Local phonon mode in a fermionic bath, and its relation to Kondo effect

TL;DR

This paper investigates how a local phonon mode in a metallic environment influences electronic properties, revealing phonon softening, damping, and potential charge-Kondo effects through bosonization analysis.

Contribution

It introduces a detailed bosonization study of a phonon in a fermionic bath, linking phonon dynamics to charge-Kondo phenomena and electronic response modifications.

Findings

Phonon frequency softens in two steps with damping.

Electrons experience an attractive, dynamic interaction due to phonons.

Charge response shows a dip around zero frequency indicating charge-Kondo potential.

Abstract

We have studied the interplay of a local phonon mode embedded in a metallic host (Holstein impurity model) using Abelian bosonization. The phonon frequency softens, which takes place in two steps: first, their frequency starts softening, and acquires finite lifetime. Then oscillations disappear from the response, and two distinct, finite dampings characterize them. Similar behaviour shows up in the spin-boson model. Due to phonons, the electrons experience an attractive, dynamic interaction. As a result, the electronic charge response enhances similarly to the spin response in the Kondo model. The local electronic density of states develops a dip around zero frequency. Thus the chance of charge-Kondo effect emerges.