Electron-hole conversion at a superconducting interface
In a Josephson junction, Andreev reflection traps electron-hole pairs as Andreev bound states with energy ε(φ) = Δ√(1 − T·sin²(φ/2)). The supercurrent is carried by these subgap states: I(φ) = (eΔ/ℏ)·T·sin(φ)/[2ε(φ)]. At T=1 (transparent), the spectrum becomes gapless at φ=π — a Josephson junction hosts a topological phase transition at perfect transmission.