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Based on first-principles calculations and symmetry analysis, we propose that EuIn$_2$As$_2$ is a long awaited axion insulator with antiferromagnetic (AFM) long range order. Characterized by the parity-based invariant $\mathbb Z_4=2$, the topological magneto-electric effect is quantized with $\theta=\pi$ in the bulk, with a band gap as large as 0.1 eV. When the staggered magnetic moment of the AFM phase is along $a/b$ axis, it's also a TCI phase. Gapless surface states emerge on (100), (010) and (001) surfaces, protected by mirror symmetries (nonzero mirror Chern numbers). When the magnetic moment is along $c$ axis, the (100) and (001) surfaces are gapped. As a consequence of a high-order topological insulator with $\mathbb Z_4=2$, the one-dimensional (1D) chiral state can exist on the hinge between those gapped surfaces. We have calculated both the topological surface states and hinge state in different phases of the system, respectively, which can be detected by ARPES or STM experiments.

We present a prediction of the Dirac semimetal (DSM) phase in MgTa2N3 based on first-principles calculations and symmetry analysis. In this material, the Fermi level is located exactly at the Dirac point without additional Fermi surface pockets. The band inversion associated with the Dirac cone involves the d orbitals of two structurally inequivalent Ta atoms with octahedral and trigonal prismatic coordination spheres. We further show that the lattice symmetry breaking can realize topological phase transitions from the DSM phase to a triple nodal point semimetal, Weyl semimetal or topological insulator. The topologically protected surface states and the non-protected Fermi arc surface states are also studied., Comment: 4 figures, 11 pages

Electronic structures of carbides with the rocksalt structure were calculated by full potential electronic codes solving the Kohn-Sham equation. Bonding characters were analyzed by constructing tight-binding Hamiltonian based on maximally-localized Wannier functions. It was found that the cations in these compounds act as an electron provider and the frame is formed by the carbon atoms. The electronic states in the vicinity of the Fermi level are mainly from the p-orbitals of C. Pressure and doping are two efficient ways to tune the magnetic and electronic properties of these compounds. It turns out that a spin gapless semiconductor can be obtained by applying hydrostatic pressure up to tens of gigaPascal. Higher pressure induced an insulator to metal transition because of band broadening. Compounds of IA group (Na, K, Rb, Cs) were magnetic semiconductor at ambient conditions. Alloying with IIA elements decrease the magnetic moment according to the law of $3-x$, where $x$ is the relative atomic ratio of the IIA elements to the IA ones. The behaviors of the compounds under the pressure and the doping effects can be understood by a rigid band model., Comment: 10 Pages, 8 figures