Effect of electron-phonon coupling on transmission through Luttinger liquid hybridized with resonant level

TL;DR

This paper investigates how electron-phonon interactions influence electron transport in a Luttinger liquid coupled with a resonant level, revealing complex phase behavior and modifications in transmission properties.

Contribution

It introduces a detailed analysis of electron-phonon effects on transport in Luttinger liquids with resonant levels, highlighting new phase transitions and transmission modifications.

Findings

Electron-phonon coupling alters the effective width of the resonant level.

The coupling induces a rich phase diagram with metal-insulator transitions.

Transport properties depend critically on the geometry of the hybridization.

Abstract

We show that electron-phonon coupling strongly affects transport properties of the Luttinger liquid hybridized with a resonant level. Namely, this coupling significantly modifies the effective energy-dependent width of the resonant level in two different geometries, corresponding to the resonant or antiresonant transmission in the Fermi gas. This leads to a rich phase diagram for a metal-insulator transition induced by the hybridization with the resonant level.