Topological origin of disorder-induced gapless states

Establish whether the disorder-induced gapless states in the disordered Kagome strip arise from a topologically non-trivial bulk, rather than solely from disorder-induced modifications of the bulk spectrum.

Background

The cluster coherent potential approximation produces gapless spectral weight enhanced near the strip edges when impurity concentration is increased. However, the calculation does not directly evaluate a bulk topological invariant for the corresponding two-dimensional disordered system.

Because edge-enhanced gapless spectral weight alone does not establish bulk topology, the topological character of the disorder-induced state remains unresolved. A bulk-invariant calculation is needed to determine whether the observed edge behavior represents a topological phase or a non-topological disorder-broadened gap closure.

References

The present calculation however, does not provide direct access to the bulk topological invariant of the corresponding two-dimensional system. The appearance of edge-enhanced gapless spectral weight should therefore not, by itself, be interpreted as evidence for a topological phase. In the absence of an explicit calculation of a bulk topological invariant, we cannot establish that the disorder-induced gapless states are the consequence of a topologically non-trivial bulk.

— Disorder-induced conducting edges on Kagomé lattice  (2608.24472 - Chmeruk et al., 25 Aug 2026) in Discussion and Outlook, Section 4