Twisting van der Waals heterostructures to induce correlated many-body states provides a novel tuning mechanism in solid-state physics, launching the field of “twistronics.” In this talk, we apply twistronics to renormalize the Dirac cone on the surface of a 3D topological insulator, with the goal of realizing tunable interacting topological phases. To achieve this goal, we consider two different platforms: 1) twisted heterostructures in 2D and 3D; and 2) the effect of a moire superlattice potential. In all cases, we consider the renormalization of the non-interacting band structure, specifically, whether magic angles are possible and where van Hove singularities appear. Finally, we show that interactions drive a magnetic instability on the surface of a TI in the presence of a superlattice potential, resulting in a novel skyrmion lattice.

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