Glass Transitions in Monodisperse Cluster-Forming Ensembles: Vortex Matter in Type-1.5 Superconductors

Abstract

At low enough temperatures and high densities, the equilibrium configuration of an ensemble of ultrasoft particles is a self-assembled, ordered, cluster-crystal. In the present work we explore the out-of-equilibrium dynamics for a two-dimensional realisation, which is relevant to superconducting materials with multi-scale intervortex forces. We find that for small temperatures following a quench, the suppression of the thermally-activated particle hopping hinders the ordering. This results in a glass transition for a monodispersed ensemble, for which we derive a microscopic explanation in terms of an "effective polydispersity" induced by multi-scale interactions. This demonstrates that a vortex glass can form in clean systems of thin films of "type-1.5" superconductors. An additional setup to study this physics can be layered superconducting systems, where the shape of the effective vortex-vortex interactions can be engineered. The vortex glass is one of the key states in the theory of magnetic and transport properties of type-2 superconductors in the presence of disorder [1][2][3][4]. Within this frame, the glassy phase is caused by the pinning of vortices by impurities and is absent in a clean sample. In this work we demonstrate that a vortex glass state can be an inherent property of a superconducting system characterised by multiple coherence lengths. In a more general context, our work demonstrates that a structurally disordered glass state of matter can be obtained in the absence of disordered substrates for a simple two-dimensional monodisperse ensemble of particles interacting via isotropic, repulsive, ultrasoft interactions [5,6]. This is surprising as those conditions are usually associated with minimal frustration [7][8][9][10]. The glass phase appears below a non-equilibrium glass transition temperature and extends to the lowest temperatures examined. We provide a description of the microscopic mechanism responsible for the appearance of glassiness in terms of an effective polydispersity that emerges following a quench due to multi-scale interactions [see Fig. 1]. In typical glass forming liquids, frustration results from polydisperse mixtures of particles [11]. In the present systems, the appearance of glassiness stems from the effective polydispersity of clusters sizes.Several works have recently discussed "type-1.5 superconductors" that are characterised by multiple coherence lengths, some of which are larger and some smaller than the magnetic field penetration length. These multiple coherence lengths arise in superconducting states that break multiple symmetries and also in materials with multiple superconducting bands. Several materials were suggested in experiments to belong to this type of superconductors [12][13][14][15], where vortices can display multi-scale attractive and repulsive inter-vortex interactions [12,14,[16][17][18]. Multiple attractive length scales come from core-core intervortex interactions. Multiple repulsive length scales can be obtained instead in (i) artificially fabrica...

Melting of a two-dimensional monodisperse cluster crystal to a cluster liquid

“…There are small finite-size effects as the peaks of N = 200 and 1000 are not at the same temperature, but they are sufficiently close to get an estimate of the phase boundaries. Our results regarding the melting temperature are in good agreement with those obtained from the evolution of φ 6 using simulated annealing [13,19].…”

“…Monodisperse systems, in which particles are all of the same type, can nonetheless exhibit very complex hierarchical structure formations such as lattices of clusters and exotic phases such as glasses [9][10][11][12][13][14][15]. The wide array of behaviors including rich self-organizing patterns, dynamics and the thermodynamic equilibrium phases in such systems are far from understood [16][17][18][19].…”

“…Particles with cluster-forming interactions emerge in various contexts ranging from soft matter, complex molecules, to cold atoms and vortices in superconductors [20,21]. The problem is also relevant for the physics of multi-component superconductors where a rich variety of vortex cluster solutions have been found [13,22,23].…”

Many-body self-localization in a translation-invariant Hamiltonian

“…Glassy behavior in the absence of disorder also appears in other contexts of systems with long-range interactions either in a lattice [65] or in the continuous [66].…”

Two dimensional vortex structures with multi scale interactions in thin film superconductors

“…The authors report that this system can form different complex phases, such as circular clusters, ribbons, etc. In several publications potentials are used which consist of combinations of Bessel functions [27,[34][35][36][37]. In those systems such very complex structures as clusters, labyrinths, etc were also found.…”