Topological Defect Densities in Type-I Superconducting Phase Transitions

The crossing of a continuous phase transition results in the formation of topological defects with a density predicted by the Kibble-Zurek mechanism (KZM). We characterize the spatial distribution of point-like topological defects in the resulting nonequilibrium state and model it using a Poisson point process in arbitrary spatial dimension with KZM density. Numerical simulations in a one-dimensional $\phi^4$ theory unveil short-distance defect-defect corrections stemming fro...

We propose a simple model for superconductors endowed with two critical temperatures, corresponding to two second-order phase transitions, in the framework of the Ginzburg-Landau mean-field theory. For very large Cooper pair self-interaction, in addition to the standard condensation occurring in the Ginzburg-Landau theory, we find another phase transition at a lower temperature with a maximum difference of 15% between the two critical temperatures.

In the field of non-equilibrium phase transitions, the Kibble-Zurek mechanism (KZM) is undoubtedly an important discovery, pointing out that some universal scaling rules are applied to a wide range of physical systems from quantum to the cosmos in complex non-equilibrium continuous phase transitions. However, except for some scaling relations in specific cases, the algebraic-based KZM can not provide further details on the topological defect generation laws. In this work, we ...

An interpretation of the quadratic parameter of the Ginzburg-Landau theory of superconductivity is presented in this paper. The negative term in the potential, which allows the spontaneous symmetry breaking, is interpreted as a direct contribution from the energy gap at the Fermi surface to the effective potential. As a result, in the London approximation of the Ginzburg-Landau theory for type-II superconductors, a strong correlation is predicted and observed between the uppe...

On the basis of coupled Ginzburg--Landau equations we study nonhomogeneous states in systems with two order parameters~(OP). Superconductors with superconducting OP~$\Delta$, and charge- or spin-density wave (CDW or SDW) with amplitude~$W$ are examples of such systems. When one of OP, say~$\Delta$, has a form of a topological defect, like, e.g., vortex or domain wall between the domains with the phases~$0$ and~$\pi$, the other OP~$W$ is determined by the Gross--Pitaevskii equ...

An extreme type II superconductor with internal insulating regions, namely cavities, is studied here. We find that the cavity-bearing superconductor has lower energy than the defect-free superconductor above a critical magnetic induction $B^*$ for insulating cavities but not for metallic ones. Using a numerical approach for the Ginzburg-Landau theory we compute and compare free energy densities for several cavity radii and at least for two cavity densities, assuming a cubic l...

Two established frameworks account for the onset of a gap in a superconducting system: one is based on spontaneous symmetry breaking via the Anderson-Higgs-Kibble mechanism, and the other is based on the recently developed paradigm of topological order. We show that, on manifolds with non trivial topology, both mechanisms yield a degeneracy of the ground state arising only from the {\it incompressibility} induced by the presence of a gap. We compute the topological entangleme...

The objective of this paper is to study the formation of defects in a non equilibrium second order phase transition by means of a numerical solution of the full dynamical equations, and to compare the results with theoretical predictions to be found in the literature. We simulate an instantaneous quench to zero temperature in a type II superconductor, measuring the actual density of defects and its theoretically expected value as a function of time. We also characterize quant...

We show that a topological quantum phase transition, generating flat bands and altering Fermi surface topology, is a primary reason for the exotic behavior of the overdoped high-temperature superconductors represented by $\rm La_{2-x}Sr_xCuO_4$, whose superconductivity features differ from what is described by the classical Bardeen-Cooper-Schrieffer theory [J.I. Bo\^zovi\'c, X. He, J. Wu, and A. T. Bollinger, Nature 536, 309 (2016)]. We demonstrate that 1) at temperature $T=0...

Defects in the atomic lattice of solids are sometimes desired. For example, atomic vacancies, single ones or more elaborated defective structures, can generate localized magnetic moments in a non magnetic crystalline lattice. Increasing their density to a few percent magnetic order can appear. Furthermore, certain two dimensional interfaces can give rise to localized superconductivity with a broad range of critical temperatures. Old and new experimental facts emphasize the ne...