Anderson transition symmetries at the band-edge of a correlated Sn/Si monolayer

Anderson localization is predicted to enhance the critical temperature of disordered superconductors. Despite a huge body of theoretical work based on non-linear sigma models, experiments are lacking to understand correlated electrons in disordered potentials. In this study, we investigate a tin monolayer on silicon, a material known for its likely antiferromagnetic Mott-correlated ground state. We analyze the statistical properties of tunneling conductance maps of increasingly localized states as we approach the edge of the valence band. Using multifractal analysis, we show that the system follows an exact symmetry relation based on the algebraic structure of nonlinear sigma-models (NLσMs). We anticipate that this symmetry may be broken in specific – e.g., chiral – electronic phases. Finally, we point out that multifractal analysis can equally be applied to universal conductance fluctuations in magneto-transport experiments, thus providing a powerful tool to probe the underlying symmetries of disordered electronic phases. Multifractality occurs in the local density of states (LDOS) in disordered electronic systems near a metal-insulator transition, and despite an abundance of theoretical studies, experimental analyses are rare. Here, using scanning tunneling microscopy, the authors investigate the correlations of the LDOS and multifractal spectra for Sn/Si monolayers and connect the localization patterns of disordered electronic systems with the Weyl group symmetry of nonlinear sigma-models.