Anisotropic Quantum Spin Hall Effect, Spin-Orbital Textures and Mott Transition

TL;DR

This paper explores the complex interplay of topological phases, spin textures, and Mott transitions in a 2D anisotropic spin-orbit coupled lattice, revealing novel magnetic and edge phenomena relevant to iridate compounds and graphene-like materials.

Contribution

It introduces a comprehensive analysis of topological, magnetic, and spin-orbital effects in an anisotropic spin-orbit coupled Hubbard model, including new insights into Mott transitions and edge spin textures.

Findings

Identification of topological and magnetic phases under varying interactions

Prediction of exotic edge spin textures due to anisotropic spin-orbit coupling

Analysis of bulk spin textures emerging at the Mott transition

Abstract

We investigate the interplay between topological effects and Mott physics in two dimensions on a graphene-like lattice, via a tight-binding model containing an anisotropic spin-orbit coupling on the next-nearest-neighbour links and the Hubbard interaction. We thoroughly analyze the resulting phases, namely a topological band insulator phase or anisotropic quantum Spin Hall phase until moderate interactions, a N\'eel and Spiral phase at large interactions in the Mott regime, as well as the formation of a spin-orbital texture in the bulk at the Mott transition. The emergent magnetic orders at large interactions are analyzed through a spin wave analysis and mathematical arguments. At weak interactions, by analogy with the Kane-Mele model, the system is described through a Z_2 topological invariant. In addition, we describe how the anisotropic spin-orbit coupling already produces an exotic spin texture at the edges. The physics at the Mott transition is described in terms of a U(1) slave rotor theory. Taking into account gauge fluctuations around the mean-field saddle point solution, we show how the spin texture now proliferates into the bulk above the Mott critical point. The latter emerges from the response of the spinons under the insertion of monopoles and this becomes more pronounced as the spin-orbit coupling becomes prevalent. We discuss implications of our predictions for thin films of the iridate compound Na2IrO3 and also graphene-like systems.