Topological phase transition in quantum spin Hall insulator in the presence of charge lattice coupling

TL;DR

This study explores how local electron-phonon interactions can induce a topological phase transition in a quantum spin Hall insulator modeled by the Kane-Mele Hamiltonian, revealing a phonon-mediated gap closing and reopening.

Contribution

It demonstrates that charge-lattice coupling can drive a topological-trivial phase transition in a quantum spin Hall insulator via a gap closing at the M point, using cluster perturbation theory.

Findings

Charge-lattice coupling induces a topological-trivial phase transition.

Phonon Green's function shows a softening peak at the transition.

Quasiparticle dispersion exhibits kinks due to electron-phonon interaction.

Abstract

By using the cluster perturbation theory, we investigate the effects of the local electron-phonon interaction in the quantum spin Hall topological insulator described by the half-filled Kane-Mele model on an honeycomb lattice. Starting from the topological non trivial phase, where the minimal gap is located at the two inequivalent Dirac points of the Graphene, $\text{K}$ and $\text{K}'$, we show that the coupling with quantum phonons induces a topological-trivial quantum phase transition through a gap closing and reopening in the $\text{M}$ point of the Brillouin zone. The average number of fermions in this point turns out to be a direct indicator of the quantum transition pointing out a strong hybridization between the two bare quasiparticle bands of the Kane-Mele model. By increasing the strength of charge-lattice coupling, the phonon Green's propagator displays a two peak structure: the one located at the lowest energy exhibits a softening that is maximum around the topological transition. Numerical simulations provide also evidence of several kinks in the quasiparticle dispersion caused by the coupling of the electrons with the bosonic lattice mode.