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Discontinuous current-phase relations in small one-dimensional Josephson junction arrays.

Jens Koch¹, Karyn Le Hur

¹Department of Physics and Applied Physics, Yale University, PO Box 208120, New Haven, Connecticut 06520, USA.

Physical Review Letters

|October 15, 2008

Summary

We investigated the Josephson effect in one-dimensional Josephson junction arrays. Distinct current-phase relationships arise from topological regions, persisting in larger systems and yielding analytical solutions.

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Area of Science:

Condensed Matter Physics
Quantum Phenomena

Background:

The Josephson effect describes quantum mechanical tunneling of superconducting charge carriers across a weak link.
Josephson junction arrays are crucial for quantum computing and sensitive measurements.
Understanding the charge stability diagram is key to controlling array behavior.

Purpose of the Study:

To investigate the Josephson effect in small one-dimensional (1D) Josephson junction arrays.
To analyze the distinct current-phase (I-phi) relationships generated by topological regions in the charge-stability diagram for weak Josephson tunneling.
To generalize findings to larger arrays and explore analytical solutions.

Main Methods:

Analysis of the charge-stability diagram for small Josephson junction arrays.
Characterization of current-phase (I-phi) relationships near charge-degeneracy lines and triple points.
Mapping the system to a tight-binding model for analytical solutions in larger arrays.

Main Results:

Topologically distinct regions in the charge-stability diagram yield unique I-phi relationships for weak tunneling.
Discontinuities in the I-phi relation at phase pi persist in larger arrays.
Maximum degeneracy allows mapping to a tight-binding model for analytical results applicable to arbitrary system sizes.

Conclusions:

The Josephson effect in 1D arrays exhibits complex I-phi relationships dependent on topological charge regions.
The observed phenomena are scalable to larger systems, maintaining key characteristics.
A tight-binding model provides a powerful analytical tool for understanding these systems.