The main subject of Klein’s research is the study of phenomena that occur in disordered systems. Impurities can change dramatically the properties of certain materials. The best known examples are transistors, which are made of certain materials whose properties are modified by impurities. Such materials are modeled by disordered systems.

Random Schrödinger operators describe an electron moving in a medium with random impurities. In the widely accepted picture, in three or more dimensions there exists a transition from an insulator region, characterized by localized states, to a very different metallic region, characterized by extended states, while in one or two dimensions there are only localized states and no metal-insulator transition. Klein’s research aims to further the mathematical understanding of this picture.