Intertwined Topological Order in Moiré Materials

Spectacular experiments during the past year, first on twisted transition metal dichalcogenides and subsequently on multilayer graphene, have realized fractional Chern insulators (FCIs) in absence of magnetic fields.

While these are milestone discoveries, all states observed so-far have the same topological order as well established fractional quantum Hall counterparts forming in (nearly) continuum Landau levels at strong magnetic fields.

Here, by contrast, we aim to theoretically explore qualitatively new possibilities entailed by the underlying (super)lattice structure and the exquisite tunability of moiré materials.

Employing a mix of analytical and numerical approaches ranging from topological field theory and quantum geometry to entanglement probes and exact diagonalization, we will focus on intertwined topological order forming in FCIs in moiré bands with higher Chern numbers, fractional Hall crystals and topological lattice defects.