Topological insulator on honeycomb lattices and ribbons without inversion symmetry

TL;DR

This paper investigates how inversion-symmetry-breaking affects topological phases in honeycomb lattice models, revealing that such symmetry breaking can both destroy and enhance topological states, with implications for edge modes in ribbons.

Contribution

It introduces a detailed analysis of the Kane-Mele-Hubbard model with inversion-symmetry-breaking, showing how this influences topological phases and edge states.

Findings

Inversion-symmetry-breaking can destroy or enhance topological states.

Moderate inversion-symmetry-breaking pushes the topological transition to higher interaction U.

Inversion symmetry removal allows gapless edge modes at certain interaction strengths.

Abstract

We study the Kane-Mele-Hubbard model with an additional inversion-symmetry-breaking term. Using the topological Hamiltonian approach, we calculate the $\mathbb{Z}_2$ invariant of the system as function of spin-orbit coupling, Hubbard interaction $U$, and inversion-symmetry-breaking on-site potential. The phase diagram calculated in that way shows that, on the one hand, a large term of the latter kind destroys the topological non-trivial state. On the other hand, however, this inversion-symmetry-breaking field can enhance the topological state, since for moderate values the transition from the non-trivial topological to the trivial Mott insulator is pushed to larger values of interaction $U$. This feature of an enhanced topological state is also found on honeycomb ribbons. With inversion symmetry, the edge of the zigzag ribbon is magnetic for any value of $U$. This magnetic moment destroys the gapless edge mode. Lifting inversion symmetry allows for a finite region in interaction strength $U$ below which gapless edge modes exist.