# Coexistence of non-Fermi liquid and Fermi liquid self-energies at all dopings in cuprates

## TL;DR

This study uses a self-consistent Hubbard model with a momentum-dependent density-fluctuation method to show that cuprates exhibit coexisting non-Fermi liquid and Fermi-liquid self-energies across all dopings, influencing their transport properties.

## Contribution

It provides a detailed momentum-dependent analysis of self-energies in cuprates, revealing their coexistence and doping-dependent behavior using a novel self-consistent approach.

## Key findings

- NFL self-energy dominates in the antinodal region at all dopings.
- Resistivity exponent n approaches 1 near optimal doping.
- Nodal regions exhibit FL-like self-energies even in NFL states.

## Abstract

Various angle-dependent measurements in hole-doped cuprates suggested that Non-Fermi liquid (NFL) and Fermi-liquid (FL) self-energies coexist in the Brillouin zone. Moreover, it is also found that NFL self-energies survive up to the overdoped region where the resistivity features a global FL-behavior. To address this problem, here we compute the momentum dependent self-energy from a single band Hubbard model. The self-energy is calculated self-consistently by using a momentum-dependent density-fluctuation (MRDF) method. One of our main result is that the computed self-energy exhibits a NFL-like frequency dependence only in the antinodal region, and FL-like behavior elsewhere, and retains its analytic form at all momenta and dopings. The dominant source of NFL self-energy in the antinodal region stems from the self-energy-dressed fluctuations between the itinerant and localized densities as self-consistency is invoked. We also calculate the DC conductivity by including the full momentum dependent self-energy. We find that the resistivity-temperature exponent n becomes 1 near the optimal doping, while the NFL self-energy occupies largest momentum-space volume. Surprisingly, even in the NFL state near the optimal doping, the nodal region contains FL-like self-energies; while in the under- and over-dopings (n ~ 2), the antinodal region remains NFL-like. These results highlight the non-local correlation physics in cuprates and in other similar intermediately correlated materials, where a direct link between the microscopic single-particle spectral properties and the macroscopic transport behavior can not be well established.