二次带交叉点的拓扑相变中的Kibble-Zurek行为

Kibble-Zurek (KZ)机制描述了在驱动系统穿越连续对称性破缺相变时的尺度行为。先前的研究表明，KZ类尺度行为也存在于Qi-Wu-Zhang模型（二维）和Su-Schrieffer-Heeger模型（一维）中的拓扑相变中，尽管此类模型中不存在对称性破缺。两种模型均包含线性带交叉，给出 $\nu=1$ 和 $z=1$。我们 conjectures whether different critical exponents can be acquired in topological transitions beyond linear band crossing. In this work, we look into the KZ behavior in a topological 2D checkerboard lattice with a quadratic band crossing. We investigate from dual perspectives: momentum distribution of the Berry curvature in clean systems for simplicity, and real-space analysis of domain-like local Chern marker configurations in disordered systems, which is a more intuitive analog to conventional KZ description. In equilibrium, we find the correlation length diverges with a power $\nu\simeq 1/2$. Then, by slowly quenching the system across the topological phase transition, we find that the freeze-out time $t_\mathrm{f}$ and the unfrozen length scale $\xi(t_\mathrm{f})$ both satisfy the KZ scaling, verifying $z\simeq 2$. We subsequently explore KZ behavior in topological phase transitions with other higher-order band crossing and find the relationship between the critical exponents and the order. Our results extend the understanding of the KZ mechanism and non-equilibrium topological phase transitions.