Noise and full counting statistics of incoherent multiple Andreev reflection

We present a general theory for the full counting statistics of multiple Andreev reflections in incoherent superconducting-normal-superconducting contacts. The theory, based on a stochastic path integral approach, is applied to a superconductor-double-barrier system. It is found that all cumulants of the current show a pronounced subharmonic gap structure at voltages V=2Δ/en. For low voltages V≪Δ/e, the counting statistics results from diffusion of multiple charges in energy space, giving the pth cumulant ⟨Qp⟩∝V2-p, diverging for p≥3. We show that this low-voltage result holds for a large class of incoherent superconducting-normal-superconducting contacts.