Dual topological insulator with mirror symmetry protected helical edge states

TL;DR

This paper investigates the electronic properties of Na$_2$CdSn, revealing it as a giant-gap dual topological insulator with protected helical edge states, combining ab initio calculations and effective modeling.

Contribution

It introduces a comprehensive effective Hamiltonian for Na$_2$CdSn and demonstrates its dual topological insulating behavior with protected edge states.

Findings

Na$_2$CdSn is a giant-gap dual topological insulator.

The material hosts two pairs of helical edge states.

The effective model accurately predicts edge state dispersions.

Abstract

Dual topological insulators (DTIs) are simultaneously protected by time-reversal and crystal symmetries, representing advantageous alternatives to conventional topological insulators. By combining ab initio calculations and the $\mathbf{k}\cdot\mathbf{p}$ approach, here, we investigate the electronic band structure of a Na$_2$CdSn triatomic layer and derive a low-energy $4\times 4$ effective model consistent with all the symmetries of this material class. We obtain the effective Hamiltonian using the L\"owdin perturbation theory, the folding-down technique, and the theory of invariants and determine its parameters by fitting our analytical dispersion relations to those of ab initio calculations. We then calculate the bulk topological invariants of the system and show that the Na$_2$CdSn triatomic layer is a giant-gap (hundreds of millielectronvolts) quasi-two-dimensional DTI characterized by both spin and mirror Chern numbers $-2$. In agreement with the bulk-boundary correspondence theorem, we find that a finite-width strip of Na$_2$CdSn possesses two pairs of counterpropagating helical edge states per interface. We obtain analytical expressions for the edge state energy dispersions and wave functions, which are shown to agree with our numerical calculations. Our work opens an avenue for further studies of Na$_2$CdSn as a potential DTI candidate with room-temperature applications in areas of technological interest, such as nanoelectronics and spintronics.