Topological edge Mott insulating state in two dimensions at finite temperatures -bulk and edge analysis-

TL;DR

This paper investigates a bilayer Kane-Mele-Hubbard model, revealing a topological edge Mott insulator with gapless spin excitations at finite temperatures, characterized by nearly quantized spin Hall conductivity and edge modes in collective spin channels.

Contribution

It introduces the topological edge Mott insulator state in a bilayer model, demonstrating gapless edge spin excitations and their evolution from a spin Hall insulator, using real-space DMFT and bosonization.

Findings

Identification of a TEMI state with gapless edge spin modes

Nearly quantized spin Hall conductivity at finite temperatures

Transition from spin Hall insulator to trivial Mott insulator

Abstract

We study a bilayer Kane-Mele-Hubbard model with lattice distortion and inter-layer spin exchange interaction under cylinder geometry. Our analysis based on real-space dynamical mean field theory with continuous-time quantum Monte Carlo demonstrates the emergence of a topological edge Mott insulating (TEMI) state which hosts gapless edge modes only in collective spin excitations. This is confirmed by the numerical calculations at finite temperatures for the spin-Hall conductivity and the single-particle excitation spectrum; the spin Hall conductivity is almost quantized, $\sigma^{xy}_\mathrm{spin}\sim2(e/2\pi)$, predicting gapless edge modes carrying the spin current, while the helical edge modes in the single-particle spectrum are gapped out with respecting symmetry. It is clarified how the TEMI state evolves from the ordinary spin Hall insulating state with increasing the Hubbard interaction at a given temperature and then undergoes a phase transition to a trivial Mott insulating state. With a bosonization approach at zero temperature, we further address which collective modes host gapless edge modes in the TEMI state.