Two-dimensional (2D) superconductivity was studied by magnetotransport measurements on single-atomic-layer Pb films on a cleaved GaAs(110) surface. The superconducting transition temperature shows only a weak dependence on the parallel magnetic field up to 14 T, which is higher than the Pauli paramagnetic limit. Furthermore, the perpendicular-magnetic-field dependence of the sheet resistance is almost independent of the presence of the parallel field component. These results are explained in terms of an inhomogeneous superconducting state predicted for 2D metals with a large Rashba spin splitting.PACS numbers: 73.20.At,Superconductivity in ultrathin films has been studied for a long time. In Ref.[1], superconductivity was observed even for a few-monolayer thickness in quenchcondensed films of Bi and Pb deposited on a glazed alumina substrate coated with amorphous Ge. Very recently, it has been revealed that superconductivity can occur in single atomic layers of Pb and In grown epitaxially on a Si(111) substrate [2,3]. A single-atomic-layer metal film on an insulating substrate is an interesting system for studies of superconductivity, not only because it is a complete two-dimensional (2D) system but also because of the broken spatial inversion symmetry. The asymmetry of the confining potential in the direction perpendicular to the 2D plane, combined with atomic spin-orbit coupling, is expected to cause the Rashba effect, which lifts the spin degeneracy of the 2D electronic states [4,5]. Actually, angle-resolved photoelectron spectroscopy measurements showed a large Rashba spin splitting of the order of 100 meV on the surfaces of heavy elements, such as Au [6], W [7], and Bi [8], and those of lighter elements, such as Si and Ge, covered with a monolayer of heavy elements, such as Bi [9][10][11].In this Letter, we report magnetotransport measurements on superconducting monolayer Pb films produced by quench condensation onto a cleaved GaAs(110) surface. Here, we focus on the effect of the magnetic field applied parallel to the surface. While the perpendicular component H ⊥ of the magnetic field strongly affects the orbital motion of electrons in the 2D plane, the parallel component H is expected to couple only to the spin degree of freedom. We show that the reduction of the superconducting transition temperature T c is very small even in strong parallel magnetic fields (H ⊥ = 0), which are much larger than the Pauli paramagnetic limit. Furthermore, the H ⊥ dependence of the sheet resistance at low temperature is found to be almost independent of the presence of H . These results are explained by assuming an inhomogeneous superconducting state predicted for Rashba spin-split 2D systems.In order to measure the sheet resistance R sq of ultrathin films, we apply the experimental procedure developed for studies on adsorbate-induced surface inversion layers on InAs [13][14][15] and InSb [16]. In this work, we used a nondoped insulating GaAs single-crystal substrate so as not to create conduction channels in the substrate...

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The parallel-magnetic-field H dependence of the superconducting transition temperature T c is studied for ultrathin films of In, Bi, and Al grown on GaAs(110). In the case of In films in the monolayer regime, T c exhibits a quadratic-like H dependence, which is one order of magnitude stronger than that previously observed in monolayer Pb films by the present authors [Phys. Rev. Lett. 111, 057005 (2013)]. The results are well reproduced by a model developed for an inhomogeneous two-dimensional superconducting state in the presence of a moderate Rashba spin-orbit interaction. The Rashba spin splitting is estimated to be 0.04 eV, which is much smaller than that expected for monolayer Pb films. In a few-monolayer Bi film, the suppression of T c with increasing H is comparable to that in monolayer Pb films. On the other hand, much stronger suppression, which is attributed to the Pauli paramagnetic effect, was observed for the Al film.

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.