Topological states of quantum matter have attracted great attention in condensed matter physics and materials science. The study of time-reversal-invariant topological states in quantum materials has made tremendous progress. However, the study of magnetic topological states falls much behind due to the complex magnetic structures. 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. The ferromagnetic phase of MnBi2Te4 might lead to a minimal ideal Weyl semimetal.

The dynamical axion field is a new state of quantum matter where the magnetoelectric response couples strongly to its low-energy magnetic fluctuations. It is fundamentally different from an axion insulator with a static quantized magnetoelectric response. The dynamical axion field exhibits many exotic phenomena such as axionic polariton and axion instability. However, these effects have not been experimentally confirmed due to the lack of proper topological magnetic materials. Combining analytic models and first-principles calculations, here we predict a series of van der Waals layered Mn2Bi2Te5-related topological antiferromagnetic materials that could host the long-sought dynamical axion field with a topological origin. We also show that a large dynamical axion field can be achieved in antiferromagnetic insulating states close to the topological phase transition. We further propose the optical and transport experiments to detect such a dynamical axion field. Our results could directly aid and facilitate the search for topological-origin large dynamical axion field in realistic materials.

Large unsaturated magnetoresistance (XMR) with magnitude ∼10 3 % is observed in topological insulator candidate TaSe 3 from our high field (up to 38 T) measurements.Two oscillation modes are detected associated with the bulk pockets from our Shubnikov-de Hass (SdH) measurements, consistent with our first-principles calculations. However, our SdH measurements fails to determine the existence of topological surface states in TaSe 3 , calling for more powerful means to detect on this compound. Moreover, our two-band model analysis exhibits that an imperfect density ratio / ≈ 0.9 accounts for XMR at T< 20 K. At T> 20 K, a sudden change of density of carriers suggests a reconstruction of the Fermi surface. Thus, TaSe 3 may provide an opportunity to allow us to observe XMR in a topological insulator and to exploit the potential interplay between the XMR and topological surface states for the first time.