Topological states of matter support quantised 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 realisations. 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. We show that subgap Yu–Shiba–Rusinov states on the magnetic moments 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 scanning tunnelling microscopy measurements probing the topological edge mode. Our discovery demonstrates the physical feasibility of amorphous topological quantum matter, presenting a concrete route to fabricating new topological systems from nontopological materials with random dopants.

Amorphous systems have rapidly gained promise as novel platforms for topological matter. In this work we establish a scaling theory of amorphous topological phase transitions driven by the density of lattice points in two dimensions. By carrying out a finite-size scaling analysis of topological invariants averaged over discrete and continuum random geometries, we discover unique critical properties of Chern and Z2 glass transitions. Even for short-range hopping models the Chern glass phase may persist down to the fundamental lower bound given by the classical percolation threshold. While the topological indices accurately satisfy the postulated one-parameter scaling, they do not generally flow to the closest integer value in the thermodynamic limit. Furthermore, the value of the critical exponent describing the diverging localization length varies continuously along the phase boundary and is not fixed by the symmetry class of the Hamiltonian. We conclude that the critical behaviour of amorphous topological systems exhibit characteristic features not observed in disordered systems, motivating a wealth of new research directions.

When a swift heavy ion (SHI) penetrates amorphous SiO 2 , a core/shell (C/S) ion track is formed, which consists of a lower-density core and a higher-density shell. According to the conventional inelastic thermal spike (iTS) model represented by a pair of coupled heat equations, the C/S tracks are believed to form via "vaporization" and melting of the SiO 2 induced by SHI (V-M model). However, the model does not describe what the vaporization in confined ion-track geometry with a condensed matter density is. Here we reexamine this hypothesis. While the total and core radii of the C/S tracks determined by small angle x-ray scattering are in good agreement with the vaporization and melting radii calculated from the conventional iTS model under high electronic stopping power (S e) irradiations (>10 keV/nm), the deviations between them are evident at lowS e irradiation (3-5 keV/nm). Even though the iTS calculations exclude the vaporization of SiO 2 at the low S e , both the formation of the C/S tracks and the ion shaping of nanoparticles (NPs) are experimentally confirmed, indicating the inconsistency with the V-M model. Molecular dynamics (MD) simulations based on the two-temperature model, which is an atomic-level modeling extension of the conventional iTS, clarified that the "vaporlike" phase exists at S e ∼ 5 keV/nm or higher as a nonequilibrium phase where atoms have higher kinetic energies than the vaporization energy, but are confined at a nearly condensed matter density. Simultaneously, the simulations indicate that the vaporization is not induced under 50-MeV Si irradiation (S e ∼ 3 keV/nm), but the C/S tracks and the ion shaping of nanoparticles are nevertheless induced. Even though the final density variations in the C/S tracks are very small at the low stopping power values (both in the simulations and experiments), the MD simulations show that the ion shaping can be explained by flow of liquid metal from the NP into the transient low-density phase of the track core during the first ∼10 ps after the ion impact. The ion shaping correlates with the recovery process of the silica matrix after emitting a pressure wave. Thus, the vaporization is not a prerequisite for the C/S tracks and the ion shaping.

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