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Chern insulators are two-dimensional magnetic topological materials that conduct electricity along their edges via the one-dimensional chiral modes. The number of these modes is a topological invariant called the first Chern number $C$, that defines the quantized Hall conductance as $S_{xy}= C e^2/h$. Increasing $C$ is pivotal for the realization of low-power-consumption topological electronics, but there has been no clear-cut solution of this problem so far, with the majority of existing Chern insulators showing $C=1$. Here, by using state-of-the-art theoretical methods, we propose an efficient approach for the realization of the high-$C$ Chern insulator state in MnBi$_2$Te$_4$/hBN van der Waals multilayer heterostructures. We show that a stack of $n$ MnBi$_2$Te$_4$ films with $C=1$ intercalated by hBN monolayers gives rise to a high Chern number state with $C=n$, characterized by $n$ chiral edge modes. This state can be achieved both under the external magnetic field and without it, both cases leading to the quantized Hall conductance $S_{xy}= C e^2/h$. Our results therefore pave way to practical high-$C$ quantized Hall systems., Comment: 10 pages, 5 figures

Using density functional theory and Monte Carlo calculations, we study the thickness dependence of the magnetic and electronic properties of a van der Waals interlayer antiferromagnet in the two-dimensional limit. Considering $\mathrm{MnBi_2Te_4}$ as a model material, we find it to demonstrate a remarkable set of thickness-dependent magnetic and topological transitions. While a single septuple layer block of $\mathrm{MnBi_2Te_4}$ is a topologically trivial ferromagnet, the thicker films made of an odd (even) number of blocks are uncompensated (compensated) interlayer antiferromagnets, which show wide bandgap quantum anomalous Hall (zero plateau quantum anomalous Hall) states. Thus, $\mathrm{MnBi_2Te_4}$ is the first stoichiometric material predicted to realize the zero plateau quantum anomalous Hall state intrinsically. This state has been theoretically shown to host the exotic axion insulator phase.

An interplay of spin-orbit coupling and intrinsic magnetism is known to give rise to the quantum anomalous Hall and topological magnetoelectric effects under certain conditions. Their realization could open access to low power consumption electronics as well as many fundamental phenomena like image magnetic monopoles, Majorana fermions and others. Unfortunately, being realized very recently, these effects are only accessible at extremely low temperatures and the lack of appropriate materials that would enable the temperature increase is a most severe challenge. Here, we propose a novel material platform with unique combination of properties making it perfectly suitable for the realization of both effects at elevated temperatures. The key element of the computational material design is an extension of a topological insulator (TI) surface by a thin film of ferromagnetic insulator, which is both structurally and compositionally compatible with the TI. Following this proposal we suggest a variety of specific systems and discuss their numerous advantages, in particular wide band gaps with the Fermi level located in the gap., Comment: The version of the article accepted for publication including all changes made as a result of the peer review process

Despite immense advances in the field of topological materials, the antiferromagnetic topological insulator (AFMTI) state, predicted in 2010, has been resisting experimental observation up to now. Here, using density functional theory and Monte Carlo method we predict and by means of structural, transport, magnetic, and angle-resolved photoemission spectroscopy measurements confirm for the first time realization of the AFMTI phase, that is hosted by the van der Waals layered compound MnBi$_2$Te$_4$. An interlayer AFM ordering makes MnBi$_2$Te$_4$ invariant with respect to the combination of the time-reversal ($\Theta$) and primitive-lattice translation ($T_{1/2}$) symmetries, $S=\Theta T_{1/2}$, which gives rise to the $Z_2$ topological classification of AFM insulators, $Z_2$ being equal to 1 for this material. The $S$-breaking (0001) surface of MnBi$_2$Te$_4$ features a giant bandgap in the topological surface state thus representing an ideal platform for the observation of such long-sought phenomena as the quantized magnetoelectric coupling and intrinsic axion insulator state.