At a superconducting interface, an incoming electron can be reflected as a hole — Andreev reflection. Particle-hole symmetry of the BCS Hamiltonian suggests the conductance should be symmetric under bias reversal: electrons at +V and holes at -V should see the same transmission. For a sharp interface, this is exactly true.
For an extended interface — one with finite spatial extent — it's false. The paper shows that electrons and holes accumulate different phases when traversing a normal region adjacent to the superconductor. The phase difference arises from quantum interference within the extended interface, which acts as an Andreev interferometer: multiple coherent reflections between the interface boundaries create interference patterns that differ for particles and antiparticles.
The asymmetry manifests as damped oscillations in the conductance difference between positive and negative bias. The oscillation period is set by the interface length and the Fermi wavelength; the damping comes from the mismatch between electron and hole Fermi wavevectors. The effect is entirely quantum-mechanical — it vanishes in the semiclassical limit.
The superconducting gap controls the bias scale of the asymmetry, appearing as a sharp crossover: below the gap energy, the asymmetry is pronounced; above it, it fades. This crossover is visible even when traditional Andreev signatures (like the conductance doubling at zero bias) are washed out by disorder or finite temperature.
Bias asymmetry as spectroscopy. The broken symmetry isn't an artifact — it's information about the interface width, the Fermi surface, and the gap energy, encoded in a quantity most experiments assume is zero.