Quasiperiodic potential induced corner states in a quadrupolar insulator

We systematically investigate the topological and localization properties of a quadrupolar insulator represented by the celebrated Benalcazar-Bernevig-Hughes model in the presence of quasiperiodic (QP) disorder instilled in its hopping amplitude. While disorder can be detrimental to the existence of the topological order in a system, we observe the emergence of a disorder-driven topological phase where the original (clean) system demonstrates trivial behavior. This phenomenon is confirmed by the re-emergence of zero-energy states in the band structure together with a nonzero bulk quadrupole moment, which in turn establishes the bulk-boundary correspondence (BBC). Furthermore, the distribution of the excess electronic charge shows a pattern that is reminiscent of the bulk quadrupole topology. To delve into the localization properties of the midband states, we compute the inverse participation and normalized participation ratios. It is observed that the in-gap states become critical (multifractal) at the point that discerns a transition from a topological localized to a trivial localized phase. Finally, we carry out a similar investigation to ascertain the effect of the QP disorder on the quadrupolar insulator when the model exhibits topological properties in the absence of disorder. Again, we note a multifractal behavior of the eigenstates in the vicinity of the transition.