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 quasistatic limit $\pi T\gg {\omega }_{\mathrm{sf}},$ found in the intermediate (pseudoscaling) regime of the magnetic phase diagram of cuprate superconductors, 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 $\mathbf{k}=(\pi ,0)]$ and cold [around $\mathbf{k}=(\pi /2,\pi /2)]$ 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. Due to this transfer of spectral weight to higher energies, the low frequency spectral weight of hot states is strongly reduced but couples very strongly to the spin excitations of the system. For realistic values of the antiferromagnetic correlation length, their Fermi surface changes its general shape only slightly but the strong scattering of hot states makes the Fermi surface crossing invisible above a pseudogap temperature $T_{*}.$ 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.