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The study of topology in solids is undergoing a renaissance following renewed interest in the properties of ferroic domain walls as well as recent discoveries regarding topological insulators and skyrmionic lattices. Each of these systems possess a property that is `protected in a symmetry sense, and is defined rigorously using a branch of mathematics known as topology. In this article we review the formal definition of topological defects as they are classified in terms of homotopy theory, and discuss the precise symmetry-breaking conditions that lead to their formation. We distinguish topological defects from geometric defects, which arise from the details of the stacking or structure of the material but are not protected by symmetry. We provide simple material examples of both topological and geometric defect types, and discuss the implications of the classification on the resulting material properties.
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Recent reports on the intriguing features of vector vortex bearing beams are analyzed using geometric phases in optics. It is argued that the spin redirection phase induced circular birefringence is the origin of topological phase singularities arising in the inhomogeneous polarization patterns. A unified picture of recent results is presented based on this proposition. Angular momentum shift within the light beam (OAM) has exact equivalence with the angular momentum holonomy associated with the geometric phase consistent with our conjecture.
Many physical systems can be modeled as large sets of domains glued together along boundaries - biological cells meet along cell membranes, soap bubbles meet along thin films, countries meet along geopolitical boundaries, and metallic crystals meet along grain interfaces. Each class of microstructures results from a complex interplay of initial conditions and particular evolutionary dynamics. The statistical steady-state microstructure resulting from isotropic grain growth of a polycrystalline material is canonical in that it is the simplest example of a cellular microstructure resulting from a gradient flow of a simple energy, directly proportional to the total length or area of all cell boundaries. As many properties of polycrystalline materials depend on their underlying microstructure, a more complete understanding of the grain growth steady-state can provide insight into the physics of a broad range of everyday materials. In this paper we report geometric and topological features of these canonical two- and three-dimensional steady-state microstructures obtained through large, accurate simulations of isotropic grain growth.
Chemical oxidation of multilayer graphene grown on silicon carbide yields films exhibiting reproducible characteristics, lateral uniformity, smoothness over large areas, and manageable chemical complexity, thereby opening opportunities to accelerate both fundamental understanding and technological applications of this form of graphene oxide films. Here, we investigate the vertical inter-layer structure of these ultra-thin oxide films. X-ray diffraction, atomic force microscopy, and IR experiments show that the multilayer films exhibit excellent inter-layer registry, little amount (<10%) of intercalated water, and unexpectedly large interlayer separations of about 9.35 {AA}. Density functional theory calculations show that the apparent contradiction of little water but large interlayer spacing in the graphene oxide films can be explained by considering a multilayer film formed by carbon layers presenting, at the nanoscale, a non-homogenous oxidation, where non-oxidized and highly oxidized nano-domains coexist and where a few water molecules trapped between oxidized regions of the stacked layers are sufficient to account for the observed large inter-layer separations. This work sheds light on both the vertical and intra-layer structure of graphene oxide films grown on silicon carbide, and more in general, it provides novel insight on the relationship between inter-layer spacing, water content, and structure of graphene/graphite oxide materials.
We use resonant and non-resonant X-ray diffraction measurements in combination with first-principles electronic structure calculations and Monte Carlo simulations to study the relationship between crystal structure and multiferroic orders in the orthorhombic perovskite manganites, o-$R$MnO$_3$ ($R$ is a rare-earth cation or Y). In particular, we focus on how the internal lattice parameters (Mn-O bond lengths and Mn-O-Mn bond angles) evolve under chemical pressure and epitaxial strain, and the effect of these structural variations on the microscopic exchange interactions and long-range magnetic order. We show that chemical pressure and epitaxial strain are accommodated differently by the crystal lattice of o-$R$MnO$_3$, which is key for understanding the difference in magnetic properties between bulk samples and strained films. Finally, we discuss the effects of these differences in the magnetism on the electric polarization in o-$R$MnO$_3$.
The spontaneous transformations associated with symmetry-breaking phase transitions generate domain structures and defects that may be topological in nature. The formation of these defects can be described according to the Kibble-Zurek mechanism, which provides a generic relation that applies from cosmological to interatomic lengthscales. Its verification is challenging, however, in particular at the cosmological scale where experiments are impractical. While it has been demonstrated for selected condensed-matter systems, major questions remain regarding e.g. its degree of universality. Here we develop a global Kibble-Zurek picture from the condensed-matter level. We show theoretically that a transition between two fluctuation regimes (Ginzburg and mean-field) can lead to an intermediate region with reversed scaling, and we verify experimentally this behavior for the structural transition in the series of multiferroic hexagonal manganites. Trends across the series allow us to identify additional intrinsic features of the defect formation beyond the original Kibble-Zurek paradigm.
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