Metal-Insulator Quantum Phase Transitons: From Fundamental Challenges to Modern Developments

Metals and Insulators are reasonably well understood, but very different states of matter. Most interesting materials, however, are obtaining by introducing a few carriers in insulators, and the action often takes place in the metal-insulator transition region. Here, the electrons move slowly as they barely conduct, and they interact strongly, displaying unfamiliar quantum dynamics that are difficult to understand. In this talk, we shall give an overview of the key physical concepts that describe this regime, and discuss modern theoretical methods that prove capable to capture many of the puzzling phenomena. Examples will be given of several new experimental platforms, ranging from two-dimensional electron liquids in semiconductors to organic molecular solids, and the recently discovered “moiré” bilayer devices. In all these systems, narrow electronic bands can be engineered and fine-tuned to access the strong-coupling regime, revealing remarkable universality across the metal-insulator quantum critical region. These discoveries suggest that soon we’ll be able to design and fabricate “materials by design”, with properties that can be hand-tailored to the needs of modern quantum information technology.