A 2D model of the pseudogap state is considered on the basis of the scenario of strong electron scattering by short-range-order fluctuations of the “dielectric” (antiferromagnetic or charge density wave) type. A system of recurrence relations is constructed for a one-particle Green’s function and the vertex part, describing the interaction of electrons with an external field. This system takes into account all Feynman diagrams for electron scattering at short-range-order fluctuations. The results of detailed calculations of optical conductivity are given for various geometries (topologies) of the Fermi surface, demonstrating both the effects of pseudogap formation in the electron spectrum and the localization effects. The obtained results are in qualitative agreement with experimental data for underdoped HTSC cuprates.
Anomalous properties of the normal state of a strongly correlated electron system described by an attractive extended Hubbard model are investigated. The equations of motion of the Green’s functions are calculated with the two-pole approximation which gives rise to quasiparticle renormalized bands. The two-pole approximation leads to a set of correlation functions. In particular, the antiferromagnetic correlation function plays an important role as a source of anomalies in the normal state of the model. The uniform static magnetic susceptibility as a function of occupation n T and temperature is calculated. At low temperatures, the susceptibility presents a peak for n T ≃ 0.80. The results suggest that it is the onset of short-range antiferromagnetic correlations, which could be a mechanism for the pseudogap. The Fermi surface, defined by the spectral function , is presented for different dopings. It has been observed that above n T ≃ 0.80 the ordinary Fermi surface evolves to a hole pocket with pseudogaps near the antinodal points (0,π) and (π,0).
We have studied the pseudogap formation in the single-particle spectra of the half-filling two-dimensional Hubbard model. Using a Green's function with the one-loop self-energy correction of the spin and charge fluctuations, we have numerically calculated the self-energy, the spectral function, and the density of states in the weak-coupling regime at finite temperature. Pseudogap formations have been observed in both the density of states and the spectral function at the Fermi level. The pseudogap in the spectral function is explained by the non-Fermi-liquid-like nature of the self-energy. The anomalous behavior in the self-energy is caused by both the strong antiferromagnetic spin fluctuation and the nesting condition on the non-interacting Fermi surface. In the present approximation, we find a logarithmic singularity in the integrand of the imaginary part of the self-energy. Concerning the energy dependence of the spectral function and the self-energy, two theorems are proved. They give a necessary condition in the self-energy to produce the pseudogap at the Fermi level. The pseudogap in the spectral function is highly momentum dependent on the Fermi surface. It opens initially in the
(±π,0),
(0,±π) regions as the normal state pseudogap observed in the high-
Tc superconductors and if the interaction is increased, it spreads to other Fermi surface sectors. The anisotropy of the pseudogap is produced by the low-energy enhancement of the spin excitation around
Q=(π,π) and the flatness of the band dispersion around the saddle point.
We have studied the pseudogap formation in the single-particle spectra of the half-filling two-dimensional Hubbard model. Using a Green's function with the one-loop self-energy correction of the spin and charge fluctuations, we have numerically calculated the self-energy, the spectral function, and the density of states in the weak-coupling regime at finite temperatures. Pseudogap formations have been observed in both the density of states and the spectral function at the Fermi level. The pseudogap in the spectral function is explained by the non-Fermi-liquid-like nature of the self-energy. The anomalous behavior in the self-energy is caused by both the strong antiferromagnetic spin fluctuation and the nesting condition on the non-interacting Fermi surface. In the present approximation, we find a logarithmic singularity in the integrand of the self-energy imaginary part. The pseudogap in the spectral function is highly momentum dependent on the Fermi surface. This anisotropy of the pseudogap is produced by the flatness of the band dispersion around the saddle point rather than the nesting condition on the Fermi level.
An exactly soluble one-dimensional model of electrons interacting with order-parameter fluctuations associated with short-range order is considered. The energy and momentum dependence of the electronic self-energy and spectral function are calculated and found to exhibit non-Fermi-liquid features similar to that seen for the two-dimensional Hubbard model: a pseudogap, shadow bands, anomalies in the self-energy, and breakdown of the quasiparticle picture. Deviations from Fermi-liquid behavior are largest close to the Fermi surface and as the correlation length increases.
It is generally believed that in a 2D metal, whose ground state is antiferromagnetically ordered with
Q=(π,π), thermal (static) magnetic fluctuations give rise to precursor behavior above
TN, in which the spectral function of a hot fermion (the one for which
k and
k+Q are Fermi surface points) contains two peaks, separated by roughly the same energy as in the antiferromagnetically ordered state. The two peaks persist in some range of
T>TN and eventually merge into a single peak at zero frequency. This behavior is obtained theoretically by departing from free fermions in a paramagnet and evaluating the dressed fermionic Green's function by summing up infinite series of diagrams with contributions from thermal magnetic fluctuations. We show, following [Y.M. Vilk and A.-M. S. Tremblay, J. Phys. I France
7 1309 (1997)] that keeping vertex renormalization diagrams in these series is crucial as other terms only broaden the spectral function of a hot fermion, but do not shift its maximum away from zero frequency. As the consequence, the magnetic pseudogap should be treated as an input for theories that neglect vertex corrections, like, e.g., Eliashberg theory for magnetically-mediated superconductivity. We also analyze the potential pseudogap behavior at
T=0. We argue that it may exist, but only at a finite correlation length, and not as a precursor to antiferromagnetism.