Two-dimensional (2D) boron nitride (BN) is a promising candidate for aerospace materials due to its excellent mechanical and thermal stability properties. However, its unusually prominent band gap limits its application prospects. In this work, we report a gapless monolayer BN, t-BN, which has four anisotropic Dirac cones in the first Brillouin zone exactly at the Fermi level. To further confirm the semimetallic character, the nontrivial topological properties are proven through the topologically protected edge states and the invariant non-zero Z 2. Additionally, the Young’s modulus and Poisson ratio characterize the strong mechanical strength of t-BN. Our theoretical predictions provide more possibilities for exploring the Dirac cone in BN, which will enhance the 2D boron derivative materials.

Realizing stable two-dimensional (2D) Dirac points against spin-orbit coupling (SOC) has attracted much attention because it provides a platform to study the unique transport properties. In previous work, Young and Kane [Phys. Rev. Lett. 115, 126803 (2015)] proposed stable 2D Dirac points with SOC, in which the Berry curvature and edge states vanish due to the coexistence of inversion and time-reversal symmetries. Herein, using the tight-binding model and k•p effective Hamiltonian, we present that 2D Dirac points can survive in the presence of SOC without inversion symmetry. Such 2D Dirac semimetals possess nonzero Berry curvature near the crossing nodes, and two edge states are terminated at one pair of Dirac points. In addition, according to symmetry arguments and high-throughput first-principles calculations, we identify a family of ideal 2D Dirac semimetals, which has nonzero Berry curvature in the vicinity of Dirac points and visible edge states, thus facilitating the experimental observations. Our work shows that 2D Dirac points can emerge without inversion symmetry, which not only enriches the classification of 2D topological semimetals but also provides a promising avenue to observe exotic transport phenomena beyond graphene, e.g., nonlinear Hall effect.

The exploration of carbon phases with intact massless Dirac fermions in the presence of defects is critical for practical applications to nanoelectronics. Here, we identify by first-principles calculations that the Dirac cones can exist in graphene with stacking fault (SF) induced periodic line defects. These structures are width (n)-dependent to graphene nanoribbon and are thus termed as (SF) n -graphene. The electronic properties reveal that the semimetallic features with Dirac cones occur in (SF) n -graphene with n = 3m + 1, where m is a positive integer, and then lead to a quasi-one-dimensional conducting channel. Importantly, it is found that the twisted Dirac cone in the (SF) 4 -graphene is tunable among type-I, type-II, and type-III through a small uniaxial strain. The further stability analysis shows that (SF) ngraphene is thermodynamic stable. Our findings provide an artificial avenue for exploring Dirac Ffermions in carbon-allotropic structures in the presence of defects.

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