论文标题
k空间，几何阶段和$π$的偶然变性
Accidental Degeneracy in k-space, Geometrical Phase, and the Perturbation of $π$ by Spin-orbit Interactions
论文作者
论文摘要
由于{\ it意外}的封闭线被证明是有可能的，甚至是频繁的，即1937年的鲱鱼，因此八十年来没有进一步的发展。在真实材料中最早的报道（铝）进行了叙述和详细说明。节点循环半学已成为最近活动的重点，重点是其他问题。毕竟，归化性材料中的拓扑阶段的起源是晶体材料的起源。旋转轨道相互作用提高了意外的带归化，因此在此提供了所得的光谱。几何相$γ（C）= \pmπ$用于电路$ c $周围的这种退化，这完全没有变化。变化取决于在绝热进化过程中旋转的固定方式。对于沿着内部自旋轨道场固定的自旋，$γ（c）$降低到零，因为电路围绕着脱落的线倒塌。对于沿垂直轴固定的自旋，圆锥形的交点持续存在，$γ（c）= \pmπ$不变。
Since closed lines of {\it accidental} electronic degeneracies were demonstrated to be possible, even frequent, by Herring in 1937, no further developments arose for eight decades. The earliest report of such a nodal loop in a real material -- aluminum -- is recounted and elaborated on. Nodal loop semimetals have become a focus of recent activity, with emphasis on other issues. Band degeneracies are, after all, the origin of topological phases in crystalline materials. Spin-orbit interaction lifts accidental band degeneracies, with the resulting spectrum being provided here. The geometric phase $γ(C)=\pmπ$ for circuits $C$ surrounding a line of such degeneracy cannot survive completely unchanged. The change depends on how the spin is fixed during adiabatic evolution. For spin fixed along the internal spin-orbit field, $γ(C)$ decreases to zero as the circuit collapses around the line of lifted degeneracy. For spin fixed along a perpendicular axis, the conical intersection persists and $γ(C)=\pmπ$ is unchanged.
