Topological Property

Electro-optic modulators, which convert signals from the electrical to the optical domain, are at the heart of optical communications, terahertz wireless communications, microwave signal processing, and quantum technology. Next-generation electro-optic modulators require high-density integration, compact footprints, large bandwidths, and low power consumption. They are challenging to achieve with established…

Researchers from the Hong Kong University of Science and Technology, Xiangtan University and Southern University of Science and Technology recently unveiled a possible connection between catastrophe theory, an area of mathematics that focuses on modeling sudden changes (i.e., catastrophes) and non-Hermitian physics. Their paper, published in Nature Physics, specifically shows that a structurally rich degeneracy,…

Over last few decades, study of topological phases of matter in solid-state electron systems has been extended to other research fields, including synthetic dimensions, and motivates extensive research on topological materials in many systems. Synthetic dimensions in photonics constructed by coupling internal degrees of freedom of light has manifested as a powerful platform for creating synthetic lattices with…

Researchers at the Weizmann Institute of Science, the Barcelona Institute of Science and Technology and the National Institute for Material Science in Tsukuba (Japan) have recently probed a Chern mosaic topology and Berry-curvature magnetism in magic-angle graphene. Their paper, published in Nature Physics, offers new insight about topological disorder that can occur in condensed matter physical systems.

As an interested outsider, I have been intrigued by the number of times that homotopy theory seems to have revamped its foundations over the past fifty years or so. Sometimes there seems to have b...

Microsoft and Nokia are developing a contentious new type of quantum computer

The types of spaces where data resides - graphs, meshes, grids, manifolds - are becoming increasingly varied and heterogeneous. Therefore, translating ideas, models, and theoretical results between different domains is becoming more and more challenging. Nonetheless, two fundamental principles unite all these settings. The first states that data is localised, meaning that data is associated with some regions of the…

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A joint research team from the Hong Kong University of Science and Technology (HKUST) and the University of Tokyo discovered an unusual topological aspect of sodium chloride, commonly known as table salt, which will not only facilitate the understanding of the mechanism behind salt's dissolution and formation, but may also pave the way for the future design of nanoscale conducting quantum wires.

Albert Einstein revolutionized the early conceptions of gravity in 1915 when he presented a theory of general relativity which was based primarily on the fact that mass and energy warp the fabric of…

Being part of the subject of algebraic topology, this post assumes the reader has read our previous primers on both topology and group theory. As a warning to the reader, it is more advanced than m…

Mathematicians picked the most dazzling, thought-provoking and compelling equations they know

Researchers led by Prof. Xiaoyong Hu at Peking University, China, are interested in topological photonics. They have proposed an interdisciplinary approach to study the topological systems through information entropy (IE) in real space.

The Warsaw circle is a well-known path-connected space that involves the usual topologist's sine curve. This space provides a fundamental example in shape theory. Specifically, one many const…

It is second nature to think of integer dimensions:  A line is one dimensional.  A plane is two dimensional. A volume is three dimensional.  A point has no dimensions. It is harder t…

How topology helps (and what it is)

Researchers from the UvA Institute of Physics and ENS de Lyon have discovered how to design materials that necessarily have a point or line where the material doesn't deform under stress, and that even remember how they have been poked or squeezed in the past. These results could be used in robotics and mechanical computers, while similar design principles could be used in quantum computers.

The peculiar topological properties of some forms of matter have been researched for decades. Now, researchers at the Institute of Science and Technology Austria (ISTA) have discovered topological properties of simple diatomic molecules driven to rotation by laser pulses.

New technique could lead to clearer tests of whether this fundamental constant is truly constant

Theoretical work establishes a connection for the many-electron quantum states of metals between topology and entanglement, two powerful principles for characterizing complex quantum states.