Executive Summary : | Topological protection is an important feature that can be implemented for fault-tolerant quantum computation and information technology. Topology is long desired in the magnetic systems so that the applications of the colossal magnetoresistance (CMR) and spintronic can be made robust and protected from decoherence and decay. Skyrmions bring in the topology in the magnetism matrix, and promise a better substitute for racetrack memory, spin-based quantum technology, and quantum computing. The skyrmions' present research status is that only a specific type of skyrmion is realizable so far; the existing skyrmions are much smaller in size than what is required to achieve topological hardiness; and the tunability and materials flexibility to read and write skyrmions is lacking. These issues are mainly rooted in the fact that skyrmions solutions are studied so far only in three-dimensional (3D) magnetic materials. By taking full advantage of the newly discovered 2D Van der Waals (VdW) magnets, we propose to initiate the quest for novel twisted Moiré magnetic bilayers (a superlattice structure of the twisted bilayer geometry). We will theoretically investigate various engineered geometries and heterostructures of 2D magnetic layers without and with relative twists and strain between the layers. Our focus will be to take full advantage of the twisted magnets' exclusivity and unprecedented tunability to breed and control different types of skyrmions and related topological structures of spins. Since a skyrmion can be as large as a Moiré supercell's size, we can easily achieve large-sized skyrmions by controlling twist angle, strain, among other parameters. Moiré supercell has much fewer crystalline symmetries than bulk systems, and the number of nearest neighbors increases with decreasing twist angle. These features help strengthen long-range magnetic interactions than their bulk materials' values, thereby helping stabilize many new and topologically distinct skyrmions within the same system. Skyrmion charge fractionalizes near a phase transition between two distinct non-trivial topological phases. However, since so far only a single type of skyrmion is attained in a given material, such fractional skyrmion charges have not been obtained both theoretically and experimentally. The Moiré platform can host multiple skyrmions phases as a function of twist angle, strain, interaction etc., and hence give a unique opportunity to obtain fractional skyrmion charge. Similarly, the coexistence of skyrmion and anti-skyrmions can render topological dipole and higher-order moments, and properties such as BTK transition can then be studied for the first time in the skyrmion field. The layer-by-layer mechanism in 2D magnets can be utilized to generate coupling between skyrmions and various quasiparticles, and thus the topological protection, localization/delocalization of Majorana, and other exotic quasiparticles can be achieved within the skyrmion matrix. |