The strange topology that is reshaping physics

Abstract

Charles Kane never thought he would be cavorting with topologists. "I don't think like a mathematician, " admits Kane, a theoretical physicist who has tended to focus on tangible problems about solid materials. He is not alone. Physicists have typically paid little attention to topology -the mathematical study of shapes and their arrangement in space. But now Kane and other physicists are flocking to the field.In the past decade, they have found that topology provides unique insight into the physics of materials, such as how some insulators can sneakily conduct electricity along a single-atom layer on their surfaces.Some of these topological effects were uncovered in the 1980s, but only in the past few years have researchers begun to realize that they could be much more prevalent and bizarre than anyone expected. Topological materials have been "sitting in plain sight, and people didn't think to look for them", says Kane, who is at the University of Pennsylvania in Philadelphia.Now, topological physics is truly exploding: it seems increasingly rare to see a paper on solid-state physics that doesn't have the word topology in the title. And experimentalists are about to get even busier. A study on page 298 of this week's Nature unveils an atlas of materials that might host topological effects 1 , giving physicists many more places to go looking for bizarre states of matter such as Weyl fermions or quantum-spin liquids.Scientists hope that topological materials could eventually find applications in faster, more efficient computer chips, or even in fanciful quantum computers. And the materials are already being used as virtual laboratories to test predictions about exotic and undiscovered elementary particles and the laws of physics. Many researchers say that the real reward of topological physics will be a deeper understanding of the nature of matter itself. "Emergent phenomena in topological physics are probably all around us -even in a piece of rock, " says Zahid Hasan, a physicist at Princeton University in New Jersey.Some of the most fundamental properties of subatomic particles are, at their heart, topological. Take the spin of the electron, for example, which can point up or down. Flip an electron from up to down, and then up again, and you might think that this 360° rotation would return the THE SHAPE OF THINGS TO COME Strange topological effects might be hiding inside perfectly ordinary materials. Finding them could reveal new particles, deliver superfast transistors and even bolster quantum computing.

Validity of Weyl fermion picture for transition metals monopnictides TaAs, TaP, NbAs, and NbP from ab initio studies

“…More, interesting applications were suggested. They range from optical devices, Veselago lenses 22 , 23 , to Qubits 24 . These studies were supported or even driven by theoretical investigations of the electronic structure 10 , 12 – 15 , 25 , 26 .…”

Discovery of topological Weyl fermion lines and drumhead surface states in a room temperature magnet

“…T opological phases of matter can host analogs of particles relevant for high-energy physics and may enable fresh pathways for the application of quantum materials (1)(2)(3)(4)(5)(6)(7)(8)(9)(10). To date, most topological phases have been discovered in nonmagnetic materials (6)(7)(8), thus limiting their magnetic field tunability, as well as their electronic and magnetic functionality.…”

Nonlocal chiral symmetry breaking in curvilinear magnetic shells

“…T he behavior of any physical system from cosmological objects in field theories 1 through living organisms in biology 2 up to synthetic objects in condensed 3 and soft 4 matter is determined by the order parameter that lives in spacetime. The spatial distribution of the order parameter is governed by the geometry of the physical space of the object, in particular its dimensionality and curvature 5,6 .…”