Superhoneycomb lattice is an edge-centered honeycomb lattice that represents a hybrid fermionic and bosonic system. It contains pseudospin-1/2 and pseudospin-1 Dirac cones, as well as a flat band in its band structure. In this paper, we cut the superhoneycomb lattice along short-bearded boundaries and obtain the corresponding band structure. The states very close to the Dirac points represent approximate Dirac cone states that can be used to observe conical diffraction during light propagation in the lattice. In comparison with the previous literature, this research is carried out using the continuous model, which brings new results and is simple, direct, accurate, and computationally efficient.

Topological edge states have recently garnered a lot of attention across various fields of physics. The topological edge soliton is a hybrid edge state that is both topologically protected and immune to defects or disorders, and a localized bound state that is diffraction-free, owing to the self-balance of diffraction by nonlinearity. Topological edge solitons hold great potential for on-chip optical functional device fabrication. In this report, we present the discovery of vector valley Hall edge (VHE) solitons in type-II Dirac photonic lattices, formed by breaking lattice inversion symmetry with distortion operations. The distorted lattice features a two-layer domain wall that supports both in-phase and out-of-phase VHE states, appearing in two different band gaps. Superposing soliton envelopes onto VHE states generates bright-bright and bright-dipole vector VHE solitons. The propagation dynamics of such vector solitons reveal a periodic change in their profiles, accompanied by the energy periodically transferring between the layers of the domain wall. The reported vector VHE solitons are found to be metastable.

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In article number 1900295, Yiqi Zhang and co‐workers investigate conical diffraction in the superhoneycomb lattice, based on the continuous model. To excite Dirac cone states, the lattice is cut along short‐bearded boundaries and the states close to the Dirac points are obtained, which are called the approximated Dirac cone states. Conical diffraction due to both pseudospin‐1/2 and pseudospin‐1 Dirac cones is displayed graphically and discussed theoretically. The avenue to observe conical diffraction developed here avoids mathematical complexity and is quite direct.