论文标题
参数随机矩阵模型中Chern号的波动
Fluctuation of Chern Numbers in a Parametric Random Matrix Model
论文作者
论文摘要
Weyl半法中的带触摸weyl点产生了许多新颖的特征，其中一种具有拓扑保护的表面Fermi-Arc状态。此类状态的数量可以由Chern数量在不同动量切片上计算出来，这会随着动量的变化而波动，并取决于Brillouin区域中的Weyl点的分布。对于现实的系统，可能很难找到这些Weyl点和Fermi-Arc状态出现的动量。因此，我们扩展了Walker和Wilkinson提出的参数随机矩阵模型的分析，以找到其分布的统计数据。我们的数值数据表明，具有相反极性的Weyl点短距离相关，而Chern数量波动仅在有限动量差异之前线性增长。我们还发现，饱和值尺度具有带的总数。然后，我们从扰动理论计算出短距离相关长度，并得出Chern数量波动对动量差异的依赖性，表明饱和度来自短距离相关性。
Band-touching Weyl points in Weyl semimetals give rise to many novel characteristics, one of which the presence of surface Fermi-arc states that is topologically protected. The number of such states can be computed by the Chern numbers at different momentum slices, which fluctuates with changing momentum and depends on the distribution of Weyl points in the Brillouin zone. For realistic systems, it may be difficult to locate the momenta at which these Weyl points and Fermi-arc states appear. Therefore, we extend the analysis of a parametric random matrix model proposed by Walker and Wilkinson to find the statistics of their distributions. Our numerical data shows that Weyl points with opposite polarities are short range correlated, and the Chern number fluctuation only grows linearly for a limited momentum difference before it saturates. We also find that the saturation value scales with the total number of bands. We then compute the short-range correlation length from perturbation theory, and derive the dependence of the Chern number fluctuation on the momentum difference, showing that the saturation results from the short-range correlation.
