Zero-bias anomaly in nanoscale hole-doped Mott insulators on a triangular silicon surface

Adsorption of 1/3 monolayer of Sn on a heavily doped $p$-type Si(111) substrate results in the formation of a hole-doped Mott insulator, with electronic properties that are remarkably similar to those of the high-${T}_{c}$ copper oxide compounds. In this work, we show that the maximum hole-density of this system increases with decreasing domain size as the area of the Mott insulating domains approaches the nanoscale regime. Concomitantly, scanning tunneling spectroscopy (STS) data at 4.4 K reveal an increasingly prominent zero-bias anomaly (ZBA). We consider two different scenarios as potential mechanisms for this ZBA: chiral ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}+\phantom{\rule{4pt}{0ex}}\mathrm{i}{d}_{xy}$ wave superconductivity and a dynamical Coulomb blockade (DCB) effect. The latter arises due to the formation of a resistive depletion layer between the nanodomains and the substrate. Both models fit the tunneling spectra with weaker ZBAs, while the DCB model clearly fits better to spectra recorded at higher temperatures or from the smallest domains with the strongest ZBA. Consistently, STS spectra from the lightly doped substrates display oscillatory behavior that can be attributed to conventional Coulomb staircase behavior, which becomes stronger for smaller sized domains. We conclude that the ZBA is predominantly due to a DCB effect, while a superconducting instability is absent or a minor contributing factor.