Superconducting fluctuations and paraconductivity in ultrathin amorphous Pb films near superconductor-insulator transitions

Superconductivity in two dimensions has attracted renewed interest in the context of two-dimensional (2D) van der Waals materials. Key questions remain regarding the nature and manifestations of the superconductivity in these materials. One open question is whether superconducting fluctuations in such 2D systems can be described by the classic Aslamazov-Larkin (A-L) equation. While the A-L model has long been found to accurately describe the paraconductivity of some conventional 2D superconductors, its applicability in ultrathin limit near the superconductor-insulator transition (SIT) has not been established. Here, we report a systematic study of superconducting fluctuation and paraconductivity in ultrathin 2D amorphous Pb films near the SIT. Pb films were incrementally deposited, and the electrical measurements were performed in situ at each thickness in a dilution refrigerator, resulting in a series of sheet resistance curves $[{R}_{\ensuremath{\square}}(T)]$ across the SIT. Paramagnetic impurities (Cr) were then deposited on the same superconducting film, driving it back to the insulating state and yielding another set of ${R}_{\ensuremath{\square}}$($T$). Both types of ${R}_{\ensuremath{\square}}$($T$) curves were analyzed with the A-L equation. At all film thicknesses (and ${T}_{C}$'s), we observed a background paraconductivity significantly greater than the A-L value. As the film thickness decreases and the SIT is approached, the paraconductivity increases precipitously, reaching more than an order of magnitude higher than that of the A-L value at the immediate vicinity of the SIT. Accompanying the presence of excess paraconductivity and its increase with decreasing thickness, the paraconductivity exhibits exponential scaling with $T$ above ${T}_{C}$, whose temperature range and slope show concomitant variations with decreasing film thickness. In contrast, suppression of ${T}_{C}$ by magnetic impurity results in much weaker increase of the excess paraconductivity and little change in the temperature range and slope of the exponential $T$ scaling. These observations are consistent with the presence of emergent localized superconducting pairing above ${T}_{C}$ in the strongly disordered, morphologically nominally uniform amorphous films. The spatially localized superconductivity likely causes excess paraconductivity beyond the A-L theory and percolative superconducting transitions. Such electronic inhomogeneities proliferate with decreasing film thickness, especially near the SIT.