Dirac cones in a snub trihexagonal tiling lattice with reflective symmetry breaking.

The present models of the two-dimensional (2D) Dirac materials always have reflective symmetry, but the essentiality has never been proved. Here we present an exceptional case: a snub trihexagonal tiling (STT) lattice without reflective symmetry. We demonstrate the existence of Dirac cones in this reflection-symmetry-free lattice by using a single-orbital tight-binding (TB) Hamiltonian. The SST lattice is also topologically nontrivial, because the Dirac cone can be gapped by spin-orbit coupling (SOC) effect associated with robust gapless edge states. Using first-principles calculations, we predict a promising candidate 2D material, BeC monolayer to realize this toy model. The Fermi velocities in this unique lattice are even higher than that in graphene. The stability and plausibility of the BeC monolayer are verified by positive phonon modes, molecular dynamical simulations and mechanical criteria. This work eliminates the need for reflective symmetry in 2D Dirac materials, opening an avenue for designing new 2D Dirac materials.