The Physics Colloquium

Chirality is a very active field of research in inorganic and organic chemistry [1], closely linked to the concept of structural symmetry and of high importance for catalysis of pharmaceutical molecules. Topology, a well-established concept in mathematics, has nowadays become essential to describe most condensed matter systems [2-4]. At its core are chiral electron states on the bulk, surfaces and edges of the condensed matter systems, in which spin and momentum of the electrons are locked parallel or anti-parallel to each other. Magnetic and non-magnetic Weyl semimetals, for example, exhibit chiral bulk states that have enabled the realization of predictions from high energy and astrophysics involving the chiral quantum number, such as the chiral anomaly, the mixed axial-gravitational anomaly and axions [5-8]. The chiral anomaly experimentally realized in Weyl semimetals is one potential explanation for the asymmetry of matter and anti-matter. Chiral topological crystals, combing topology with chirality [9], exist in two chiral forms, exhibit distinguished chiral surface states [10], Chern numbers [11], different orbital angular momentum for the enantiomers [12], and distinguished Weyl points, multifold Fermions with different energies. All these properties can eventually be advantageous in asymmetric catalysis [12]. Chiral topological crystals are an opportunity to bridge and study the two worlds, homochirality of molecules and crystals and chirality of particles such as electrons and phonons. The potential for connecting chirality as a quantum number to other chiral phenomena across different areas of science, including the asymmetry of matter and antimatter and the homochirality of life, brings topological materials to the fore [13].