论文标题
非亚伯kagome lattice中的平板乐队和$ z_2 $拓扑阶段
Flat bands and $Z_2$ topological phases in a non-Abelian kagome lattice
论文作者
论文摘要
我们介绍了一个非亚伯kagome晶格模型，该模型具有时间反转和反转对称性，并研究了该模型的平坦带物理和拓扑阶段。由于时间逆转和反转对称性的共存，能量频段由三个双重变性带组成，它们的能量和存在平坦带的能量和条件可以分析获得，从而使我们能够将平面带与其他两个分散带，从中间和底部的三个频段的顶部到底部。我们进一步研究了模型的间隙阶段，并表明它们属于相同的阶段，与频带差距仅在参数空间的离散点接近，使任何两个间隙阶段绝热地相互连接而无需缩小频带间隙。我们根据反转对称性的时间反转对称和平均表征使用PFAFFIAN方法，我们计算了批量的拓扑不变式，并证明了唯一的间隙阶段属于$ Z_2 $ Quantum Spin Hall阶段，这是边缘状态计算进一步证实的。
We introduce a non-Abelian kagome lattice model that has both time-reversal and inversion symmetries and study the flat band physics and topological phases of this model. Due to the coexistence of both time-reversal and inversion symmetries, the energy bands consist of three doubly degenerate bands whose energy and conditions for the presence of flat bands could be obtained analytically, allowing us to tune the flat band with respect to the other two dispersive bands from the top to the middle and then to the bottom of the three bands. We further study the gapped phases of the model and show that they belong to the same phase as the band gaps only close at discrete points of the parameter space, making any two gapped phases adiabatically connected to each other without closing the band gap. Using the Pfaffian approach based on the time-reversal symmetry and parity characterization from the inversion symmetry, we calculate the bulk topological invariants and demonstrate that the unique gapped phases belong to the $Z_2$ quantum spin Hall phase, which is further confirmed by the edge state calculations.
