标题： 具有时间反演对称性破缺超导性的铀基化合物UTe$_2$的高阶拓扑相 显示英文标题

标题： Higher-order topological phases for time-reversal-symmetry breaking superconductivity in UTe$_2$

摘要： 重费米子超导体UTe$_2$的最新发现拓宽了实现奇异破时反演对称超导的可能性。然而，关于UTe$_2$超导态中的拓扑相的全面理解仍然缺乏。在这里，我们系统地分类了UTe$_2$所有可能破坏时间反演对称性的配对对称性的拓扑相。利用K理论分类方法，我们发现36种可能的配对态中有25种被归类为高阶拓扑相，其中一些通过铰链态和角态之间的复杂相互作用表现出混合阶拓扑性。 此外，在对偶势的弱耦合条件下，可能的配对对称性被限制为 $B_{ju} + i B_{ku}$, $A_{u} + i B_{j u}$, 和 $B_{j g} + iA_u$ ($j,k = 1,2,3$; $j \neq k$)，这些符号表示点群的不可约表示 $D_{2h}$。 对于这些配对态，拓扑不变量通过费米面公式与费米面拓扑相关联，使我们能够系统地诊断高阶拓扑相。 使用紧束缚模型，我们展示了混合奇偶性的 $A_u + iB_{1g}$ 超导体的高阶拓扑相，其中当包围时间反演不变动量的费米面数量从两个演变为四个时，二阶和混合阶拓扑相出现。 研究结果表明，UTe$_2$是探索具有多种拓扑表面态的高阶拓扑超导体的一个很有前景的平台。 显示英文摘要

摘要： The recent discovery of heavy-fermion superconductor UTe$_2$ has broadened the possibility of realizing exotic time-reversal-symmetry-breaking superconductivity. However, a comprehensive understanding of the topological phases in the superconducting states of UTe$_2$ is still lacking. Here, we present an exhaustive classification of topological phases for all time-reversal symmetry breaking pairing symmetries of UTe$_2$. Using the K theoretical classification approach, we uncover that 25 out of 36 possible pairing states are classified as higher-order topological phases, with some demonstrating hybrid-order topology through an intricate interplay of hinge and corner states. Furthermore, under the weak-coupling condition of the pair potentials, the possible pairing symmetries are constrained to $B_{ju} + i B_{ku}$, $A_{u} + i B_{j u}$, and $B_{j g} + iA_u$ ($j,k = 1,2,3$; $j \neq k$), where these symbols denote the irreducible representations of the point group $D_{2h}$. For these pairing states, the topological invariants are related to the Fermi surface topology via the Fermi-surface formula, enabling us to systematically diagnose higher-order topological phases. Using a tight-binding model, we demonstrate the higher-order topological phases of the mixed-parity $A_u + iB_{1g}$ superconductors, where the second-order and hybrid-order topological phases emerge as the number of Fermi surfaces enclosing the time-reversal invariant momentum evolves from two to four. The findings suggest that UTe$_2$ serves as a compelling platform for exploring higher-order topological superconductors with diverse topological surface states.