We systematically address superconductivity of Pb nano-islands with different thicknesses and lateral sizes via a scanning tunneling microscopy/spectroscopy. Reduction of the superconducting gap (Δ) is observed even when the island is larger than the bulk coherence length (ξ) and becomes very fast below ~ 50 nm lateral size. The suppression of Δ with size depends to a good approximation only on the volume of the island and is independent of its shape. Theoretical analysis indicates that the universal quenching behavior is primarily manifested by the mean number of electronic orbitals within the pairing energy window.
2The remarkable properties of a superconductor are due to its Cooper pair condensate (formed from a macroscopic number of electrons), which can be described by a single quantum wave function. According to the celebrated Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity 1 , there is a minimum length scale (the coherence length, ξ) on which the condensate order parameter can vary. The fate of superconductivity in systems with spatial dimensions smaller than the coherence length, ξ, has been the subject of intense interest for decades because it is dependent on quantum confinement, interaction, and quantum coherence effects in an intrinsically many-particle context--ingredients that drive much modern research in quantum many-body physics [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] . Attention has often focused on two-dimensional (2-d) systems which can have fragile order because of quantum and thermal fluctuations. In this context, the recent discovery of robust superconductivity in epitaxial thin Pb films with thicknesses that are orders of magnitude smaller than ξ seems surprising 4,10,11 . Even at a thickness of only two atomic layers (~ 0.6 nm), the superconducting transition temperature (T C ~ 5 K) of Pb films is only slightly smaller than the bulk value 7.2 K 4 . Nevertheless, there remain disputes regarding the thickness dependence of T C at thickness below 10 MLs. Although this observation is already interesting, much more telling information on the fate of superconductivity at small length scales emerges when the lateral dimensions of the ultra-thin films are also reduced. The experiments were conducted in a home-built low temperature STM system with an in-situ sample preparation chamber. The striped incommensurate (SIC) phase of the Pb-Si surface shown in Fig. 1 , where a and b are lengths along the major and minor axes, respectively. Recently Brun et al. 15 reported a study of thickness dependence of the superconducting gap of Pb 2-d islands with lateral size larger than ξ which they interpreted to represent the superconducting properties of extended films. They found that the superconducting gap scales with the inverse of island thickness and superconductivity should vanish at a thickness of 2 ML.While the recent observation of strong superconductivity at 2ML already implied the breakdown of the 1/d scaling 4 , the current result that gap reduc...