding infinite set of exact functional equations. Being mapped to the physical plane (H,J), these boundaries yield the dependence of the critical transport current J{sub c} on H. Contrary to a widespread belief, the exact analytical dependence J{sub c}=J{sub c}(H) proves to be multivalued even for arbitrarily small W. What is more, the exact solution reveals the existence of unquantized Josephson vortices carrying fractional flux and located near one of the junction edges, provided that J is sufficiently close to J{sub c} for certain finite values of H. This conclusion (as well as other exact analytical results) is illustrated by a graphical analysis of typical cases.
- OSTI ID:
- 21052755
- Journal Information:
- Physical Review. B, Condensed Matter and Materials Physics, Vol. 76, Issue 17; Other Information: DOI: 10.1103/PhysRevB.76.174515; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1098-0121
- Country of Publication:
- United States
- Language:
- English
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