Related papers: On the relationship between topological and geomet…
The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress has been made in controlling and measuring colloidal inclusions…
Topological defects in crystalline lattices are considered. In relation to physical realizability of such defects, criteria for geometric compatibility of the lattice distortions are formulated. For 2D lattices it is shown that the answer…
A crystalline topological phase is a topological phase with spatial symmetries. In this work, we give a very general physical picture of such phases: a topological phase with spatial symmetry $G$ (with internal symmetry $G_{\mathrm{int}}…
We consider two-dimensional (2d) quantum many-body systems with long-range orders, where the only gapless excitations in the spectrum are Goldstone modes of spontaneously broken continuous symmetries. To understand the interplay between…
We present a generalization of free fermionic topological insulators that are composed of topological subsystems of differing dimensionality. We specifically focus on topological subsystems of nonzero co-dimension are embedded within a…
We investigate experimentally and numerically the defect configurations emerging when a cholesteric liquid crystal is confined to a spherical shell. We uncover a rich scenario of defect configurations, some of them non-existent in nematic…
Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…
Searching for topological insulators/superconductors is a central subject in recent condensed matter physics. As a theoretical aspect, various classification methods of symmetry-protected topological phases have been developed, where the…
Structure formation with topological defects is described. The main differences from inflationary models are highlighted. The results are compared with recent observations. It is concluded that all the defect models studied so far are in…
We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of…
Because of the inevitably disordered background, structural defects are not well-defined concepts in amorphous solids. In order to overcome this difficulty, it has been recently proposed that topological defects can be still identified in…
For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…
A hallmark feature of topologically ordered states of matter is the dependence of ground state degeneracy (GSD) on the topology of the manifold determined by the global shape of the system. Although the topology of a physical system is…
In a previous effort [arXiv:1708.05492] we have created a framework that explains why topological structures naturally arise within a scientific theory; namely, they capture the requirements of experimental verification. This is…
Active matter encompasses different nonequilibrium systems in which individual constituents convert energy into non-conservative forces or motion at the microscale. This review provides an elementary introduction to the role of topology in…
Formation and evolution of topological defects in course of non-equilibrium symmetry breaking phase transitions is of wide interest in many areas of physics, from cosmology through condensed matter to low temperature physics. Its study in…
Topological defects play a key role in a variety of physical systems, ranging from high-energy to solid state physics. They yield fascinating emergent phenomena and serve as a bridge between the microspic and macroscopic world. A skyrmion…
The topological classification of gapped band structures depends on the particular definition of topological equivalence. For translation-invariant systems, stable equivalence is defined by a lack of restrictions on the numbers of occupied…
Robustness against small perturbations is a crucial feature of topological properties. This robustness is both a source of theoretical interest and a drive for technological applications, but presents a challenge when looking for new…
On the basis of the principle that topological quantum phases arise from the scattering around space-time defects in higher dimensional unification, a geometric model is presented that associates with each quantum phase an element of a…