Quasiperiodic potential induced corner states in a quadrupolar insulator

TL;DR

This paper explores how quasiperiodic disorder can induce and affect topological corner states in a quadrupolar insulator, revealing disorder-driven topological phases and multifractal localization transitions.

Contribution

It demonstrates that quasiperiodic disorder can induce topological phases in a quadrupolar insulator and analyzes the localization properties of the resulting states.

Findings

Disorder induces a topological phase with zero energy states and non-zero quadrupole moment.

In-gap states become multifractal at the topological transition.

Quasiperiodic disorder affects the localization and topological properties of the system.

Abstract

We systematically investigate the topological and localization properties of a quadrupolar insulator represented by the celebrated Benalcazar-Bernevig-Hughes model in presence of a quasiperiodic 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 bandstructure together with a non-zero 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 mid-band 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 quasiperiodic 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.