Anderson transition symmetries at the band-edge of a correlated tin monolayer

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 Mott and antiferromagnetic behavior, as it undergoes a metal-insulator transition near a band edge. By analyzing spatial correlations of the local density of states (LDOS) using scanning tunneling spectroscopy, we precisely identify the mobility edge and determine its critical exponent as $\nu$ = 0.75 $\pm$ 0.1. We show that both the LDOS distribution functions and the multifractal spectra obey two exact symmetry relations, which are based on the Weyl group symmetry of nonlinear sigma-models. These symmetries hold across the entire transition, from extended to strongly localized states, in excellent agreement with theoretical predictions. Overall, using tunneling spectroscopy maps on a model tin monolayer in combination with numerical models, we connect the localization patterns of disordered electronic systems with their Hamiltonian symmetry class.