Dielectric response of electrons with strong local correlations and long-ranged Coulomb interactions

TL;DR

This paper investigates the dielectric response of electrons in 2D cuprates considering both strong local correlations and long-range Coulomb interactions, using an advanced theoretical framework to compute various dynamical charge and current susceptibilities.

Contribution

It introduces a novel set of formulas for dynamical charge susceptibility and dielectric function within the extremely correlated Fermi liquid theory for a model including long-range Coulomb interactions.

Findings

Calculated charge density fluctuations and dielectric functions for the model.

Identified a characteristic energy scale 3p(3q) related to peaks in the imaginary part of the charge susceptibility.

Presented a comprehensive framework for analyzing dynamical responses in strongly correlated electron systems.

Abstract

Motivated by recent experiments, we append long ranged Coulomb interactions to dominant strong local correlations and study the resulting $t$-$J$-$V_C$ model for the 2-dimensional cuprate materials. This model includes the effect of short ranged Hubbard-Gutzwiller-Kanamori type correlations and long ranged Coulomb interactions on tight binding electrons. We calculate the $ \{\vec{q},\omega\}$ dependent charge density fluctuations in this model using the extremely correlated fermi liquid theory, characterized by quasiparticles with very small weight $Z$. We develop a novel set of formulae to represent the dynamical charge susceptibility and the dielectric function, using a version of the charge-current continuity equation for a band system valid for arbitrary $\vec{q}$. Combining these ingredients, we present results for the dynamical charge susceptibility $\widetilde{\chi}_{\rho\rho}(\vec{q},\omega)$, (longitudinal) dielectric function $\varepsilon(\vec{q},\omega)$, current susceptibility $\widetilde{\chi}_{J J}(\vec{q},\omega)$, conductivity $\sigma(\vec{q},\omega)$, and the plasma frequency for any $\vec{q}$. We also present calculations for the first moment of the structure function and discuss a characteristic energy scale $\Omega_p(\vec{q})$, which locates a peak in $\Im m \, \widetilde{\chi}_{\rho\rho}(\vec{q},\omega)$.