论文标题
三维狄拉克半学和广义量子旋转厅系统的拓扑
Topology of three-dimensional Dirac semimetals and generalized quantum spin Hall systems without gapless edge modes
论文作者
论文摘要
通常，量子旋转厅状态有望具有无间隙的螺旋边缘模式。是否有没有无间隙的边缘模式的干净，非相互作用的量子旋转大厅状态？我们显示了三维，稳定的Dirac半金属的通用，$ n $折叠的，动量平面，这与节点分离方向是正交的，是这种广义量子旋转厅系统的示例。我们证明了位于两个狄拉克点之间的飞机和著名的Bernevig-Zhang-Hughes模型支持相同量化的，非亚伯利亚浆果的数量级$2π$。因此，两个系统都响应电磁，$π$ -Flux Vortex，均表现出旋转电荷分离。狄拉克点被识别为$（5）$贝里连接的单位强度，单孔，描述了广义，量子自旋霍尔和琐碎的绝缘子之间的拓扑量子相变。我们的工作确定了狄拉克半法的精确散装和量化的响应，并表明许多二维高阶拓扑绝缘子可以理解为具有间隙边缘状态的广义量子旋转霍尔系统。
Usually the quantum spin Hall states are expected to possess gapless, helical edge modes. Are there clean, non-interacting, quantum spin Hall states without gapless, edge modes? We show the generic, $n$-fold-symmetric, momentum planes of three-dimensional, stable Dirac semi-metals, which are orthogonal to the direction of nodal separation are examples of such generalized quantum spin Hall systems. We demonstrate that the planes lying between two Dirac points and the celebrated Bernevig-Zhang-Hughes model support identical quantized, non-Abelian Berry flux of magnitude $2 π$. Consequently, both systems exhibit spin-charge separation in response to electromagnetic, $π$-flux vortex. The Dirac points are identified as the unit-strength, monopoles of $SO(5)$ Berry connection, describing topological quantum phase transitions between generalized, quantum spin Hall and trivial insulators. Our work identifies precise bulk invariant and quantized response of Dirac semimetals and shows that many two-dimensional higher-order topological insulators can be understood as generalized quantum spin Hall systems, possessing gapped edge states.
