Quantized Circulation of Anomalous Shift in Interface Reflection

Discovery of a maximally charged Weyl point

The hypothetical Weyl particles in high-energy physics have been discovered in three-dimensional crystals as collective quasiparticle excitations near two-fold degenerate Weyl points. Such momentum-space Weyl particles carry quantised chiral charges, which can be measured by counting the number of Fermi arcs emanating from the corresponding Weyl points. It is known that merging unit-charged Weyl particles can create new ones with more charges. However, only very recently has it been realised that there is an upper limit - the maximal charge number that a two-fold Weyl point can host is four - achievable only in crystals without spin-orbit coupling. Here, we report the experimental realisation of such a maximally charged Weyl point in a three-dimensional photonic crystal. The four charges support quadruple-helicoid Fermi arcs, forming an unprecedented topology of two non-contractible loops in the surface Brillouin zone. The helicoid Fermi arcs also exhibit the long-pursued type-II van Hove singularities that can reside at arbitrary momenta. This discovery reveals a type of maximally charged Weyl particles beyond conventional topological particles in crystals.

Weyl Monoloop Semi-Half-Metal and Tunable Anomalous Hall Effect

Nodal monoloop, enjoying the cleanest scenario with a single loop, is recognized as the basic building block of intricate linked loops including chains, nets, and knots. Here, we explore the interplay of magnetic ordering and band topology in one system by introducing a brand-new quantum state, referred to as Weyl monoloop semi-half-metal, which is characterized by a single loop at the Fermi level stemming from the same spin channel. Such a nodal line Fermion, yielding 100% spin polarization, is protected by mirror (Mz) symmetry. As a prominent example, a realistic rutile-type metal fluorides LiV₂F₆ achieves the hitherto unmaterialized state, featuring fully spin-polarized ultraflat surface states. More interestingly, LiV₂F₆ has a "soft" ferromagnetic property, which is one of the desired systems to control the anomalous Hall effect by rotating the magnetization direction. Our findings offer a promising candidate for exploring the topology and magnetism with intriguing effects.

Shifting beams at normal incidence via controlling momentum-space geometric phases

When hitting interfaces between two different media, light beams may undergo small shifts. Such beam shifts cannot be described by the geometrical optics based on Snell's law and their underlying physics has attracted much attention. Conventional beam shifts like Goos-Hänchen shifts and Imbert-Fedorov shifts not only require obliquely incident beams but also are mostly very small compared to the wavelength and waist size of the beams. Here we propose a method to realize large and controllable polarization-dependent lateral shifts for normally incident beams with photonic crystal slabs. As a proof of the concept, we engineer the momentum-space geometric phase distribution of a normally incident beam by controlling its interaction with a photonic crystal slab whose momentum-space polarization structure is designed on purpose. The engineered geometric phase distribution is designed to result in a large shift of the beam. We fabricate the designed photonic crystal slab and directly observe the beam shift, which is ~5 times the wavelength and approaches the waist radius. Based on periodic structures and only requiring simple manipulation of symmetry, our proposed method is an important step towards practical applications of beam shifting effects.

Time-reversal-breaking Weyl nodal lines in two-dimensional A3C2 (A = Ti, Zr, and Hf) intrinsically ferromagnetic materials with high Curie temperature

Most materials that feature nontrivial band topology are spin-degenerate and three dimensional, strongly restricting them from application in spintronic nanodevices. Hence, two-dimensional (2D) intrinsically spin-polarized systems with rich topological elements are still in extreme scarcity. Here, 2D A₃C₂ (A = Ti, Zr, and Hf) materials with the P6[combining macron]m2 type structure are reported as new ferromagnetic materials with intrinsic magnetism and good stability. Unlike the Weyl nodal lines existing in nonmagnetic 2D systems, A₃C₂ hosts time-reversal-breaking Weyl nodal rings (two Γ-centered, one K-centered, and one K'-centered) without spin-orbit coupling (SOC). These nodal rings still remained under SOC with magnetization along the z direction (easy magnetization axis). More interestingly, the Curie temperatures (T_C) of A₃C₂ were determined based on the Monte Carlo simulation. Ti₃C₂ features an extraordinary T_C (above 800 K), and those of Zr₃C₂ and Hf₃C₂ are above room temperature. Therefore, A₃C₂ materials are excellent platforms to study magnetic Weyl nodal lines in high T_C ferromagnetic 2D materials.

Momentum space toroidal moment in a photonic metamaterial

Berry curvature, the counterpart of the magnetic field in the momentum space, plays a vital role in the transport of electrons in condensed matter physics. It also lays the foundation for the emerging field of topological physics. In the three-dimensional systems, much attention has been paid to Weyl points, which serve as sources and drains of Berry curvature. Here, we demonstrate a toroidal moment of Berry curvature with flux approaching to π in judiciously engineered metamaterials. The Berry curvature exhibits a vortex-like configuration without any source and drain in the momentum space. Experimentally, the presence of Berry curvature toroid is confirmed by the observation of conical-frustum shaped domain-wall states at the interfaces formed by two metamaterials with opposite toroidal moments.

The appearance of toroidal multipolar moments in electrodynamics interrogates the question for their existence in Berry curvature, which can be seen as the “magnetic field” in the momentum space. Here, the authors observe 3D vortex distributions in the Berry curvature within a photonic metamaterial.

Novel topological states of nodal points and nodal rings in 2D planar octagon TiB4

Topological states of matter in two-dimensional (2D) materials have received increasing attention due to their potential applications in nanoscale spintronics. Here, we report the presence of unique topological electronic properties in a 2D planar octagon TiB₄ compound. Particularly, without considering the spin-orbit coupling (SOC), we found that the material showed a coexistence of novel quadratic node (QN), and two different types of nodal rings (NRs), namely type-I and type-II. The protection mechanism of fermions has been fully clarified in this study. Furthermore, these fermions showed clear edge states. It is worth noting that QN had a topological charge of 2 since it is different from linear nodes and exhibit clear Fermi arc edge states. Under lattice strain, we found that the system could further exhibit rich topological phase transition. When SOC was included, we determined that these crossing points open very tiny energy gaps, which were smaller than previously reported 3D and 2D examples. These results show that monolayer TiB₄ is an excellent nodal point and nodal ring semimetal, which also provides a feasible member for studying potential entanglements among multiple fermions.