Anderson Localization in a Two-Dimensional Metal

Anderson localization is anticipated to play a pivotal role in the manifestation of superconducting phases, optimal thermoelectric properties, and the quantum anomalous Hall effect. Dimensionality plays a central role in the physics of Anderson localization. Previous studies of localization in 2D conductors have relied on thin metallic films produced by vapor deposition, but challenges such as domain size effects, grain boundaries, and strain continue to complicate interpretation. Here, we overcome these challenges by investigating localization physics in Pd_{5}AlI_{2}, a van der Waals metal that can be exfoliated to the 2D limit. Using scanning tunneling spectroscopy, we demonstrate Anderson localization of electrons in monolayer Pd_{5}AlI_{2} from the presence of a Coulomb gap at the Fermi level and a unique density of state distribution characteristic of wave function localization. Moreover, we show evidence of phonon localization in Pd_{5}AlI_{2} from the layer-dependent broadening and softening of phonon modes. These signatures of electron and phonon localization, absent in multilayer samples, provide spectroscopic evidence for the theoretical predictions that localization is enhanced at reduced dimensionality.