Derivation of effective Hamiltonian for Na₂XY (X=Mg,Cd;Y=Pb,Sn) dual topological insulators via k.p theory

Dual topological insulators (DTIs) are characterized by spin and mirror Chern numbers – stemming from time reversal and crystalline symmetries, respectively – that make them more robust as compared to ordinary TIs. Here, we apply the k.p method [1] and theory of invariants [2] to derive an effective Hamiltonian for Na₂XY (X=Mg,Cd;Y=Pb,Sn) materials, predicted to be quasi-2D DTIs by ab-initio calculations. The next step is to calculate the topological invariants and investigate the behavior of the edge states and their robustness in the presence of an external magnetic field. Our study is important for a better understanding of DTIs, specially Na₂XY, and their potential applications. The authors acknowledge Julian Zanon for helpful discussions.

[1] R. S. Calsaverini, E. Bernardes, J. C. Egues and D. Loss. Phys. Rev. B 78, 155313 (2008).

[2] J. Fu, P. H. Penteado, D. R. Candido, G. J. Ferreira, D. P. Pires, E. Bernardes and J. C. Egues. Phys. Rev. B 101, 134416 (2020).