Size-dependent superconducting state of individual nanosized Pb islands grown on Si(111) by tunneling spectroscopy

Abstract

By measuring the temperature-dependent tunneling spectroscopy of a set of flat-top Pb islands from 3.2 to 15 K, the limiting size of a nine-monolayer-thick Pb island with superconductivity above 3.2 K was determined to be ∼ 30 nm(2), in good agreement with the Anderson criterion. Further analysis indicates that the zero-temperature energy gap decreases significantly faster than the transition temperature when the Pb island size approaches this limit. This leads to a decrease of 2Δ(0)/k(B)T(C) from 4.5 to 3.3, thus showing that the Pb island superconductors undergo a change from strong to weak electron-phonon coupling.

Phonon limited superconducting correlations in metallic nanograins

“…A scanning tunneling microscope (STM) was used to detect the superconducting gap in a single physically isolated ultra-small Pb/Sn grain 1 43 44 . These studies traced the size evolution of superconductivity in isolated nanoparticles that were grown on a substrate.…”

“…A reduction of the superconducting gap of ultrathin islands was observed. Layer-dependent ab initio density functional calculations for freestanding Pb films showed that the electron-phonon coupling decreases with decreasing film thickness and hence results in the size-dependent destruction of superconductivity 44 . Interestingly the suppression of superconductivity with size depends to a good approximation only on the volume of the island and is independent of its shape 47 .…”

Dynamical Coulomb Blockade Observed in Nanosized Electrical Contacts

“…The temperature was below the critical temperature of bulk lead (T c = 7.2 K) and one could expect the Pb islands to display superconducting properties for voltages below the superconducting gap of bulk Pb, |eV |/2 < ∆ = 1.3 meV [24]. However, recent experiments have shown that both T c and ∆ decrease below their bulk values for small systems [24,26] and superconducting gap features give a negligible contribution to the conductance under our experimental conditions. On larger voltage scales the quasi-particle transport between the islands and their normal-state substrates is the same as for islands in their normal-state as we checked by performing experiments at temperatures above T c .…”

Closing the superconducting gap in small Pb nanoislands with high magnetic fields

“…Despite their increased resilience to magnetic fields, smaller islands feature a reduced order parameter as signified by a reduced superconducting gap at zero field, ∆ 0 . We extracted ∆ 0 from the dI/dV spectra recorded at 0 T by fitting the Dynes formula [34,39] (see Figure S1 for details). Figure 4a shows ∆ 0 as a function of island diameter which we find to fit well to ∆ 0 = ∆ ∞ − m/d.…”