Hedgehog spin texture and competing orders associated with strains on the surface of a topological crystalline insulator

TL;DR

This study explores how applied strains influence spin textures, gap formation, and competing orders on the surface of topological crystalline insulators, revealing tunable topological properties and phase diagrams relevant for low-power electronics.

Contribution

It introduces a comprehensive analysis of strain-induced effects on spin textures and topological phases in topological crystalline insulators using a four-band model, including interaction effects.

Findings

Strains breaking mirror symmetry induce hedgehog-like spin textures.

Strain and Zeeman field can tune the Chern number of surface states.

Interaction effects lead to a rich phase diagram with competing orders.

Abstract

We have investigated spin reorientation phenomena and interaction driven effects under the presence of applied strains on the (001) surface of Pb$_{1-x}$Sn$_x$(Te, Se) topological crystalline insulators, which host multiple Dirac cones. Our analysis is based on a four-band $k\cdot p$ model, which captures the spin and orbital textures of the surface states at low energies around the $\bar{X}$ and $\bar{Y}$ points, including the Lifshitz transition. Even without breaking the time-reversal symmetry, we find that certain strains which break the mirror symmetry can induce hedgehog-like spin texture associated with gap formation at the Dirac points. The Chern number of the gapped surface ground state is shown to be tunable through the interplay of strains and a perpendicular Zeeman field. We also consider effects of strain in the presence of interactions in driving competing orders, and obtain the associated phase diagram at the mean-field level. Potential applications of our results for low power consuming electronics are discussed.