Amorphous topological superconductivity in a Shiba glass

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.