Phase transitions from two to three dimensions under confinement

Investigations into confined systems suggest a novel but not yet fully understood phase transition pathway from two-dimensional (2D) to three-dimensional (3D) space. This work aims to clarify this by studying simple elements confined within 2D graphene. Using crystal structure searches and molecular dynamics based on machine-learned potentials, achieving first-principles accuracy, we have identified new structures of confined noble gases and aluminum that deviate from close-packing arrangements. Upon heating, confined monolayer melts according to the two-step continuous Kosterlitz-Thouless-Halperin-Nelson-Young theory, while confined multilayer solids first transition continuously into an intermediate layered-hexatic phase before melting discontinuously into a liquid. The evolution of defects disrupting the system's order from 2D to 3D indicates a dimension-dependent melting scenario. Our findings offer new insights into the behavior of confined materials and help bridge the gap between 2D and 3D phase transitions.