Tunable topological electronic states in the honeycomb-kagome lattices of nitrogen/oxygen-doped graphene nanomeshes

Abstract

The rich and exotic electronic properties of graphene nanomeshes (GNMs) have been attracting interest due to their superiority to pristine graphene. Using first-principles calculations, we considered three graphene meshes doped with nitrogen and oxygen atoms (C₁₀N₃, C₉N₄ and C₁₀O₃). The electronic band structures of these GNMs in terms of the proximity of the Fermi level featured a two-dimensional (2D) honeycomb-kagome lattice with concurrent kagome and Dirac bands. The position of the Fermi level can be regulated by the doping ratio, resulting in different topological quantum states, namely topological Dirac semimetals and Dirac nodal line (DNL) semimetals. More interestingly, the adsorption of rhenium (Re) atoms in the voids of the C₁₀N₃ (Re@ C₁₀N₃) GNMs induced quantum anomalous Hall (QAH) states, as verified by the nonzero Chern numbers and chiral edge states. These GNMs offer a promising platform superior to pristine graphene for regulating multiple topological states.

Fig. 1. (a) Schematic diagram of the honeycomb-kagome lattice and the first Brillouin zone. The honeycomb lattice is connected by red lines, while the kagome lattice is connected by blue lines. The red dotted line represents the unit cell. (b) The band structure of the honeycomb-kagome lattice based on the TB model. Dirac cone and DNL appear in turn as electrons are doped. (c) The 3D diagram of the Dirac cone and DNL. (d) The structure of a GNM, taking C₁₀N₃ GNM as an example.

Fig. 2. (a)–(c) Band structures of C₁₀N₃, C₉N₄ and C₁₀O₃, respectively. (d)–(f) Charge densities of the A, B and C states, respectively, decomposed from Dirac bands. (g)–(i) Charge densities of the D, E, and F states, respectively, decomposed from kagome bands. The isosurface values for (d) to (i) were set at 0.002 e Å⁻³.

Fig. 3. (a) The most stable adsorption configuration of Re@C₁₀N₃. The upper panel is a top view, the lower panel is a side view. (b) The charge density difference of the Re@C₁₀N₃ adsorption configuration; yellow and cyan regions represent electron accumulation and depletion, respectively. The isosurface values for (b) were set at 0.007 e Å⁻³. (c) and (d) the band structures of Re@C₁₀N₃ without and with considering SOC, respectively. The red and blue colored bands without SOC represent the spin-up and spin-down character, respectively. (e) and (f) the Berry curvature at the Fermi level and the energy at −0.78 eV when considering SOC, respectively.

Fig. 4. (a) and (b) the edge states along the [010] orientation at the Fermi level and the energy at −0.78 eV, respectively. (c) and (d) the winding number at the two energy levels, respectively.