Pairing and polarization in systems with retarded interactions

TL;DR

This paper investigates how finite-frequency bosons coupled to electrons induce pairing and polarization, revealing their dependence on coupling strength, boson frequency, and temperature using a path integral and DMFT approach.

Contribution

It introduces an ad hoc distribution function within a DMFT framework to distinguish and analyze electron pairing and boson polarization effects in systems with retarded interactions.

Findings

Pairing and polarization occur at similar couplings when boson frequency is below bandwidth.

For high boson frequency, pairing can exist without polarization at low temperatures.

The phenomena's relationship depends on temperature and boson frequency, with distinct regimes identified.

Abstract

In a system where a boson (e.g, a phonon) of finite frequency $\omega_0$ is coupled to electrons, two phenomena occur as the coupling is increased: electron pairing and polarization of the boson field. Within a path integral formalism and a Dynamical Mean-Field approach, we introduce {\it ad hoc} distribution function which allow us to pinpoint the two effects. When $\omega_0$ is smaller than the bandwidth $D$, pairing and polarization occur for fairly similar couplings for all considered temperatures. When $\omega_0 > D$, the two phenomena tend to coincide only for $T \gg \omega_0$, but are no longer tied for low temperatures so that a state of paired particles without finite polarization is stabilized.