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

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, ${\sigma }_{\mathrm{spin}}^{xy}\sim 2(e/2\pi )$, 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.

9 pages, 6 figures

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• Fingerprints of bosonic symmetry protected topological state in a quantum point contact
• Topological properties of magnetically ordered heavy-fermion systems in the presence of mirror symmetry
• Analytic density of states of two-dimensional Chern insulator