Topological Singularities in Periodic Media: Ginzburg–Landau and Core-Radius Approaches

We describe the emergence of topological singularities in periodic media within the Ginzburg–Landau model and the core-radius approach. The energy functionals of both models are denoted by $$E_{\varepsilon ,\delta }$$ E ε , δ , where $$\varepsilon $$ ε represent the coherence length (in the Ginzburg–Landau model) or the core-radius size (in the core-radius approach) and $$\delta $$ δ denotes the periodicity scale. We carry out the $$\Gamma $$ Γ -convergence analysis of $$E_{\varepsilon ,\delta }$$ E ε , δ as $$\varepsilon \rightarrow 0$$ ε → 0 and $$\delta =\delta _\varepsilon \rightarrow 0$$ δ = δ ε → 0 in the $$|\log \varepsilon |$$ | log ε | scaling regime, showing that the $$\Gamma $$ Γ -limit consists in the energy cost of finitely many vortex-like point singularities of integer degree. After introducing the scale parameter $$\begin{aligned} \lambda =\min \Bigl \{1,\lim _{\varepsilon \rightarrow 0} {|\log \delta _\varepsilon |\over |\log \varepsilon |}\Bigr \} \end{aligned}$$ λ = min { 1 , lim ε → 0 | log δ ε | | log ε | } (upon extraction of subsequences), we show that in a sense we always have a separation-of-scale effect: at scales smaller than $$\varepsilon ^\lambda $$ ε λ we first have a concentration process around some vortices whose location is subsequently optimized, while for scales larger than $$\varepsilon ^\lambda $$ ε λ the concentration process takes place “after” homogenization.

Linked Weyl surfaces and Weyl arcs in photonic metamaterials

Generalization of the concept of band topology from lower-dimensional to higher-dimensional (n > 3) physical systems is expected to introduce new bulk and boundary topological effects. However, theoretically predicted topological singularities in five-dimensional systems—Weyl surfaces and Yang monopoles—have either not been demonstrated in realistic physical systems or are limited to purely synthetic dimensions. We constructed a system possessing Yang monopoles and Weyl surfaces based on metamaterials with engineered electromagnetic properties, leading to the observation of several intriguing bulk and surface phenomena, such as linking of Weyl surfaces and surface Weyl arcs, via selected three-dimensional subspaces. The demonstrated photonic Weyl surfaces and Weyl arcs leverage the concept of higher-dimension topology to control the propagation of electromagnetic waves in artificially engineered photonic media.

Interconversion of multiferroic domains and domain walls

Systems with long-range order like ferromagnetism or ferroelectricity exhibit uniform, yet differently oriented three-dimensional regions called domains that are separated by two-dimensional topological defects termed domain walls. A change of the ordered state across a domain wall can lead to local non-bulk physical properties such as enhanced conductance or the promotion of unusual phases. Although highly desirable, controlled transfer of these properties between the bulk and the spatially confined walls is usually not possible. Here, we demonstrate this crossover by confining multiferroic Dy0.7Tb0.3FeO3 domains into multiferroic domain walls at an identified location within a non-multiferroic environment. This process is fully reversible; an applied magnetic or electric field controls the transformation. Aside from expanding the concept of multiferroic order, such interconversion can be key to addressing antiferromagnetic domain structures and topological singularities.

Emergence of dynamic vortex glasses in disordered polar active fluids

In equilibrium, disorder conspires with topological defects to redefine the ordered states of matter in systems as diverse as crystals, superconductors, and liquid crystals. Far from equilibrium, however, the consequences of quenched disorder on active condensed matter remain virtually uncharted. Here, we reveal a state of strongly disordered active matter with no counterparts in equilibrium: a dynamical vortex glass. Combining microfluidic experiments and theory, we show how colloidal flocks collectively cruise through disordered environments without relaxing the topological singularities of their flows. The resulting state is highly dynamical but the flow patterns, shaped by a finite density of frozen vortices, are stationary and exponentially degenerated. Quenched isotropic disorder acts as a random gauge field turning active liquids into dynamical vortex glasses. We argue that this robust mechanism should shape the collective dynamics of a broad class of disordered active matter, from synthetic active nematics to collections of living cells exploring heterogeneous media.

Condensation phenomena in gravity

Gravity can play a role in critical phenomena. Topological singularities induce ground state degeneracy and break the continuum symmetry of the vacuum. They also generate momenta oscillations about an average momentum and a positive gravitational susceptibility. Gravitational analogues of the laws of Curie and Bloch have been found for a one-dimensional model. The critical temperature for a change in phase from bound to unbound vortices has also been calculated in a XY-model.

In search of a theory of everything:

In this brief communication, we summarize an original and new approach of the Universe, which considers that the Universe could be a finite, elastic and massive solid that would move and deform in an infinite absolute vacuum. In this a priori strange concept, it is supposed that the Universe is a lattice of simple cubic crystalline structure, whose basic cells have a mass of inertia that satisfies Newtonian dynamics in absolute space, and whose elasticity is controlled by the existence of an internal energy of deformation. One also supposes that this lattice is likely to contain topological singularities, i.e. structural defects such as dislocations, disclinations and dispirations, which would be the constituent elements of Ordinary Matter.