Optical conductivity in cluster dynamical mean field theory: formalism and application to high temperature superconductors

TL;DR

This paper develops a formalism for calculating optical conductivity in the Hubbard model using cluster dynamical mean field theory, revealing how doping affects the optical response in high-temperature superconductors.

Contribution

It introduces a formalism including vertex corrections for optical conductivity within cluster DMFT and applies it to high-Tc cuprates, capturing key experimental features.

Findings

Insulating state at one electron per site with a gap matching experiments.

Emergence of a three-component optical structure with doping.

Mid-infrared feature linked to pseudogap in the density of states.

Abstract

The optical conductivity of the one-band Hubbard model is calculated using the 'Dynamical Cluster Approximation' implementation of dynamical mean field theory for parameters appropriate to high temperature copper-oxide superconductors. The calculation includes vertex corrections and the result demonstrates their importance. At densities of one electron per site, an insulating state is found with gap value and above-gap absorption consistent with measurements. As carriers are added the above gap conductivity rapidly weakens and a three component structure emerges, with a low frequency 'Drude' peak, a mid-infrared absorption, and a remnant of the insulating gap. The mid-infrared feature obtained at intermediate dopings is shown to arise from a pseudogap structure in the density of states. On further doping the conductivity evolves to the Drude peak plus weakly frequency dependent tail structure expected for less strongly correlated metals.