Reduction of $\mathbb{Z}$ classification of a two-dimensional weak topological insulator - real-space DMFT study -

TL;DR

This study investigates how temperature influences the reduction of topological classification in a bilayer honeycomb lattice model of a two-dimensional weak topological insulator, using real-space DMFT to analyze edge and bulk properties.

Contribution

It demonstrates that temperature can restore gapless edge modes and reveals the interplay between Mott behavior and topological properties in interacting systems.

Findings

Winding number remains nontrivial at zero temperature despite classification reduction.

Edge Mott behavior appears only within a finite temperature range.

Temperature can restore gapless edge modes when interaction energy is below the bulk gap.

Abstract

One of the remarkable interaction effects on topological insulators is the reduction of topological classification in free-fermion systems. We address this issue in a bilayer honeycomb lattice model by taking into account temperature effects on the reduction. Our analysis, based on the real-space dynamical mean field theory, elucidates the following results. (i) Even when the reduction occurs, the winding number defined by the Green's function can take a nontrivial value at zero temperature. (ii) The winding number taking the nontrivial value becomes consistent with the absence of gapless edge modes due to Mott behaviors emerging only at the edges. (iii) Temperature effects can restore the gapless edge modes, provided that the energy scale of interactions is smaller than the bulk gap. In addition, we observe the topological edge Mott behavior only in some finite temperature region.