Impurity with a resonance in the vicinity of the Fermi energy

TL;DR

This paper investigates how a resonance impurity at the Fermi energy affects the surrounding Fermi gas, revealing a new length scale and its implications for density and dynamics, relevant to Fermi-polaron physics.

Contribution

It introduces a model-independent analysis of impurity-induced density deformation and explores its effects across various conditions, including finite temperature and quench dynamics.

Findings

Resonance impurity causes a rapid phase shift at the Fermi surface.

A new characteristic length scale emerges from the resonance.

Density deformation depends on the resonance width.

Abstract

We study an impurity with a resonance level whose energy coincides with the Fermi energy of the surrounding Fermi gas. An impurity causes a rapid variation of the scattering phase shift for fermions at the Fermi surface, introducing a new characteristic length scale into the problem. We investigate manifestations of this length scale in the self-energy of the impurity and in the density of the bath. Our calculations reveal a model-independent deformation of the density of the Fermi gas, which is determined by the width of the resonance. To provide a broader picture, we investigate time evolution of the density in quench dynamics, and study the behavior of the system at finite temperatures. Finally, we briefly discuss implications of our findings for the Fermi-polaron problem.