Establishing coherent momentum-space electronic states in locally ordered materials.

Rich momentum-dependent electronic structure naturally arises in solids with long-range crystalline symmetry. Reliable and scalable quantum technologies rely on materials that are either not perfect crystals or non-crystalline, breaking translational symmetry. This poses the fundamental questions of whether coherent momentum-dependent electronic states can arise without long-range order, and how they can be characterized. Here we investigate BiSe, which exists in crystalline, nanocrystalline, and amorphous forms, allowing direct comparisons between varying degrees of spatial ordering. Through angle-resolved photoemission spectroscopy, we show for the first time momentum-dependent band structure with Fermi surface repetitions in an amorphous solid. The experimental data is complemented by a model that accurately reproduces the vertical, dispersive features as well as the replication at higher momenta in the amorphous form. These results reveal that well-defined real-space length scales are sufficient to produce dispersive band structures, and that photoemission can expose the imprint of these length scales on the electronic structure.