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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 quantized 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., Comment: 17 pages, 4 figures

Topological Weyl semimetals have been attracting broad interest. Recently, a new type of Weyl point with topological charge of four, termed as charge-four Weyl point (C-4 WP), was proposed in spinless systems. Here, we show the minimum symmetry requirement for C-4 WP is point-group $T$ together with $\mathcal{T}$ symmetry or point-group $O$. We establish a minimum tight-binding model for C-4 WP on a cubic lattice with time-reversal symmetry and without spin-orbit coupling effect. This lattice model is a two-band one, containing only one pair of C-4 WPs with opposite chirality around the Fermi level. Based on both the low-energy effective Hamiltonian and the minimum lattice model, we investigate the electronic, optical, and magnetic properties of C-4 WP. Several chirality-dependent properties are revealed, such as chiral Landau bands, quantized circular photogalvanic effect and quadruple-helicoid surface arc states. Furthermore, we predict that under symmetry breaking, various exotic topological phases can evolve out of C-4 WPs. Our paper not only reveals several interesting phenomena associate with C-4 WPs, but also provides a simple and ideal lattice model of C-4 WP, which will be helpful for the subsequent study on C-4 WPs.

Experimentally synthesized perovskite-type ${\mathrm{YRh}}_{3}\mathrm{B}$ with a $Pm\overline{3}m$ type structure was proposed as a topological material (TM) via first-principles calculations and the low-energy $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ effective Hamiltonian, which has a quadratic contact triple point (QCTP) at point $\mathrm{\ensuremath{\Gamma}}$ and six pairs of open nodal lines (NLs) of the hybrid type. Clear surface states observed in the surface spectrum confirmed the topological states. When spin-orbit coupling was considered, the QCTP at $\mathrm{\ensuremath{\Gamma}}$ transferred to the quadratic-type Dirac nodal point (NP). Under $1%$ tetragonal strained lattice constants, ${\mathrm{YRh}}_{3}\mathrm{B}$ hosted richer topological states, including a quadratic-type twofold degenerate NP, six pairs of open NLs of the hybrid type, and two closed NLs of type I and hybrid type. Moreover, it was proved that the NLs of ${\mathrm{YRh}}_{3}\mathrm{B}$ at its strained lattice constants contain all types of band-crossing points (BCPs) (i.e., type I, type II, and critical type). Such rich types of NP and NL states in one compound make it potentially applicable for multifunctional electronic devices as well as an appropriate platform to study entanglement among topological states.