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Motivated by the very recent experimental realization of electronic Lieblattices and research interest on topological states of matter, we study thetopological phase transitions driven by Anderson disorder on spin-orbit coupledLieb lattices in the presence of spin-independent and dependent potentials. Bycombining the numerical transport and self-consistent Born approximationmethods, we found that both time-reversal invariant and broken Lieb latticescan host disorder-induced gapful topological phases, including the quantum spinHall insulator (QSHI) and quantum anomalous Hall insulator (QAHI) phases. Forthe time-reversal invariant case, this disorder can induce a topological phasetransition directly from normal insulator (NI) to the QSHI. While for thetime-reversal broken case, the disorder can induce either a QAHI-QSHI phasetransition or a NI-QAHI-QSHI phase transition. Remarkably, the time-reversalbroken QSHI phase can be induced by Anderson disorder on the spin-orbit coupledLieb lattices without time-reversal symmetry.

Disorder-induced topological phase transitions on Lieb lattices