“…Without any further assumption or fitting parameter, we found that: i) consistent with an EFT approach, parametrically small corrections to the electric permittivity are sufficient to drive a phase transition and to match the measured behavior of the critical current as a function of the applied electric field, ii) the qualitative behaviour is independent of the charge sign of the electrodes, iii) the critical temperature is not appreciably affected by the electric field applied, iv) the effect vanishes when the thickness of the sample is increased over several coherence lengths. All these predictions are both qualitatively and quantitatively in agreement with the experiments [2,5,6,12,[16][17][18][19]. Additionally, we have proposed a way to further test our theoretical model through elec-tron tunneling, highlighting the features that could be detected in these kind of experiments.…”