Multiple non-trivial phases in quasi-2D dual topological insulators*

Dual topological insulators (DTIs) have gapped bulk bands whose topology results in conducting edge states protected by time-reversal and crystalline symmetries, i.e., they host the topological insulator and topological crystalline insulator phases simultaneously. Here, we derive a k.p Hamiltonian for mirror-symmetric Na₂CdSn trilayers predicted to be DTIs by ab-initio calculations [1]. By fitting the k.p energy bands to our density functional theory calculations for Na₂CdSn, we obtain the parameters for our effective model. Our solutions for a semi-infinite plane geometry shows that Na₂CdSn hosts two pairs of edge states with quadratic dispersion relations. Varying the parameters, we also show a topological phase transition between such non-trivial phase and a second topological phase with a single pair of quadratic edge states. Our results contribute to the understanding of Na₂CdSn as DTIs, providing a new platform for their study and hopefully encoraging their experimental verification and near-future applications in novel quantum devices.

[1] N. Mao et. al., PRB 100, 205116 (2019).