Edge states and the integer quantum Hall conductance in spin-chiral ferromagnetic kagomé lattice
Edge states and the integer quantum Hall conductance in spin-chiral ferromagnetic kagomé lattice
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DOI：
10.1103/physrevb.77.125119
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发表时间：
2007-11
影响因子：
3.7
通讯作者：
Zhigang Wang;Ping Zhang
中科院分区：
文献类型：
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作者：
Zhigang Wang;Ping Zhang
我们研究了包含自旋各向异性的二维铁磁 kagom\'{e} 晶格中的手性边缘态。该系统在 $x$ 方向上是周期性的，但在 $y$ 方向上有两个边缘。推导了求解边缘态能量的哈珀方程。我们发现每个体能隙中有两个边缘态，对应于复能量黎曼曲面（RS）上布洛赫函数的两个零点。由动量 $k_{x}$ 参数化的边缘状态能量环穿过 RS 的孔。当费米能量位于体能隙中时，量子化霍尔电导由穿过孔的边缘态的缠绕数给出，其读作 $\sigma_{xy}^{\text{edge}}$=$-\frac{e^{2}}{h}% $sgn$(\sin\phi) $，其中 $\phi$ 是自旋手性参数（参见文本）。该结果与基于拓扑体理论的结果一致。
We investigate the chiral edge states in the two-dimensional ferromagntic kagom\'{e} lattice with spin anisotropies included. The system is periodic in the $x$ direction but has two edges in the $y$ direction. The Harper equation for solving the energies of edge states is derived. We find that there are two edge states in each bulk energy gap, corresponding to two zero points of the Bloch function on the complex-energy Riemann surface (RS). The edge-state energy loops parametrized by the momentum $k_{x}$ cross the holes of the RS. When the Fermi energy lies in the bulk energy gap, the quantized Hall conductance is given by the winding number of the edge states across the holes, which reads as $\sigma_{xy}^{\text{edge}}$=$-\frac{e^{2}}{h}% $sgn$(\sin\phi) $, where $\phi$ is the spin chiral parameter (see text). This result keeps consistent with that based on the topological bulk theory.