论文标题
电子光谱拓扑和巨大密度在立方格
Electron Spectrum Topology and Giant Density-of-States Singularities in Cubic Lattices
论文作者
论文摘要
在互相空间中的同盟式表面的简单（SC），以身体为中心（BCC）和以面部为中心的（FCC）立方晶格的拓扑结构，考虑到最近和下一个邻居$ t $ t $和$ t'$之间的转移积分，以紧密结合的近似值进行了详细研究。结果表明，对于值$τ= t'/t =τ_\ ast $，对应于$ \ mathbf k $ -van hove点的表面，线和表面拓扑的变化。由于$τ$与这些单数值的微小偏差，因此在几个van Hove点附近，Van Hove Line（表面）附近的频谱被对$ \ Mathbf k $的依赖弱取代，这些货车点具有与$ | | | | | | | | | | wist-themt | ast |^ast |^{-1} $成比例的巨大质量。考虑了对特殊$τ$值附近状态密度的奇异贡献；根据椭圆积分获得的状态密度的分析表达式。结果表明，在许多情况下，以对应于Brillouin区域边缘上的$ \ Mathbf {K} $的能量，达到状态密度的最大值，而是在高度对称的方向上的内部点。特别是将对电子和磁性特性的相应贡献用于弱磁磁体。
The topology of isoenergetic surfaces in reciprocal space for simple (sc), body-centered (bcc), and face-centered (fcc) cubic lattices is investigated in detail in the tight-binding approximation, taking into account the transfer integrals between the nearest and next neighbors $t$ and $t'$. It is shown that, for values $τ= t'/t = τ_\ast$ corresponding to a change in the topology of surfaces, lines and surfaces of $\mathbf k$-van Hove points can be formed. With a small deviation of $τ$ from these singular values, the spectrum in the vicinity of the van Hove line (surface) is replaced by a weak dependence on $\mathbf k$ in the vicinity of several van Hove points that have a giant mass proportional to $|τ- τ_ \ast|^{-1}$. Singular contributions to the density of states near peculiar $τ$ values are considered; analytical expressions for the density of states being obtained in terms of elliptic integrals. It is shown that in a number of cases the maximum value of the density of states is achieved at energies corresponding not to $\mathbf{k}$-points on the Brillouin zone edges, but to its internal points in highly symmetrical directions. The corresponding contributions to electron and magnetic properties are treated, in particular, in application to weak itinerant magnets.
