# Quantum spin Hall effect and spin-charge separation in a kagome lattice

## TL;DR

This paper theoretically explores the quantum spin Hall effect and spin-charge separation in a kagome lattice, revealing quantized spin Hall conductance and topological solitons at specific fillings.

## Contribution

It introduces a simple tight-binding model for kagome lattices incorporating spin-orbit interaction, demonstrating quantized spin Hall conductance and topological solitons.

## Key findings

- Quantized spin Hall conductance of -e/2π and e/2π in insulating phases.
- Identification of spin-charge separated solitons at 1/3 and 2/3 fillings.
- Consistency with numerical and topological invariance analyses.

## Abstract

A two-dimensional kagome lattice is theoretically investigated within a simple tight-binding model, which includes the nearest neighbor hopping term and the intrinsic spin-orbit interaction between the next nearest neighbors. By using the topological winding properties of the spin-edge states on the complex-energy Riemann surface, the spin Hall conductance is obtained to be quantized as $-e/2\pi$ ($e/2\pi$) in insulating phases. This result keeps consistent with the numerical linear-response calculation and the \textbf{Z}$_{2}$ topological invariance analysis. When the sample boundaries are connected in twist, by which two defects with $\pi$ flux are introduced, we obtain the spin-charge separated solitons at 1/3 (or 2/3) filling.