Twisted bilayers of thin film magnetic topological insulators

Twisted bilayer graphene (TBG) near ``magic angles'' has emerged as a rich platform for strongly correlated states of two-dimensional (2D) Dirac semimetals. Here we show that twisted bilayers of thin film magnetic topological insulators (MTIs) with large in-plane magnetization can realize flat bands near 2D Dirac nodes. Using a simple model for thin films of MTIs, we derive a continuum model for two such MTIs, twisted by a small angle with respect to each other. When the magnetization is in plane, we show that interlayer tunneling terms act as effective SU(2) vector potentials, which are known to lead to flat bands in TBG. We show that by changing the in-plane magnetization, it is possible to tune the twisted bilayer MTI band dispersion to quadratic band touching or to flat bands, similar to the TBG. If realized, this system can be a highly tunable platform for strongly correlated phases of two-dimensional Dirac semimetals.