Andreev Bound States — Short Josephson Junction
JUNCTION PARAMETERS
Transparency τ
0.90
Phase diff φ
1.57
rad
Num channels M
5
Temperature T/Δ
0.10
↑ drag φ to animate ABS
ABS ENERGIES
E₊(φ):
—
E₋(φ):
—
Josephson current:
—
Critical current I_c:
—
ABS THEORY
Short junction (L≪ξ):
E±(φ) = ±Δ√(1−τ·sin²(φ/2))
ABS carry supercurrent:
I(φ) = (eΔ/ħ) Σ_n τ_n sin(φ)/(2E_n)
For perfect τ=1:
E±(φ) = ±Δ|cos(φ/2)|
I_c = eΔ/ħ (maximum)
Andreev reflection: e⁻ → hole
at NS interface (retroreflection)