Microscopic theory of weak pseudogap behavior in the underdoped cuprate superconductors I: General theory and quasiparticle properties

We derive in detail a novel solution of the spin fermion model which is valid in the quasi-static limit pi T<<omega_sf, found in the intermediate (pseudoscaling) regime of the magnetic phase diagram of cuprate superconductors, and use it to obtain results for the temperature and doping dependence of the single particle spectral density, the electron-spin fluctuation vertex function, and the low frequency dynamical spin susceptibility. The resulting strong anisotropy of the spectral density and the vertex function lead to the qualitatively different behavior of_hot_ (around k=(pi,0)) and_cold_ (around k=(pi/2,pi/2)) quasiparticles seen in ARPES experiments. We find that the broad high energy features found in ARPES measurements of the spectral density of the underdoped cuprate superconductors are determined by strong antiferromagnetic (AF) correlations and incoherent precursor effects of an SDW state, with reduced renormalized effective coupling constant. The electron spin-fluctuation vertex function, i.e. the effective interaction of low energy quasiparticles and spin degrees of freedom, is found to be strongly anisotropic and enhanced for hot quasiparticles; the corresponding charge-fluctuation vertex is considerably diminished. We thus demonstrate that, once established, strong AF correlations act to reduce substantially the effective electron-phonon coupling constant in cuprate superconductors.