Graphite to AlB₂ and MgB₂: a comparative study of their tight-binding model and Dirac nodal line

ABSTRACT

Recently, the AlB₂-type compounds such as AlB₂ and MgB₂ have attracted immense interest due to the Dirac Nodal Line (DNL). This unique electronic structure is very important for the design and discovery of topological superconductivity, but the DNL of AlB₂-type compounds has not been unambiguously comparative studied. Here, we systematically investigated the electronic topological properties of AlB₂ and MgB₂ by tight-binding model analysis and first-principles calculations. The Slater–Koster method fitted band structure results showed that the slope of σ-bond in Γ-A direction was mainly controlled by the absolute value of V_ppπ. Moreover, the band structure fitted by two p_z Symmetry-Adapted Wannier Function (SAWF) was consistent with the band structure obtained by the effective Hamiltonian of two orbital. In the constructed effective Hamiltonian, the external on-site energies in MgB₂ and AlB₂ were 0.075 and 2.47 eV, respectively, which were mainly due to the distance between Fermi level and Dirac point at the high-symmetry K and H points. More strikingly, it was found that the degree of bending of the topological surface state was related to the number of the selected orbits, and the larger the number of orbits, the stronger the degree of bending. This important finding might be due to the asymmetry of the crystal structure and band structure. This work provides a meaningful reference for exploration of the topological property of DNL in AlB₂-type topological superconductivity materials.

GRAPHICAL ABSTRACT

KEYWORDS:

• AlB₂-type materials
• Symmetry-Adapted Wannier Function
• Tight-Binding Model
• Dirac Nodal Line
• Effective Hamiltonian

Acknowledgements

We would like to thank Jia-Tao Sun and Hu Xu for helpful discussions. C. Cheng acknowledges financial support from National Natural Science Foundation of China (Grant No. 11904244) and China Postdoctoral Science Foundation (Grant No. 2020M683276). We also acknowledge the computing resources from the High Performance Computing Center of Sichuan Normal University.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

We acknowledge financial support from National Natural Science Foundation of China (grant number 11904244) and China Postdoctoral Science Foundation (grant number 2020M683276).