Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices

TL;DR

This paper extends the concept of higher-order topological insulators to breathing Kagome and pyrochlore lattices, demonstrating new boundary states and fractional charges at corners, and introduces a topological semimetal variant.

Contribution

It constructs and characterizes second- and third-order topological insulators on breathing Kagome and pyrochlore lattices, revealing new boundary states and fractional charges.

Findings

Corner states with fractional charges in Kagome lattice

Topological boundary states in pyrochlore lattice

Topological semimetal via stacking Kagome layers

Abstract

A second-order topological insulator in $d$ dimensions is an insulator which has no $d-1$ dimensional topological boundary states but has $d-2$ dimensional topological boundary states. It is an extended notion of the conventional topological insulator. Higher-order topological insulators have been investigated in square and cubic lattices. In this paper, we generalize them to breathing Kagome and pyrochlore lattices. First, we construct a second-order topological insulator on the breathing Kagome lattice. Three topological boundary states emerge at the corner of the triangle, realizing a 1/3 fractional charge at each corner. Second, we construct a third-order topological insulator on the breathing pyrochlore lattice. Four topological boundary states emerge at the corners of the tetrahedron with a 1/4 fractional charge at each corner. These higher-order topological insulators are characterized by the quantized polarization, which constitutes the bulk topological index. Finally, we study a second-order topological semimetal by stacking the breathing Kagome lattice.