Discovery of a maximally charged Weyl point

Two-dimensional quadratic Weyl points, nodal loops, and spin-orbit Dirac points in PtS, PtSe, and PtTe monolayers

Topological quasiparticles have garnered significant research attention in condensed matter physics. However, they are exceedingly rare in two-dimensional systems, particularly those hosting unconventional topological quasiparticles. In this work, employing first-principles calculations and symmetry analysis, we demonstrate that PtS, PtSe, and PtTe monolayers serve as high-quality two-dimensional topological semimetal materials. These materials exhibit multiple types of topological quasiparticles around the Fermi level in the absence of spin-orbit coupling, such as conventional linear Weyl points and unconventional quadratic Weyl points in the PtS monolayer, as well as nodal loops in PtSe and PtTe monolayers. When spin-orbit coupling (SOC) is introduced, a tiny gap opens, transforming the systems into quantum spin hall insulators. Simultaneously, three spin-orbit Dirac points, robust against SOC, appear at the X, Y, and M points. We illustrate the symmetry protection, low-energy effective model, and edge states of these topological states. Our work provides an excellent material platform for studying novel two-dimensional topological quasiparticles and topological insulators.

Topological quadratic-node semimetal in a photonic microring lattice

Graphene, with its two linearly dispersing Dirac points with opposite windings, is the minimal topological nodal configuration in the hexagonal Brillouin zone. Topological semimetals with higher-order nodes beyond the Dirac points have recently attracted considerable interest due to their rich chiral physics and their potential for the design of next-generation integrated devices. Here we report the experimental realization of the topological semimetal with quadratic nodes in a photonic microring lattice. Our structure hosts a robust second-order node at the center of the Brillouin zone and two Dirac points at the Brillouin zone boundary-the second minimal configuration, next to graphene, that satisfies the Nielsen-Ninomiya theorem. The symmetry-protected quadratic nodal point, together with the Dirac points, leads to the coexistence of massive and massless components in a hybrid chiral particle. This gives rise to unique transport properties, which we demonstrate by directly imaging simultaneous Klein and anti-Klein tunnelling in the microring lattice.

Coexistence of Dirac points and nodal chains in photonic metacrystal

Gapless topological phases, i.e. topological semimetals, come in various forms such as Weyl/Dirac semimetals, nodal line/chain semimetals, and surface-node semimetals. However, the coexistence of two or more topological phases in a single system is still rare. Here, we propose the coexistence of Dirac points and nodal chain degeneracies in a judiciously designed photonic metacrystal. The designed metacrystal exhibits nodal line degeneracies lying in perpendicular planes, which are chained together at the Brillouin zone boundary. Interestingly, the Dirac points, which are protected by nonsymmorphic symmetries, are located right at the intersection points of nodal chains. The nontrivial Z₂ topology of the Dirac points is revealed by the surface states. The Dirac points and nodal chains are located in a clean frequency range. Our results provide a platform for studying the connection between different topological phases.