Here, we predict the tetradymite-type compound MnBi2Te4 and its related materials host topologically nontrivial magnetic states. The magnetic ground state of MnBi2Te4 is an antiferromagetic topological insulator state with a large topologically non-trivial energy gap (0.2 eV). It presents the axion state, which has gapped bulk and surface states, and the quantized topological magnetoelectric effect. It has several advantages over the previous proposals on realizing the topological magnetoelectric effect. The intrinsic magnetic and band inversion further lead to quantum anomalous Hall effect in odd layer MnBi2Te4 thin film with combined inversion and time-reversal symmetry breaking.

The intrinsic magnetic topological states in MnBi2Te4 provides an ideal platform for studying the exotic physics of chiral Majorana fermion modes. In proximity to an s-wave superconductor with nontrivial band topology, an N=3 chiral topological superconductor is realized. A smoking gun signature of the Majorana nature of three chiral edge fermions is that the two-terminal electrical conductance of a quantized anomalous Hall-TSC junction obeys a unique distribution averaged to (2/3)e^2/h, which is due to the random edge mode mixing of chiral Majorana fermions and is distinguished from possible trivial explanations.

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