Spin textures on general surfaces of the correlated topological insulator SmB6

TL;DR

This paper analytically studies the spin textures of topological surface states on various surfaces of SmB6, revealing how these textures depend on surface orientation, model parameters, and potential topological phase transitions.

Contribution

It provides a general analytical framework for predicting surface state spin textures on arbitrary surfaces of SmB6, including phase transition analysis based on mirror Chern numbers.

Findings

Surface spin textures vary with surface orientation and model parameters.

Predictions for spin patterns on (001), (110), (111), and (210) surfaces.

Identification of topological phase transitions affecting surface spin structures.

Abstract

Employing the $\mathbf{k}\cdot\mathbf{p}$ expansion for a family of tight-binding models for SmB$_6$, we analytically compute topological surface states on a generic $(lmn)$ surface. We show how the Dirac-cone spin structure depends on model ingredients and on the angle $\theta$ between the surface normal and the main crystal axes. We apply the general theory to $(001)$, $(110)$, $(111)$, and $(210)$ surfaces, for which we provide concrete predictions for the spin pattern of surface states which we also compare with tight-binding results. As shown in previous work, the spin pattern on a $(001)$ surface can be related to the value of mirror Chern numbers, and we explore the possibility of topological phase transitions between states with different mirror Chern numbers and the associated change of the spin structure of surface states. Such transitions may be accessed by varying either the hybridization term in the Hamiltonian or the crystal-field splitting of the low-energy $f$ multiplets, and we compute corresponding phase diagrams.