A detailed theoretical description is provided of the narrow low-energy peak in the ARPES response of superconducting optimally doped and weakly underdoped BSCCO near the van Hove point. The pseudogap is taken to be due to electron-paramagnon scattering. The narrow peak is antiadiabatic: it consists of electrons which are so slow that the scattering is not effective in suppressing their spectral strength. We find two temperature regimes for the pseudogap. The low-temperature one is relevant for experiment in BSCCO, where the paramagnon band-edge is much higher than the temperature. The high-temperature regime occurs when the band-edge is lower than the temperature. It is characterized by hot spots when the band-edge is finite, and develops a macroscopic antiferromagnetic potential when it vanishes. We argue that it is relevant for the electron-doped high-Tc compounds. Our work gives a connection between the simultaneous appearance of a magnetic resonance and a narrow low-energy feature in ARPES at the superconducting transition in BSCCO. In the model, both can be obtained by switching the paramagnon damping from supercritical to subcritical, without even including the superconducting correlations explicitly. The leading edge scale of the narrow peak is controlled by the chemical potential and is incidental to the pseudogap mechanism, whose physical scale is given by the high-energy 'hump.'
Strongly correlated electrons in copper oxide planes are modeled by a random tiling of CuO4 molecules at finite temperatures. This model is a non-perturbative extension of Gutzwiller's variational assumption. An effective one-particle theory is constructed through the use of a combinatorial transform to express the problem in momentum space, without averaging over occupation numbers in real space. Temporal correlations are lost, because of the Gutzwiller approximation, implemented by taking one kind of spins to be static. Thermodynamic functions can be computed at any temperature and filling. A Mott-Hubbard transition is found in doping, but cannot be crossed in temperature. The effective Fermi liquid can be strongly renormalized, though it does not break down. In the derivation of the model, a formal connection between projected hopping and pair confinement is established.
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