A Dirac-fermion approach and its application to design high Chern numbers in magnetic topological insulator multilayers

Quantum anomalous Hall (QAH) insulators host topologically protected dissipationless chiral edge states, the number of which is determined by its Chern number. Up to now, the QAH state has been realized in a few magnetic topological insulators, but usually with a low Chern number. Here, we develop a Dirac-fermion approach which is valuable to understand and design high Chern numbers in various multilayers of layered magnetic topological insulators. Based on the Dirac-fermion approach, we demonstrate how to understand and tune high Chern numbers in ferromagentic MnBi$_{2}$Te$_{4}$ films through the van der Waals (vdW) gap modulation. Further, we also employ the Dirac-fermion approach to understand the experimentally observed high Chern numbers and topological phase transition from the Chern number $C=2$ to $C=1$ in the [3QL-(Bi,Sb)$_{1.76}$Cr$_{0.24}$Te$_{3}$]/[4QL-(Bi,Sb)$_{2}$Te$_{3}$] multilayers. Our work provides a powerful tool to design the QAH states with a high Chern number in layered magnetic topological insulator multilayers.Comment: 11 pages, 4 figure

Floquet engineering of magnetic topological insulator MnBi2_2Te4_4 films

Floquet engineering is an important way to manipulate the electronic states of condensed matter physics. Recently, the discovery of the magnetic topological insulator MnBi$_2$Te$_4$ and its family provided a valuable platform to study magnetic topological phenomena, such as, the quantum anomalous Hall effect, the axion insulator state and the topological magnetoelectric effect. In this work, based on the effective model and first-principles calculations in combination with the Floquet theory, we reveal that the circularly polarized light (CPL) induces the sign reversal of the Chern number of odd-septuple-layer (SL) MnBi$_2$Te$_4$ thin films. In contrast, the CPL drives the axion insulator state into the quantum anomalous Hall state in even-SL MnBi$_2$Te$_4$ thin films. More interestingly, if the topmost van der Waals gap between the surface layer and the below bulk in MnBi$_2$Te$_4$ films is slightly expanded, a high Chern number $|C|=2$ can be realized under the CPL. Our work demonstrates that the light can induce rich magnetic topological phases in MnBi$_2$Te$_4$ films, which might have potential applications in optoelectronic devices.Comment: 7 pages, 4 figure

Frequency-domain criterion on the stabilizability for infinite-dimensional linear control systems

A quantitative frequency-domain condition related to the exponential stabilizability for infinite-dimensional linear control systems is presented. It is proven that this condition is necessary and sufficient for the stabilizability of special systems, while it is a necessary condition for the stabilizability in general. Applications are provided.Comment: 26 Page

Tunable dynamical magnetoelectric effect in antiferromagnetic topological insulator MnBi2_2Te4_4 films

More than forty years ago, axion was postulated as an elementary particle with a low mass and weak interaction in particle physics to solve the strong $\mathcal{CP}$ (charge conjugation and parity) puzzle. Axions are also considered as a possible component of dark matter of the universe. However, the existence of axions in nature has not been confirmed. Interestingly, axions arise as pseudoscalar fields derived from the Chern-Simons theory in condensed matter physics. In antiferromagnetic insulators, the axion field can become dynamical induced by spin-wave excitations and exhibits rich exotic phenomena, such as, the chiral magnetic effect, axionic polariton and so on. However, the study of the dynamical axion field is rare due to the lack of real materials. Recently, MnBi$_2$Te$_4$ was discovered to be an antiferromagnetic topological insulator with a quantized axion field protected by the inversion symmetry $\mathcal{P}$ and the magnetic-crystalline symmetry $\mathcal{S}$. Here, we studied MnBi$_2$Te$_4$ films in which both the $\mathcal{P}$ and $\mathcal{S}$ symmetries are spontaneously broken and found that the dynamical axion field and largely tunable dynamical magnetoelectric effects can be realized through tuning the thickness of MnBi$_2$Te$_4$ films, the temperature and the element substitution. Our results open a broad avenue to study axion dynamics in antiferromagnetic topological insulator MnBi$_2$Te$_4$ and related materials, and also is hopeful to promote the research of dark matter.Comment: 6 pages, 4 figure