Flat bands and $Z_2$ topological phases in a non-Abelian kagome lattice

TL;DR

This paper introduces a non-Abelian kagome lattice model with time-reversal and inversion symmetries, revealing tunable flat bands and $Z_2$ topological phases, including quantum spin Hall states, through analytical and topological analysis.

Contribution

It presents a novel non-Abelian kagome lattice model with analytically tunable flat bands and characterizes its $Z_2$ topological phases using Pfaffian and symmetry-based invariants.

Findings

Flat bands can be tuned from top to bottom of the band structure.

All gapped phases are adiabatically connected without closing the gap.

The model exhibits $Z_2$ quantum spin Hall topological phases.

Abstract

We introduce a non-Abelian kagome lattice model that has both time-reversal and inversion symmetries and study the flat band physics and topological phases of this model. Due to the coexistence of both time-reversal and inversion symmetries, the energy bands consist of three doubly degenerate bands whose energy and conditions for the presence of flat bands could be obtained analytically, allowing us to tune the flat band with respect to the other two dispersive bands from the top to the middle and then to the bottom of the three bands. We further study the gapped phases of the model and show that they belong to the same phase as the band gaps only close at discrete points of the parameter space, making any two gapped phases adiabatically connected to each other without closing the band gap. Using the Pfaffian approach based on the time-reversal symmetry and parity characterization from the inversion symmetry, we calculate the bulk topological invariants and demonstrate that the unique gapped phases belong to the $Z_2$ quantum spin Hall phase, which is further confirmed by the edge state calculations.