中文摘要：

相比于3d和4d过渡金属元素,5d过渡金属元素既具有很强的自旋轨道耦合相互作用,同时它们的电子关联作用也不可忽略.因而5d过渡金属氧化物体系具有许多奇异的量子特性.这篇综述主要介绍我们在5d过渡金属氧化物中的一些理论进展.首先介绍烧绿石结构铱氧化物（A2Ir2O7,A=Y或稀土元素）中的Weyl拓扑半金属性.我们确定出A2Ir2O7这一类具有阻挫结构材料的磁基态,并预言其是Weyl半金属;其Weyl点受到拓扑保护而稳定,而且它的表面态在费米能级形成特别的费米弧.其次预言尖晶石结构锇氧化物（AOs2O4,A=Ca,Sr）是具有奇异磁电响应的Axion绝缘体;然后分析了电子关联、自旋轨道耦合对钙钛矿结构的锇氧化物（NaOsO3）的影响,并成功定出它的基态磁构型,最终确定其为Slater绝缘体.最后介绍了LiOsO3中铁电金属性的成因.

英文摘要：

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