Competition and coupling effect between localized and iterant electrons in graphene moiré heterostructures

<p indent="0mm">Van der Waals heterostructures constructed from two-dimensional quantum materials exhibit rich emergent interfacial quantum states and excellent tunability of those physical properties. These materials not only provide a robust platform for exploring novel quantum states and their evolution but also offer a diverse material library for developing new principles in electronic device functionalities. This article introduces the electric transport studies in graphene-based moiré heterostructures performed by us in the past few years, extensively discussing the competition and coupling effects between itinerant and localized electrons. These effects influence the formation and evolution of new quantum states and offer new perspectives for designing advanced electronic devices. We achieved high-precision observations of the quantum melting process in electron crystals by <italic>in</italic>-<italic>situ</italic> tuning the coupling strength between itinerant and localized electrons. We observed novel quantum critical behaviors, including quantum two-stage criticality and quantum pseudo criticality, for the first time. These findings underscore the substantial potential of graphene moiré heterostructures in solid-state quantum simulations, especially for investigating the evolution of quantum critical behaviors. Furthermore, the coupling between layer-resolved itinerant and localized electrons can induce unconventional electronic-type ferroelectricity. The polarization intensity of this ferroelectricity exhibits quasi-continuous and precise control over multiple states that are crucial for high-precision neuromorphic computing. Notably, electronic-type ferroelectricity allows the coexistence of ferroelectricity and other quantum states such as Chern insulators, offering a unique platform for designing noise-immune neuromorphic computing and other new physical computing hardware.