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Ukrainian Journal of Physics

Potential Electron Scattering by Phosphorus Atom

Irina Bariakhtar, Alexander Nazarenko

Published Jun 1, 2014• 0 citations
Publisher

Abstract

The normal state temperature one- and two-particle Green’s functions are calculated within the framework of the conserving self-consistent approximation accounting for the fluctuations in the particle-particle channel for the attractive Hubbard model. The Pad´e continuation to the complex plane is used to study the pole structure of the retarded one-particle Green’s function. The momentum and temperature dependences of the positions of the leading quasiparticle poles are consistent with Bogolyubov’s picture, when the second leading pole emerges and rapidly moves toward the real axes. The non-Fermi liquid behavior of the first leading pole is detected at the intermediate coupling. The two-particle Green’s function is used to calculate the temperature dependence of the uniform static spin susceptibility, which is shown to exhibit the diamagnetic tendency, as the system approaches the superconducting phase transition.

DOI
10.15407/ujpe59.06.0596

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The normal state temperature one- and two-particle Green’s functions are calculated within the framework of the conserving self-consistent approximation accounting for the fluctuations in the particle-particle channel for the attractive Hubbard model. The Pad´e continuation to the complex plane is used to study the pole structure of the retarded one-particle Green’s function. The momentum and temperature dependences of the positions of the leading quasiparticle poles are consistent with Bogolyubov’s picture, when the second leading pole emerges and rapidly moves toward the real axes. The non-Fermi liquid behavior of the first leading pole is detected at the intermediate coupling. The two-particle Green’s function is used to calculate the temperature dependence of the uniform static spin susceptibility, which is shown to exhibit the diamagnetic tendency, as the system approaches the superconducting phase transition.
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 h~Si · ~Sji 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 nT and temperature is calculated. At low temperatures, the susceptibility presents a peak for nT ≃ 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 A(ω = 0,~k), is presented for different dopings. It has been observed that above nT ≃ 0.80 the ordinary Fermi surface evolves to a hole-pocket with pseudogaps near the antinodal points (0, π) and (π, 0).
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).
A frequency- and momentum-renormalization-group acceleration together with an analytical approach is used to obtain the retarded Green's function in the self-consistent and conserving fluctuation-exchange (FLEX) approximation for the two-dimensional Hubbard model in the normal state and in the superconducting state. The analytical expressions for this approach are given. For band-fillings near half filling the self-energy in the normal state exhibits Fermi-liquid behaviour for, low temperatures and frequencies near the chemical potential, if the momentum is chosen near the Fermi-surface. However due to the presence of large many body effects the observed Fermi-liquid region near the chemical potential and near the Fermi-surface is very small. Results for the single particle density of states, the occupation number and the spectral function are presented. The superconducting state with symmetry is obtained for U = 2 to U = 6 and a (U, n)-phase diagram for the transition temperature Tc is presented. A maximum Tc/t of 0.0275 is obtained for U = 6 near half filling.
The effect of static fluctuations in the phase of the order parameter on the normal and superconducting properties of a 2D system with attractive four-fermion interaction is studied. Analytic expressions for the fermion Green’s function, its spectral density, and the density of states are derived in the approximation where the coupling between the spin and charge degrees of freedom is neglected. The resulting single-particle Green’s function clearly demonstrates a non-Fermi-liquid behavior. The results show that as the temperature increases through the 2D critical temperature, the widths of the quasiparticle peaks broaden significantly.
We analyse the behaviour of correlated electrons described by Hubbard-like models at intermediate coupling. We argue that with increasing interaction a pole in a generic two-particle Green function is approached. The pole signals condensation of electron-hole pairs and a metal-insulator transition at half-filling. The two-particle singularity calls for a sophisticated renormalization of the interaction strength. A self-consistent diagrammatic technique with renormalized two-particle Green functions is developed. The theory is based on a linked-cluster expansion for the thermodynamic potential with electron-electron interaction as the propagator. The simplest theory with full vertex renormalization, summing self-consistently multiple scatterings from two electron-hole channels, is proposed. We obtain an approximation with a generating functional in closed form enabling us to handle appropriately singularities in two-particle Green functions. The approximation is shown to be asymptotically exact in an external magnetic field close to the fully polarized ferromagnetic state at half-filling and zero temperature.
We have investigated the attractive Hubbard model in the low-density limit for the 2D square lattice using the ladder approximation for the vertex function in a self-consistent, conserving formulation. In the parameter region where the on-site attraction is of the order of the bandwidth, we found no evidence of a pseudo-gap. Furthermore, we have observed that the suppression of the Fermi surface known to destroy superconductivity in one and two dimensions, when these systems are treated using a non-self-consistent theory (Schmitt-Rink, Varma C M and Ruckenstein A E 1989 Phys. Rev. Lett. 63 445), does not occur when pair-pair interactions are included. However, we do find a quasi-particle lifetime that varies linearly with temperature, which is similar to the findings from many experiments. Thus, although this system has a Fermi surface, it shows non-Fermi-liquid-type behaviour over a wide temperature range. We stress that our work uses thermal Green's functions along the real-time axis, and thus allows for a more accurate determination of the dynamical properties of a model than theories that require extrapolations from the imaginary-frequency axis.