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

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.