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

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