We investigate the topological phase transitions driven by band warping and a transverse magnetic field, for three-dimensional Weyl semimetals. First, we use the Chern number as a mathematical tool to derive the topological phase diagram. Next, we associate each of the topological sectors to a given angular momentum state of a rotating wave packet. Then we show how the position of the Weyl nodes can be manipulated by a transverse external magnetic field that ultimately quenches the wave packet rotation, first partially and then completely, thus resulting in a sequence of field-induced topological phase transitions. Finally, we calculate the current-induced magnetization and the anomalous Hall conductivity of a prototypical warped Weyl material. Both observables reflect the topological transitions associated with the wave packet rotation and can help to identify the elusive 3D quantum anomalous Hall effect in three-dimensional, warped Weyl materials.
Bulk-edge correspondence in two-dimensional topological semimetals: A transfer matrix study of antichiral edge modes
我们研究拓扑半金属中的边模，它具有普通半金属的能带结构，但可以用陈数来表征。更具体地说，我们专注于Qi-Wu-Zhang型正方形晶格模型和Haldane型蜂窝模型，这两种模型都表现出反手征边缘模式，其波包在条带的两个平行边缘沿相同方向传播。为了获得边缘模式的这些解析解，我们应用了在先前工作中开发的传递矩阵方法[Phys. Rev. B \textbf{101}，014442（2020）]。其结果是，我们表明，散装边缘对应被打破了一定范围内的模型参数。更准确地说，当增加的强度的跳跃振幅的Qi-Wu-Zhang型模型，边缘模式突然消失，虽然非平凡的陈数没有改变。在Haldane型模型中，改变模型参数，边缘模不一定消失，非平凡的陈数也不改变。然而，从价带到导带的边缘模的能谱流在一定的模型参数下突然中断。
