Kibble-Zurek behavior in a topological phase transition with a quadratic band crossing

Abstract

Kibble-Zurek (KZ) mechanism describes the scaling behavior when driving a system across a continuous symmetry-breaking transition. Previous studies have shown that the KZ-like scaling behavior also lies in the topological transitions in the Qi-Wu-Zhang model (2D) and the Su-Schrieffer-Heeger model (1D), although symmetry breaking does not exist here. Both models with linear band crossings give that $\nu =1$ and $z=1$. We wonder 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.

8 pages, 10 figures

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Cited by in corpus (3)

• Anti Kibble-Zurek behavior in the quantum XY spin-1/2 chain driven by correlated noisy magnetic field and anisotropy
• Tricritical Kibble-Zurek scaling in Rydberg atom ladders
• Quantum anomalous Hall domains in a Quenched Topological Mott Insulator