# Finite frequency noise in chiral Luttinger liquid coupled to phonons

## TL;DR

This paper investigates how electron-phonon interactions influence transport and noise in quantum Hall edge states at filling factor one, revealing significant modifications to current and noise characteristics.

## Contribution

It introduces a Bogoliubov-Valatin transformation to analyze the low-energy spectrum of electron-phonon coupled systems and computes tunneling current and noise in this context.

## Key findings

- Electron-phonon coupling splits the spectrum into distinct modes with different velocities.
- Electron-phonon interaction significantly alters noise and current relations compared to free electrons.
- The study provides perturbative calculations of tunneling current and finite frequency noise under dc and ac biases.

## Abstract

We study transport between Quantum Hall (QH) edge states at filling factor $\nu = 1$ in the presence of electron-acoustic-phonon coupling. Performing a Bogoliubov-Valatin (BV) trasformation the low-energy spectrum of interacting electron-phonon system is presented. The electron-phonon interaction splits the spectrum into charged and neutral "downstream" and neutral "upstream" modes with different velocities. In the regimes of dc and periodic ac biases the tunelling current and non-equilibrium finite frequency non-symmetrized noise are calculated perturbatively in tunneling coupling of quantum point contact (QPC). We show that the presence of electron-phonon interaction strongly modifies noise and current relations compared to free-fermion case.