# Extremely Correlated Fermi Liquid theory of the $t$-$J$ model in 2 dimensions: Low Energy properties

## TL;DR

This paper develops an extremely correlated Fermi liquid theory for the 2D t-J model, analyzing low energy properties, quasiparticle behavior, and transport phenomena across various doping levels and temperatures.

## Contribution

It introduces a set of equations for Greens functions that captures low energy features of the 2D t-J model, including momentum dependence and doping effects, extending previous high-dimensional results.

## Key findings

- Quasiparticle weight and decay rate vary with density and temperature.
- Resistivity and Hall conductivity show strong thermal sensitivity.
- Doping sign change alters resistivity curvature, explaining experimental differences.

## Abstract

Low energy properties of the metallic state of the 2-dimensional tJ model are presented at various densities and temperatures for second neighbor hopping t', with signs that are negative or positive corresponding to hole or electron doping. The calculation employs a closed set of equations for the Greens functions obtained from the extremely correlated Fermi liquid theory. These equations, when used in $d=\infty$ reproduce most of the known low energies features of the $U=\infty$ Hubbard model. In 2-dimensions we are able to study the variations due to the superexchange J. The resulting Dyson self energy is found to be momentum dependent as expected. The density and temperature dependent quasiparticle weight, decay rate and the peak spectral heights over the Brillouin zone are calculated. We also calculate the resistivity, Hall conductivity and cotangent of the Hall angle in experimentally relevant units. These display significant thermal sensitivity for density n >~ 0.8, signifying an effective Fermi-liquid temperature scale which is two or three orders of magnitude below the bare bandwidth. Flipping the sign of the hopping t', i.e. studying hole versus electron doping, is found to induce a change in curvature of the temperature dependent resistivity from convex to concave at low temperatures. Our results provide a natural route for understanding the observed difference in the temperature dependent resistivity of strongly correlated electron-doped and hole-doped matter.