The Rashba superconductor, in which spin-splitting bands become superconducting, is fascinating as a novel superconducting system in low-dimensional systems. Here, we present the results of in-situ transport measurements on a Rashba-Type surface state of the striped incommensurate (SIC) phase of a Pb atomic layer on Ge(111) surface with additional Pb islands/clusters on it. We found that two-step superconducting transitions occurred at around 7 K and 3 K. The latter superconducting transition is suggested to be induced at the non-superconducting Rashba SIC area because of the lateral proximity effect caused by the superconducting Pb clusters. Our results propose a new type of Rashba superconductor, which is a platform to understand the Rashba superconducting systems.
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