Song Zhida, Fang Zhong, Fang Chen
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
University of Chinese Academy of Sciences, Beijing 100049, China.
Phys Rev Lett. 2017 Dec 15;119(24):246402. doi: 10.1103/PhysRevLett.119.246402. Epub 2017 Dec 11.
We study fourfold rotation-invariant gapped topological systems with time-reversal symmetry in two and three dimensions (d=2, 3). We show that in both cases nontrivial topology is manifested by the presence of the (d-2)-dimensional edge states, existing at a point in 2D or along a line in 3D. For fermion systems without interaction, the bulk topological invariants are given in terms of the Wannier centers of filled bands and can be readily calculated using a Fu-Kane-like formula when inversion symmetry is also present. The theory is extended to strongly interacting systems through the explicit construction of microscopic models having robust (d-2)-dimensional edge states.
我们研究了二维和三维（d = 2, 3）具有时间反演对称性的四重旋转不变带隙拓扑系统。我们表明，在这两种情况下，非平凡拓扑都由（d - 2）维边缘态的存在体现出来，这些边缘态存在于二维中的一个点或三维中的一条线上。对于无相互作用的费米子系统，体能带拓扑不变量由填充能带的万尼尔中心给出，并且当存在空间反演对称性时，可以使用类似傅 - 凯恩公式轻松计算。通过明确构建具有稳健的（d - 2）维边缘态的微观模型，该理论被扩展到强相互作用系统。
