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Data from angle resolved photo-emission spectroscopy (ARPES) often serves asa smoking-gun evidence for the existence of topological materials. It providesthe energy dispersion curves of the topological boundary modes whichcharacterize these phases. Unfortunately this method requires a sufficientlyregular boundary such that these boundary modes remain sharp in momentum space.Here the seemingly random data obtained from performing ARPES on stronglydisordered topological insulators and Weyl semimetals is analyzed theoreticallyand numerically. Expectedly the disorder averaged ARPES spectra appearfeatureless. Surprisingly however, correlations in these spectra betweendifferent energies and momenta reveal delta-sharp features in momentum space.Measuring such correlations using nano-ARPES may verify the topological natureof the suggested weak topological insulator ($Bi_{14} Rh_3 I_9$) which thus farwas not studied using ARPES due to the rough nature of its metallic surfaces.

Sharp correlations in the ARPES spectra of strongly disordered topological boundary modes