Direct measurement of phase fluctuations in atomically thin single crystal superconductors

A conventional superconductor (SC) in the two-dimensional (2D) limit has a low transition temperature $T_c$, and low superfluid density (SFD), resulting in fragile superconductivity [1-3]. Previous investigations using highly disordered granular films have also shown a rapid suppression of both $T_c$ and the SFD with thickness reduction, eventually resulting in a superconductor-insulator transition [4-8]. The emergence of single crystal films, however, reveals surprises: at a thickness of only five atoms, Pb films still show remarkably high superfluid rigidity with robust superconductivity [9], indicating the need for a close examination of phase rigidity in single crystal superconducting films. Using Indium $\sqrt{7}\times\sqrt{3}$ on Si(111) as a single layer superconductor [10], we study phase fluctuations by $in\ situ$ measurement of both the macroscopic SFD and the microscopic quasi-particle excitation spectrum. We demonstrate a quantitative control of the superfluid phase rigidity by systematically increasing point defects. We further reveal how the density and morphology of defects impact the superconducting order parameter at both local and global scales. We measure both the Bardeen-Cooper-Schrieffer (BCS) [11] and Berezinskii-Kosterlitz-Thouless (BKT) [12-15] transition temperatures as the phase rigidity is varied, from which a 2D SC phase diagram is established, with generic features applicable to other ultrathin superconducting systems.