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Amorphous solids remain outside of the classification and systematic discovery of new topological materials, partially due to the lack of realistic models that are analytically tractable. Nevertheless, experiments have recently shown that topological surface states exist in amorphous systems.

We introduce the topological Weaire-Thorpe class of models, which are defined on amorphous lattices with fixed coordination number, a realistic feature of covalently bonded amorphous solids. Their symmetry under permutation of orbitals allows us to compute analytically topological phase diagrams by introducing symmetry indicators for the first time in amorphous systems.

Their lack of translational invariance complicates the interpretation of angular-resolved photoemission spectroscopy (ARPES) spectra. To understand these, we compute the spectral function of an amorphous system. Our results indicate that amorphous systems can display sharp ARPES spectra, allowing experiments to identify their topological nature, even in the absence of a well defined crystal momentum.

[1] Q. Marsal et al., arXiv:2003.13701 (2020).