Fully self-consistent bulk-edge disorder embedding

Derive a coupled set of self-consistency equations that treats disorder in the bulk and consistently communicates its effects to the edge within the cluster coherent potential approximation for the disordered Kagome strip.

Background

The calculation considers a disordered chain in which gapless edge states result indirectly from disorder-induced changes in the bulk spectrum. The effective-medium description does not explicitly and self-consistently couple bulk and edge disorder effects.

A complete treatment would require coupled self-consistency equations linking the bulk and edge sectors. The paper identifies this as a concrete unresolved extension, noting that its computational cost would be substantially higher than that of the present framework.

References

A fully self-consistent treatment would require deriving a coupled set of self-consistency equations that capture the effects of disorder in the bulk and consistently communicate these modifications to the edge. Although this extension is, in principle, a natural generalization of the present framework, it is computationally significantly more demanding. We leave this analysis for future work

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