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Figure 2.2: Josephson Tunnel Junction – a) Physical structure: Two superconducting
regions separated by an insulating barrier. b) Circuit symbol: Possibly
depicting point-contact used in early junction fabrication. c) Effective circuit element:
The physical structure forms a parallel plate capacitor shunting the tunnel
junction. d) Current-voltage response: The junction’s response to an oscillating
bias is hysteretic and highly non-linear.
Here, the voltage V (t), the current I(t), and the superconducting phase difference
δ(t) across the junction are classical variables. I c is the “critical current” of the
junction, which depends on the barrier thickness, and Φ 0 = h 2e
is the flux quantum.
Figure 2.2d shows the electrical response of a Josephson junction on an I/V
plot. The plot shows three distinct features:
• The vertical line along the I-axis is commonly called the “zero-voltage state”
or the “supercurrent branch”. In this regime, the value of δ(t) is constant
(
−
π
2 < δ(t) < π 2
)
, which implies V (t) = 0. It can be seen from Equation 2.9
that the maximum current that can be conducted in this way is |I(t)| ≤ I c .
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