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

We use a solution of the spin fermion model which is valid in the quasistat ic limit pi T much greater than omega(sf), found in the intermediate (pseud oscaling) regime of the magnetic phase diagram of cuprate superconductors, to obtain results for the temperature and doping dependence of the single p article spectral density, the electron-spin fluctuation vertex function, an d the low frequency dynamical spin susceptibility. The resulting strong ani sotropy of the spectral density and the vertex function lead to the qualita tively 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 h igh energy features found in ARPES measurements of the spectral density of the underdoped cuprate super conductors are determined by strong antiferrom agnetic (AF) correlations and incoherent precursor effects of an SDW state, with reduced renormalized effective coupling constant. Due to this transfe r of spectral weight to higher energies; the low frequency spectral weight of hot states is strongly reduced but couples very strongly to the spin exc itations of the system. For realistic values of the antiferromagnetic corre lation length, their Fermi surface changes its general shape only slightly but the strong scattering of hot states makes the Fermi surface crossing in visible above a pseudogap temperature T-*. The electron spin-fluctuation ve rtex function, i.e., the effective interaction of low energy quasiparticles and spin degrees of freedom, is found to be strongly anisotropic and enhan ced 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. [S0163-1829(99)01421-6].