Andreev bound states
Coherent electron–hole reflection forms subgap states.
$$E_A(\phi)=\Delta\sqrt{1-T\sin^2(\phi/2)}$$
Physical intuition
Coherent electron–hole reflection forms subgap states.
Deep dive: physical mechanism
In a short single-channel junction, Andreev reflections produce phase-dependent bound-state energies.
What is measured experimentally?
Microwave spectroscopy detects transitions between Andreev levels.
Assumptions, noise and limitations
The formula assumes a short junction and a single transmission channel.
Research and simulation exercise
Plot Andreev energy versus superconducting phase.
Connect the ideas
Explore the chapter overview, learning path, and references.