Sheng D N, Weng Z Y, Sheng L, Haldane F D M
Department of Physics and Astronomy, California State University, Northridge, California 91330, USA.
Phys Rev Lett. 2006 Jul 21;97(3):036808. doi: 10.1103/PhysRevLett.97.036808.
We present a topological description of the quantum spin-Hall effect (QSHE) in a two-dimensional electron system on a honeycomb lattice with both intrinsic and Rashba spin-orbit couplings. We show that the topology of the band insulator can be characterized by a 2 x 2 matrix of first Chern integers. The nontrivial QSHE phase is identified by the nonzero diagonal matrix elements of the Chern number matrix (CNM). A spin Chern number is derived from the CNM, which is conserved in the presence of finite disorder scattering and spin nonconserving Rashba coupling. By using the Laughlin gedanken experiment, we numerically calculate the spin polarization and spin transfer rate of the conducting edge states and determine a phase diagram for the QSHE.
我们给出了在具有本征和Rashba自旋轨道耦合的蜂窝晶格二维电子系统中量子自旋霍尔效应（QSHE）的拓扑描述。我们表明，带绝缘体的拓扑结构可以由一个2×2的第一陈数矩阵来表征。非平凡的QSHE相由陈数矩阵（CNM）的非零对角矩阵元来确定。从CNM导出一个自旋陈数，在存在有限无序散射和自旋非守恒Rashba耦合的情况下，该自旋陈数是守恒的。通过使用劳克林思想实验，我们数值计算了导电边缘态的自旋极化和自旋转移率，并确定了QSHE的相图。
