Topological insulators (TIs) are an exciting discovery because of their robustness against disorder and interactions. Recently, second-order TIs have been attracting increasing attention, because they host topologically protected 1D hinge states in 3D or 0D corner states in 2D. A significantly critical issue is whether the second-order TIs also survive interactions, but it is still unexplored. We study the effects of weak Coulomb interactions on a 3D second-order TI, with the help of renormalization-group calculations. We find that the 3D second-order TIs are always unstable, suffering from two types of topological phase transitions. One is from second-order TI to TI, the other is to normal insulator. The first type is accompanied by emergent time-reversal and inversion symmetries and has a dynamical critical exponent $\kappa =1$. The second type does not have the emergent symmetries but has nonuniversal dynamical critical exponents $\kappa <1$. Our results may inspire more inspections on the stability of higher-order topological states of matter and related novel quantum criticalities.

中文翻译：

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三维高阶拓扑绝缘体的库仑不稳定性

拓扑绝缘体 (TI) 是一个令人兴奋的发现，因为它们对无序和相互作用具有鲁棒性。最近，二阶 TI 引起了越来越多的关注，因为它们在 3D 或 2D 的 0D 角状态中具有拓扑保护的一维铰链状态。一个非常关键的问题是二阶 TI 是否也能在相互作用中幸存下来，但它仍未得到探索。我们在重整化群计算的帮助下研究了弱库仑相互作用对 3D 二阶 TI 的影响。我们发现 3D 二阶 TI 总是不稳定的，存在两种类型的拓扑相变。一种是从二阶TI到TI，另一种是到普通绝缘体。第一种类型伴随着涌现的时间反转和反演对称性，并具有动态临界指数$\kappa =1$. 第二种类型不具有涌现对称性但具有非普遍动态临界指数$\kappa <1$. 我们的结果可能会激发对物质高阶拓扑状态稳定性和相关新量子临界性的更多检查。