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

TL;DR

This paper investigates the symmetry properties of Anderson localization at the band-edge in a correlated Sn/Si monolayer, revealing exact symmetry relations through multifractal analysis and suggesting broader applications in disordered electronic phases.

Contribution

It demonstrates that the statistical properties of localized states in a correlated monolayer follow exact symmetry relations predicted by nonlinear sigma-models, linking theory and experiment.

Findings

Multifractal analysis reveals symmetry relations in localized states.

The system follows algebraic symmetry structures of nonlinear sigma-models.

Potential for applying multifractal analysis to magneto-transport data.

Abstract

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 groundstate. 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 (NLsMs). 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.