Related papers: Topologically Linked Crystals

This is an unrefereed lecture note based on lectures in 'Introductory Workshop on Discrete Differential Geometry' at Korea University on January 21--24, 2019. In this note, we discuss topological crystallography, which is a mathematical…

We theoretically show how two impurity defects in a crystalline structure can be entangled through coupling with the crystal. We demonstrate this with a harmonic chain of trapped ions in which two ions of a different species are embedded.…

We give new examples of 2-component links with linking number one and unknotted components that are topologically concordant to the positive Hopf link, but not smoothly so - in fact they are not smoothly concordant to the positive Hopf link…

Topological nodal rings as the simplest topological nodal lines recently have been extensively studied in optical lattices. However, the realization of complex nodal line structures like nodal chains in this system remains a crucial…

For almost finite groupoids, we study how their homology groups reflect dynamical properties of their topological full groups. It is shown that two clopen subsets of the unit space has the same class in H_0 if and only if there exists an…

Nodal chain is a typical topological phase in nodal line semimetals. Here, we propose a new topological phase -- interlocking nodal chains, in which two sets of nodal chains are interlocked each other. It includes one- (1D), two- (2D) and…

Knots and links are fascinating and intricate topological objects. Their influence spans from DNA and molecular chemistry to vortices in superfluid helium, defects in liquid crystals and cosmic strings in the early universe. Here, we find…

We investigate a simplified continuum model of a twisted homotrilayer TMD with negligible next-nearest layer couplings. We systematically analyze band structure and topology of various stacking configurations in a twist angle range from…

We prove the existence of topological rings in (0,2) theories containing non-anomalous left-moving U(1) currents by which they may be twisted. While the twisted models are not topological, their ground operators form a ring under…

We present an all-dielectric photonic crystal structure that supports two-dimensionally confined helical topological edge states. The topological properties of the system are controlled by the crystal parameters. An interface between two…

We demonstrate that higher-order electric susceptibilities in crystals can be enhanced and understood through nontrivial topological invariants and quantum geometry, using one-dimensional $\pi$-conjugated chains as representative model…

Topological phases based on tight-binding models have been extensively studied in recent decades. By mimicking the linear combination of atomic orbitals in tight-binding models based on the evanescent couplings between resonators in…

Multi-connected universe models with space identification scales smaller than the size of the observable universe produce topological images of cosmic sources. We generalise to locally hyperbolic spaces the crystallographic method, aimed to…

Topological semimetals have energy bands near the Fermi energy sticking together at isolated points/lines/planes in the momentum space, which are often accompanied by stable surface states and intriguing bulk topological responses. Although…

The link between crystal and electronic structure is crucial for understanding structure-property relations in solid-state chemistry. In particular, it has been instrumental in understanding topological materials, where electrons behave…

Topology and interactions are foundational concepts in the modern understanding of quantum matter. Their nexus yields three significant research directions: competition between distinct interactions, as in the multiple intertwined phases,…

The fundamental, or first, band gap is of unmatched importance in the study of photonic crystals. Here, we address precisely where this gap can be opened in the band structure of three-dimensional photonic crystals. Although strongly…

We put the theory of interacting topological crystalline phases on a systematic footing. These are topological phases protected by space-group symmetries. Our central tool is an elucidation of what it means to "gauge" such symmetries. We…

By means of group theory, topological quantum chemistry, first-principles and Monte Carlo calculations, we analyze the topology of the 2D buckled honeycomb lattice phonon spectra. Taking the pure crystal structure as an input, we show that…

Vortex crystals are geometric arrays of vortices found in various physics fields, owing their regular internal structure to mutual interactions within a spatially confined system. In optics, vortex crystals may form spontaneously within a…