Three-dimensional Topological Insulators on the Pyrochlore Lattice

TL;DR

This paper demonstrates that electrons on a three-dimensional pyrochlore lattice can form various topologically non-trivial insulating phases influenced by spin-orbit coupling and lattice distortions, revealing potential topological insulators among pyrochlore materials.

Contribution

It identifies and characterizes multiple topological phases in the pyrochlore lattice model, including a strong topological insulator at half-filling and various phases at quarter filling, expanding understanding of topological insulators in complex lattices.

Findings

Nine of sixteen topological classes are realized in the model.

A strong topological insulator with Z2 index (1;000) is found at half-filling.

Various topological phases emerge at quarter filling with lattice distortions.

Abstract

Electrons hopping on the sites of a three-dimensional pyrochlore lattice are shown to form topologically non-trivial insulating phases when the spin-orbit (SO) coupling and lattice distortions are present. Of 16 possible topological classes 9 are realized for various parameters in this model. Specifically, at half-filling undistorted pyrochlore lattice with SO term yields a 'pristine' strong topological insulator with Z2 index (1;000). At quarter filling various strong and weak topological phases are obtained provided that both SO coupling and uniaxial lattice distortion are present. Our analysis suggests that many of the non-magnetic insulating pyrochlores should be topological insulators.