Effects of disorder on Thouless pumping in higher-order topological insulators

Abstract

We investigate the effects of random onsite disorder on higher-order Thouless pumping of noninteracting fermionic Benalcazar--Bernevig--Hughes (BBH) model. The interplay of disorder-induced topological phase transition and delocalization-localization transition is extensively explored. The higher-order Thouless pumping is characterized by the quantized corner-to-corner charge transport and nonzero Chern number, and the delocalization-localization transition is analyzed by utilizing both inverse participation ratio and finite-size scaling. The results show that the quantized corner-to-corner charge transport is broken for the strong disorder, where the instantaneous bulk energy gap is closed. Although the instantaneous eigenstates are localized for the weak disorder, the charge transport remains quantized. This is attributed to delocalized Floquet states caused by the periodic driving. Furthermore, the phase transition from the quantized charge transport to topologically trivial pumping is accompanied by the disorder-induced delocalization-localization transition of Floquet states.