Josephson effecteffect
In 1962, the British physicist Brian Josephson, then a graduate student, theoretically predicted that a current would flow through a superconductor–insulator–superconductor junction even at zero voltage. The stationary effect: current I = I_c sin φ, where I_c is the critical current, φ is the phase difference of the order parameters. The non-stationary effect: at a constant voltage V, the phase changes at a rate dφ/dt = 2eV/ħ, which gives an alternating current with a frequency of 483.6 GHz per millivolt. This is a direct manifestation of quantum coherence of a macroscopic superconducting state.
How it works
The most famous device based on the Josephson effect is the SQUID (Superconducting Quantum Interference Device), capable of detecting magnetic fields a hundred billion times weaker than Earth's. It is used in medical magnetoencephalography.
💡 Using the Josephson effect, scientists have built volt standards accurate to 10⁻¹⁰, linking electrical voltage exclusively to the fundamental constants e and h.
I = I_c \sin \varphi
I is the current through the junction, I_c is the critical current (maximum supercurrent, depending on material and temperature), φ = θ₂ - θ₁ is the phase difference of the superconducting order parameters in the two banks of the junction (dimensionless).
\frac{d\varphi}{dt} = \frac{2e}{\hbar} V
φ is the phase difference (dimensionless), t is time, V is the constant voltage across the junction, e is the elementary charge (e ≈ 1.602×10⁻¹⁹ C), ħ is the reduced Planck constant (ħ ≈ 1.0546×10⁻³⁴ J·s). The coefficient 2e/ħ ≈ 3.038×10⁹ s⁻¹/V.