Keywords: 
• Weyl半金属 /
• Axion绝缘体 /
• Slater绝缘体 /
• 铁电金属

Abstract: The spin-orbit coupling (SOC) in the 5d transition metal element is expected to be strong due to the large atomic number and ability to modify the electronic structure drastically. On the other hand, the Coulomb interaction in 5d transition is non-negligible. Hence, the interplay of electron correlations and strong spin-orbit interactions make the 5d transition metal oxides (TMOs) specially interesting for possible novel properties. In this paper, we briefly summarize our theoretical studies on the 5d TMO. In section 2, we systematically discuss pyrochlore iridates. We find that magnetic moments at Ir sites form a non-colinear pattern with moment on a tetrahedron pointing to all-in or all-out from the center. We propose that pyrochlore iridates be Weyl Semimetal (WSM), thus providing a condensed-matter realization of Weyl fermion that obeys a two-component Dirac equation. We find that Weyl points are robust against perturbation and further reveal that WSM exhibits remarkable topological properties manifested by surface states in the form of Fermi arcs, which is impossible to realize in purely two-dimensional band structures. In section 3, based on density functional calculation, we predict that spinel osmates (AOs2O4, A = Ca, Sr) show a large magnetoelectric coupling characteristic of axion electrodynamics. They show ferromagnetic order in a reasonable range of the on-site Coulomb correlation U and exotic electronic properties, in particular, a large magnetoelectric coupling characteristic of axion electrodynamics. Depending on U , other electronic phases including a 3D WSM and Mott insulator are also shown to occur. In section 4, we comprehensively discuss the electronic and magnetic properties of Slater insulator NaOsO3, and successfully predict the magnetic ground state configuration of this compound. Its ground state is of a G-type antiferromagnet, and it is the combined effect of U and magnetic configuration that results in the insulating behavior of NaOsO3 We also discuss the novel properties of LiOsO3, and suggest that the highly anisotropic screening and the local dipole-dipole interactions are the two most important keys to forming LiOsO3-type metallic ferroelectricity in section 5. Using density-functional calculations, we systematically study the origin of the metallic ferroelectricity in LiOsO3. We confirm that the ferroelectric transition in this compound is order-disorder-like. By doing electron screening analysis, we unambiguously demonstrate that the long-range ferroelectric order in LiOsO3 results from the incomplete screening of the dipole-dipole interaction along the nearest-neighboring Li-Li chain direction.