Monolayer 1T-LaN2: Dirac spin-gapless semiconductor of p-state and Chern insulator with a high Chern number

Two-dimensional transition-metal dinitrides have attracted considerable attention in recent years due to their rich magnetic properties. Here, we focus on rare-earth-metal elements and propose a monolayer of lanthanum dinitride with a 1T structural phase, 1T-LaN2. Using first-principles calculations, we systematically investigated the structure, stability, magnetism, and band structure of this material. It is a flexible and stable monolayer exhibiting a low lattice thermal conductivity, which is promising for future thermoelectric devices. The monolayer shows the ferromagnetic ground state with a spin-polarized band structure. Two linear spin-polarized bands cross at the Fermi level forming a Dirac point, which is formed by the p atomic orbitals of the N atoms, indicating that monolayer 1T-LaN2 is a Dirac spin-gapless semiconductor of p-state. When the spin-orbit coupling is taken into account, a large nontrivial indirect bandgap (86/354meV) can be opened at the Dirac point, and three chiral edge states are obtained, corresponding to a high Chern number of C=3, implying that monolayer 1T-LaN2 is a Chern insulator. Importantly, this kind of band structure is expected to occur in more monolayers of rare-earth-metal dinitride with a 1T structural phase.