Ambegaokar-Baratoff Calculator

Convert between Josephson energy E_J and normal-state resistance R_N of a Josephson junction, including finite-temperature gap suppression.

Superconducting gap Δ(0) at zero temperature: Temperature T [K]: Calculate: Empirical E_J × R_N constant K (optional): E_J = K / R_N Calculate

Formulas

Quantity	Formula
AB formula (Ic RN)	IcRN = πΔ(T) / (2e) × tanh(Δ(T) / (2kBT))
EJ from RN	EJ = hΔ(T) / (8e²RN) × tanh(Δ(T) / (2kBT))
T = 0 limit	EJ = hΔ(0) / (8e²RN)
T-dependent gap	Δ(T) ≈ Δ(0) × tanh(1.74 × √(Tc/T − 1))  for T < Tc
BCS relation	Tc = Δ(0) / (1.76 kB)
Josephson energy	EJ = Φ0 Ic / (2π) = ℏ Ic / (2e)
Empirical constant K	EJ = K / RN    RN = K / EJ    KAB = hΔ(T) × tanh(Δ(T)/(2kBT)) / (8e²)