Vol. 7, Issue 2, Part E (2025)

The synthesis of two-dimensional (2D) van der Waals (vdW) heterostructures has ushered in a new era of designer quantum matter, leveraging the geometric tunability of Moiré superlattices to stabilize novel electronic phases. This Roadmap reviews the convergence of topology and strong correlation in these systems, highlighting breakthroughs from 2024-2026. Research is focused on two primary domains: the observation and characterization of unconventional superconductivity (USC) in magic-angle graphene systems, evidenced by non-Bardeen-Cooper-Schrieffer (BCS) signatures and coexisting pseudogap phases [1], and the realization of topological phase transitions (TPTs) controlled by electrical gating and interlayer spacing in engineered heterostructures [3]. A critical evaluation identifies the ongoing challenges, notably the thermal limitations on achieving room-temperature topological gaps [5] and the complex theoretical task of modeling unconventional pairing mechanisms [6]. Finally, this report charts the future trajectory, emphasizing the necessity of advanced spectroscopic techniques, such as Spin-Resolved and Time-Resolved Angle-Resolved Photoemission Spectroscopy (Spin/TR-ARPES), and interdisciplinary theoretical approaches, such as Effective Field Theory, for solving the grand challenges of emergent quantum phenomena [7].