Tunable topological order of pseudo spins in semiconductor heterostructures

In this talk we discuss how frustrated Hubbard models can be realized in multi-layer moire structures. By identifying a synthetic layer spin degree of freedom, we can retain SU(2) symmetry, while controlling ring exchange processes with large external magnetic fields. This way, we can investigate various interacting Hofstadter states and their transitions. Remarkably, once the system turns Mott insulating we find exceptionally stable spin liquid phases which are induced by the magnetic field. As such fields are easily tunable in moire systems, our platform provides a promising route for inducing and controlling topologically ordered phases of matter.