📝 SummarXiv

Abstract

The interplay between Anderson localization and Coulomb repulsion reveals deep connections to superconductivity and many-body localization in quantum systems. In this study, we investigate a tin monolayer on silicon, a material known for its likely antiferromagnetic Mott-correlated ground-state. From the spatial correlations of local density of states (LDOS) maps measured by scanning tunneling spectroscopy, we precisely identify the mobility edge between extended and localized states at the valence band-edge. Using theoretical analysis to explain the energy-dependent LDOS fluctuations, we estimate the system's conductivity change across this effective metal-insulator transition. Then, we compute the multifractal spectra of iso-energy LDOS maps and show that they follow an exact symmetry relation based on the algebraic structure of nonlinear sigma-models (NL$\sigma$Ms) - the field theory of mesoscopic electronic systems. This observation suggests that NL$\sigma$Ms are valid even in a strongly correlated 2D system, down to conductivity levels as low as g ~ 0.1. We anticipate that the relation may be different in the chiral-superconducting phase reported for p-doped Sn/Si monolayer. Finally, we point out that multifractal analysis could equally be applied to universal conductance fluctuations in magneto-transport experiments.