Axion mass estimates from resonant Josephson junctions
  Recently it has been proposed that dark matter axions from the galactic halo
can produce a small Shapiro step-like signal in Josephson junctions whose
Josephson frequency resonates with the axion mass [C. Beck, PRL 111, 231801
(2013)]. Here we show that the axion field equations in a voltage-driven
Josephson junction environment allow for a nontrivial solution where the
axion-induced electric current manifests itself as an oscillating supercurrent.
The linear change of phase associated with this nontrivial solution implies the
formal existence of a large magnetic field in a tiny surface area of the weak
link region of the junction which makes incoming axions decay into microwave
photons. We derive a condition for the design of Josephson junction experiments
so that they can act as optimum axion detectors. Four independent recent
experiments are discussed in this context. The observed Shapiro step anomalies
of all four experiments consistently point towards an axion mass of $(110 \pm
2)\mu $eV. This mass value is compatible with the recent BICEP2 results and
implies that Peccei-Quinn symmetry breaking was taking place after inflation.
