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We propose a novel platform to realize highly-tunable, frustrated Hubbardphysics with topological order in multi-layer moire structures. Identifying alayer degree of freedom as a pseudo spin, allows us to retain SU(2) symmetry,while controlling ring exchange processes and concurrently quenching thekinetic energy by large external magnetic fields. This way, a broad class ofinteracting Hofstadter states and their transitions can be studied. Remarkably,in the limit of strong interactions the system becomes Mott insulating and wefind exceptionally stable spin liquid phases which are induced by the magneticfield. As the magnetic flux can be easily tuned in moire systems, our approachprovides a promising route towards the experimental realization and control oftopologically ordered phases of matter. We also discuss how layer pseudo-spincan be probed in near-term experiments

Tunable topological order of pseudo spins in semiconductor heterostructures