We have studied the parallel-magnetic-field dependence of the superconducting transition temperature by magnetotransport measurements on one-atomic-layer Pb and indium films deposited on cleaved GaAs surfaces. Superconductivity was observed even in the parallel magnetic field much higher than Pauli paramagnetic limit. For the case of the Pb film, the parabolic parallel-magneticfield dependence of the superconducting transition temperature is quantitatively explained in terms of an inhomogeneous superconducting state, called a helical state, theoretically proposed for a twodimensional superconductor with a large Rashba spin splitting. For the case of the indium film, we developed the theory for a moderate Rashba spin splitting. It is estimated to be 35 meV, which is one order of magnitude smaller than that of heavy elements.
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