Characterize HOTI topology under disorder

Determine whether the topology of higher-order topological insulators can be characterized in the presence of disorder.

Background

The paper motivates a scattering-theoretic framework for intrinsic higher-order topological phases, noting that protection of surface states in HOTIs arises from global spatial symmetries. Prior scattering invariants for strong topological insulators do not directly apply because HOTI surface states can be moved around and may be removed by changes to the termination, especially in extrinsic cases.

To motivate their approach, the authors explicitly pose two open questions. The first concerns whether HOTI topology can be characterized when disorder is present, given that disorder acts locally while protection relies on global symmetry, and that existing real-space invariants can be sensitive to the precise location of edge states.