Motivated by the very recent experimental realization of electronic Lieb lattices and research interest on topological states of matter, we study the topological phase transitions driven by Anderson-type disorder on spin-orbit coupled Lieb lattices in the presence of spin-independent and -dependent staggered potentials. By combining the recursive Green's-function and self-consistent Born approximation methods, we found that both time-reversal-invariant and time-reversal-symmetry-broken spin-orbit coupled Lieb lattice systems can host the disorder-induced gapful topological phases, including the quantum spin Hall insulator (QSHI) and quantum anomalous Hall insulator (QAHI) phases. For the time-reversal-invariant case, the disorder induces a topological phase transition directly from a normal insulator (NI) to the QSHI, while for the time-reversal-symmetry-broken case, the disorder can induce either a QAHI-QSHI phase transition or a NI-QAHI-QSHI phase transition, depending on the initial state of the system. Remarkably, the time-reversal-symmetry-broken QSHI phase can be induced by Anderson-type disorder on the spin-orbit coupled Lieb lattices without time-reversal symmetry.

中文翻译：

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Lieb晶格上无序诱导的拓扑相变

受电子李布（Lieb）晶格最近的实验实现以及对物质拓扑状态的研究兴趣的激励，我们研究了自旋轨道耦合李布（Lieb）晶格在自旋无关和相依交错存在的情况下，由安德森型紊乱驱动的拓扑相变潜力。通过结合递归格林函数和自洽的Born逼近方法，我们发现时间逆不变和时间逆对称破碎的自旋轨道耦合的Lieb晶格系统都可以容纳由疾病引起的空白拓扑阶段，包括量子自旋霍尔绝缘体（QSHI）和量子异常霍尔绝缘体（QAHI）相。对于时间反向不变的情况，该异常会直接导致从正常绝缘体（NI）到QSHI的拓扑相变，而对于时间反转对称中断的情况，根据系统的初始状态，该疾病会导致QAHI-QSHI相变或NI-QAHI-QSHI相变。值得注意的是，自旋轨道耦合的Lieb晶格上的安德森型无序可以诱导时间逆转对称性破裂的QSHI相位，而没有时间逆转对称性。