Interplay of electron-phonon interaction and Rashba spin-orbit coupling in the Kane-Mele model

Abstract

The quantum phase transition from mobile to immobile polaron within the framework of the Kane-Mele-Holstein model is investigated. The phonon degrees of freedom in the model are eliminated using a variational ansatz based on modified Lang-Firsov transformation within the variational approach to obtain the effective or polaronic Kane-Mele model. The effective model is then studied to understand the effect of electron-phonon interaction on the electronic structure of both bulk graphene and zigzag nanoribbons. The results reveal a significant band renormalization, abrupt (or continuous) nature of the quantum phase transition in the adiabatic (or anti-adiabatic) regime, and the disruption of topological insulating behavior due to strong electron-phonon interaction.