Irrelevance of disorder in the superconductor to insulator transition of granular aluminum

We find excellent agreement between tunneling and optical conductivity gap values in superconducting granular aluminum films, up to the Metal to Insulator transition. This behavior, in strong contrast with that recently reported in atomically disordered samples for which the optical gap becomes smaller than the tunneling gap, rules out disorder as being at the origin of the transition. Rather, it confirms that it is of the Mott type. The large increase seen in the strong coupling ratio is interpreted as a sign of a BCS to BEC cross over, consistent with a Mott transition.