Josephson Effect

The Josephson effect is phase-coherent current through a weak link between two superconductors. It is a tunneling effect, but not an ordinary single-particle rectangular-barrier problem: the key variable is the gauge-invariant phase difference between superconducting condensates.

Formula Hook

For the ideal DC Josephson effect,

$$I_s=I_c\sin\phi,$$

where $I_c$ is the critical current and $\phi$ is the superconducting phase difference. With voltage $V$ across the junction,

$$\hbar\frac{d\phi}{dt}=2eV.$$

The Josephson energy is often written

$$E_J=\frac{\hbar I_c}{2e}.$$

The superconducting flux quantum is

$$\Phi_0=\frac{h}{2e}.$$

Canonical Home

The detailed canonical home is Josephson Effect, which develops gauge-invariant phase, DC and AC relations, junction energy, RCSJ dynamics, interference, SQUIDs, metrology, and circuit applications. This page remains the compact named-effect lookup. For the wave-mechanics bridge, see Tunneling Applications: First Encounters, Quantum Tunneling, and Rectangular Barrier Tunneling.

Common Confusions

• Josephson current is coherent pair tunneling; it is not just ordinary single-electron tunneling.
• The physically relevant phase difference is gauge-invariant and includes electromagnetic potentials when needed.
• Circuit models add capacitance, dissipation, noise, bias, and environmental modes.
• The sign convention for $\phi$ determines the sign convention for the current.

Related Entries

• Circuit QED Overview
• Amplitude
• Superposition
• Aharonov–Bohm Effect

References

• B. D. Josephson, “Possible new effects in superconductive tunnelling,” Physics Letters 1, 251-253, 1962.
• A. Barone and G. Paterno, Physics and Applications of the Josephson Effect, Wiley, 1982.
• M. Tinkham, Introduction to Superconductivity, 2nd ed., Dover, 2004.