# Quantum Hall effect induced by electron-phonon interaction

## TL;DR

This paper explores how electron-phonon interactions in 2D semimetals can induce quantum Hall effects through topologically nontrivial insulating phases characterized by Chern-Simons terms.

## Contribution

It demonstrates that phonon-induced insulating phases in 2D semimetals exhibit quantized Hall conductivities linked to topological invariants, revealing a new mechanism for quantum Hall effects.

## Key findings

- Insulating phases break time reversal and sublattice symmetries.
- Effective field theories contain characteristic Chern-Simons terms.
- Quantized Hall conductivities are related to topological invariants.

## Abstract

When phonons couple to fermions in 2D semimetals, the interaction may turn the system into an insulator. There are several insulating phases in which the time reversal and the sublattice symmetries are spontaneously broken. Examples are many-body states commensurate to Haldane's staggered flux model or to lattice models with periodically modulated strain. We find that the effective field theories of these phases exhibit characteristic Chern-Simons terms, whose coefficients are related to the topological invariants of the microscopic model. This implies that the corresponding quantized Hall conductivities characterize these insulating states.