  Topological states of matter support quantized nondissipative responses and
exotic quantum particles that cannot be accessed in common materials. The
exceptional properties and application potential of topological materials have
triggered a large-scale search for new realizations. Breaking away from the
popular trend focusing almost exclusively on crystalline symmetries, we
introduce the Shiba glass as a platform for amorphous topological quantum
matter. This system consists of an ensemble of randomly distributed magnetic
atoms on a superconducting surface. The collection of magnetic moments gives
rise to subgap Yu-Shiba-Rusinov states that form a topological superconducting
phase at critical density despite a complete absence of spatial order.
Experimental signatures of the amorphous topological state can be obtained by
STM measurements probing the topological edge mode. Our discovery demonstrates
the physical feasibility of amorphous topological quantum matter and presents a
concrete route to fabricating new topological systems from nontopological
materials with random dopants.
