Topological quantum transition driven by charge-phonon coupling in the Haldane Chern insulator

Abstract

In condensed matter physics many features can be understood in terms of their topological properties. Here we report evidence of a topological quantum transition driven by the charge-phonon coupling in the spinless Haldane model on a honeycomb lattice, a well-known prototypical model of Chern insulator. Starting from parameters describing the topological phase in the bare Haldane model, we show that the increasing of the strength of the charge lattice coupling drives the system towards a trivial insulator. The average number of fermions in the Dirac point, characterized by the lowest gap, exhibits a finite discontinuity at the transition point and can be used as direct indicator of the topological quantum transition. Numerical simulations show, also, that the renormalized phonon propagator exhibits a two peak structure across the quantum transition, whereas, in absence of the mass term in the bare Hadane model, there is indication of a complete softening of the effective vibrational mode signaling a charge density wave instability.

5 pages, 4 figures

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• Holstein polaron in a pseudospin-$1$ quantum spin Hall system: first and second order topological phase transitions
• Phonon-mediated intrinsic topological superconductivity in Fermi arcs
• Emergent topological phases and coexistence of gapless and spectral-localized Floquet quantum spin Hall states via electron-phonon interaction
• Topological characterization of magnon-polaron bands and thermal Hall conductivity in a frustrated kagome antiferromagnet
• Emergence of charge density wave and superconducting phase transitions through Lorentz-invariant interactions in the Haldane-Hubbard model
• Real-space topology and charge order in the Haldane-Holstein Model