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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.

We propose a class of nodal line semimetals that host an eightfold-degenerate double Dirac nodal line (DDNL) with negligible spin-orbit coupling. We find only 5 of the 230 space groups host the DDNL. The DDNL can be considered as a combination of two Dirac nodal lines, and has a trivial Berry phase. This leads to two possible but completely different surface states, namely, a torus surface state covering the whole surface Brillouin zone and no surface state at all. Based on first-principles calculations, we predict that the hydrogen storage material LiBH is an ideal DDNL semimetal, where the line resides at Fermi level, is relatively flat in energy, and exhibits a large linear energy range. Interestingly, both the two novel surface states of DDNL can be realized in LiBH. Further, we predict that with a magnetic field parallel to DDNL, the Landau levels of DDNL are doubly degenerate due to a Kramers-like degeneracy and have a doubly degenerate zero mode.

We have performed angle-resolved photoemission spectroscopy on EuIn2As2 which is predicted to be an axion insulator in the antiferromagnetic state. By utilizing soft-x-ray and vacuum-ultraviolet photons, we revealed a three-dimensional hole pocket centered at the Gamma point of bulk Brillouin zone together with a heavily hole-doped surface state in the paramagnetic phase. Upon entering the antiferromagnetic phase, the band structure exhibits a marked reconstruction characterized by the emergence of a "M"-shaped bulk band near the Fermi level. The qualitative agreement with first-principles band-structure calculations suggests the occurrence of bulk-band inversion at the Gamma point in the antiferromagnetic phase. We suggest that EuIn2As2 provides a good opportunity to study the exotic quantum phases associated with possible axion-insulator phase., 8 pages, 5 figures

Monolayer AlB$_2$ is composed of two atomic layers: honeycomb borophene and triangular aluminum. In contrast with the bulk phase, monolayer AlB$_2$ is predicted to be a superconductor with a high critical temperature. Here, we demonstrate that monolayer AlB$_2$ can be synthesized on Al(111) via molecular beam epitaxy. Our theoretical calculations revealed that the monolayer AlB$_2$ hosts several Dirac cones along the $\Gamma$--M and $\Gamma$--K directions; these Dirac cones are protected by crystal symmetries and are thus resistant to external perturbations. The extraordinary electronic structure of the monolayer AlB$_2$ was confirmed via angle-resolved photoemission spectroscopy measurements. These results are likely to stimulate further research interest to explore the exotic properties arising from the interplay of Dirac fermions and superconductivity in two-dimensional materials., Comment: 5 pages, 4 figures