Unconventional long-range interaction in Twisted Bilayer Graphene.

Twistronics with incommensurate twist angles has attracted interest because of its controllability and the peculiar effects of aperiodic structures on electronic states. Most theoretical studies on correlated phenomena, such as superconductivity and magnetism, have focused on short-range interactions, leaving long-range correlations unaddressed. In this letter, we explore the anomalous long-range interactions that arise from the unique electronic states in incommensurately twisted multilayer systems. By examining the static susceptibility between widely separated electrons in a 30-degree twisted bilayer graphene, we show that strong quasiperiodicity-resulting from strong interlayer hopping relative to intralayer hopping-can significantly amplify the interaction strength even at large distances. These enhanced interactions could enable the manipulation of stable quantum entanglement over long distances. Our findings open avenues for controlling strong correlation phenomena driven by these long-range interactions in twisted multilayer systems.