Band gap and magnetism engineering in Dirac half-metallic Na2C nanosheet via layer thickness, strain and point defects

Na2C is a novel two-dimensional material with Dirac Half-metal (DHM) characteristic, exhibiting a combination of single-spin massless Dirac fermions and half-semimetal. In this paper based on the first-principles calculations, we studied the mechanical, electronic, magnetic and optical properties of Na2C nanosheet. The elastic modulus of Na2C was measured to 18.5 N/m and isotropic, whereas it shows anisotropic tensile strengths of 2.85 and 2.04 N/m, for the loading along the zigzag and armchair directions, respectively. We found that Na2C, is a DHM with band gap of 0.7 eV in the up-spin channel and has 2 mu(B) magnetic moment per unit cell. In addition, we investigated the effects of number of atomic layers (thickness), electric field and strain on the possibility of further tuning of the electronic and magnetic properties of Na2C. Our calculations show that by increasing the number of layers from monolayer to bulk, a transition from DHM to ferromagnetic metal occurs with a high magnetic moments in the range of 16-30 mu(B). With applying an electric field on the Na2C bilayer (within the ferromagnetic and anti-ferromagnetic orders), energy band gap is slightly increased. In addition our results indicate that the electronic structure can be significantly modified by applying the mechanical straining. In this regard, under the biaxial strain (from 0% to - 8%) or large uniaxial strains (> - 6%), we observed the DHM to ferromagnetic-metal transition. Moreover, vacancy defects and atom substitutions can also effect the electronic and magnetic properties of Na2C nanosheet. Defective Na2C with single and double vacancies, was found to show the metallic response. With various atom substitutions this nanosheet exhibits; ferromagnetic-metal (Si and Be) with 5.2 and 3 mu(B); dilute-magnetic semiconductor (B and N) with 3 and 7 mu(B) magnetic moments, respectively. In the case of B or N atoms replacing the native C atom, the down-spin channel yields about 1 eV band gap. Interestingly, replacing the Na atoms in the native Na2C lattice with the Li can result in the formation of magnetic topological insulator phase with nontrivial band gap in the down-spin channel (25 meV and 0.15 eV) and up-spin channel (0.75 eV), in addition exhibit 8 mu(B) magnetic moment in the ground state.