论文标题
二维$ z_2 $拓扑相变的系统研究在所有层组中的高对称点
Systematic study for two-dimensional $Z_2$ topological phase transitions at high-symmetry points in all layer groups
论文作者
论文摘要
我们构建了$ z_2 $拓扑相变的一般理论，并在二维系统中，具有时间反转对称性。我们研究了所有80层组中$ k $ - 空间中所有高对称点的$ z_2 $拓扑相变的可能性。我们排除具有反转对称性的层组，因为已知$ z_2 $拓扑相变与带有奇偶群交换的频段反转相关。在其他层组中，我们发现具有带有带反转的绝缘体到绝缘体过渡的21个层组，最终将此问题降低到五个分组$ C_3，C_4，C_6，C_6，S_4 $和$ C_ {3H} $。我们展示了在频段倒置上$ Z_2 $拓扑不变的变化完全由高对称点的占领和无人占用的频段的毫无疑问决定。例如，在$ c_3 $的情况下，我们表明$ z_2 $拓扑不变性在频段反转发生在两个kramers对之间的$ c_3 $ eigenvalues之间是$ \ {e^{πi / 3}，e^{^{πi / 3}这些结果不包括在基于对称的指标或拓扑量子化学理论中。
We construct a general theory of $Z_2$ topological phase transitions in two-dimensional systems with time-reversal symmetry. We investigate the possibilities of $Z_2$ topological phase transitions at band inversions at all high-symmetry points in $k$-space in all the 80 layer groups. We exclude the layer groups with inversion symmetry because the $Z_2$ topological phase transition is known to be associated with band inversions with an exchange of parities. Among the other layer groups, we find 21 layer groups with insulator-to-insulator transitions with band inversion, and this problem is finally reduced to five point groups $C_3, C_4, C_6, S_4$, and $C_{3h}$. We show how the change of the $Z_2$ topological invariant at a band inversion is entirely determined by the irreps of occupied and unoccupied bands at the high-symmetry point. For example, in the case of $C_3$, we show that the $Z_2$ topological invariants change whenever the band inversion occurs between two Kramers pairs whose $C_3$ eigenvalues are $\{e^{πi / 3}, e^{-πi / 3}\}$ and $\{-1, -1\}$. These results are not included in the theory of symmetry-based indicators or topological quantum chemistry.
