Size dependent superconductivity of Pb islands grown on Si (111)

The superconductivity of nano-sized Pb islands grown on Si (111) with different size at 9 monolayer thickness was studied by low temperature scanning tunneling spectroscopy. By measuring the zero bias conductance as a function of temperature, for larger islands we observed a transition from pseudogap state at high temperature to superconductivity state at low temperature through two distinct slopes, where the superconductivity transition temperature ($T$c) of the island can be determined. For island size of $\sim $58 nm$^{2}$, a large drop in $T$c is found; when the size is further reduced to about 30 nm$^{2}$, no superconducting state was observed down to the measured temperature of 3.2 K. By properly subtracting the background and pseudogap effect, information on the temperature dependent superconductivity gap can be obtained. The ratio of $\frac{2\Delta _0 }{k_B T_c }$ decreased from 4.5 to 3.3 with the reduction of island size, showing that the electron-phonon coupling becomes weaker as the size decreases.