Magnetic moiré surface states and flat Chern bands in topological insulators

We propose the magnetic moir\'e surface states of topological insulators as a platform for time-reversal symmetry breaking flat Chern bands. We construct a generic continuum model of Dirac electrons with a single Dirac cone moving in a time-reversal symmetry breaking periodic potential containing minimal parameters. The Zeeman-type moir\'e potentials generically gap out the moir\'e surface Dirac cones and give rise to isolated flat Chern minibands with Chern number $\ifmmode\pm\else\textpm\fi{}1$. Interestingly, the bandwidth of such isolated flat minibands is insensitive to the twisting angle, which originates from the completely flat band of the $p$ orbitals on the honeycomb lattice. This result provides a promising platform for realizing time-reversal breaking correlated topological phases and circumvents two main experimental difficulties in correlated states with twisted graphene: that the bandwidth varies rapidly with angle as well as the moir\'e disorder. Furthermore, in a ${C}₆$ periodic potential, with the interplay of the scalar potential and the Zeeman moir\'e potential, the $\mathrm{\ensuremath{\Gamma}}$-valley moir\'e surface electrons simulate two-dimensional honeycomb lattice physics, leading to emergent moir\'e surface Dirac cones as well as the Haldane model.