Photon assisted tunneling as an origin of the Dynes density of states

We show that the effect of a high-temperature environment in current transport through a normal metal-insulator-superconductor tunnel junction can be described by an effective density of states (DOS) in the superconductor. In the limit of a resistive low-ohmic environment, this DOS reduces into the well-known Dynes form. Our theoretical result is supported by experiments in engineered environments. We apply our findings to improve the performance of a single-electron turnstile, a potential candidate for a metrological current source.