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

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.Comment: 13 NJP pages, 7 figure

Mott physics and band topology in materials with strong spin-orbit interaction

Recent theory and experiment have revealed that strong spin-orbit coupling can have dramatic qualitative effects on the band structure of weakly interacting solids. Indeed, it leads to a distinct phase of matter, the topological band insulator. In this paper, we consider the combined effects of spin-orbit coupling and strong electron correlation, and show that the former has both quantitative and qualitative effects upon the correlation-driven Mott transition. As a specific example we take Ir-based pyrochlores, where the subsystem of Ir 5d electrons is known to undergo a Mott transition. At weak electron-electron interaction, we predict that Ir electrons are in a metallic phase at weak spin-orbit interaction, and in a topological band insulator phase at strong spin-orbit interaction. Very generally, we show that with increasing strength of the electron-electron interaction, the effective spin-orbit coupling is enhanced, increasing the domain of the topological band insulator. Furthermore, in our model, we argue that with increasing interactions, the topological band insulator is transformed into a "topological Mott insulator" phase, which is characterized by gapless surface spin-only excitations. The full phase diagram also includes a narrow region of gapless Mott insulator with a spinon Fermi surface, and a magnetically ordered state at still larger electron-electron interaction.Comment: 10+ pages including 3+ pages of Supplementary Informatio