Three-Dimensional Topological Insulators on the Pyrochlore Lattice

Electrons hopping on the sites of a three-dimensional pyrochlore lattice are shown to form topologically nontrivial 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 an undistorted pyrochlore lattice with a SO term yields a “pristine” strong topological insulator with a $Z_2$ 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 nonmagnetic insulating pyrochlores could be topological insulators.

Figure 1

(a) Pyrochlore lattice is a face-centered cubic Bravais lattice with a 4-point basis forming a shaded tetrahedron. (b) The first Brillouin zone of the fcc lattice with high-symmetry lines and points indicated. (c) Band structure of the tight-binding model Eq. (1). (d) Band structure with spin-orbit coupling Eq. (3) for $\lambda =-0.1t$ (solid line) and $\lambda =0.1t$ (dashed line).

Figure 2

Band structures for a slab with a 111 face in various insulating phases with $\lambda =-0.1t$ and $|\eta |=0.2t$. The $Z_2$ index refers to quarter filling. At half filling all four panels represent a (1;000) STI. The inset shows the surface BZ with high-symmetry points marked.