Fermi Liquid Properties of a Two Dimensional Electron System With the Fermi Level Near a van Hove Singularity

We use a diagrammatic approach to study low energy physics of a two dimensional electron system where the Fermi level is near van-Hove singularies in the energy spectrum. We find that in most regions of the $\epsilon_F-T$ phase diagram the system behaves as a normal Fermi liquid rather than a marginal Fermi liquid. Particularly, the imaginary part of the self energy is much smaller than the excitation energy, which implies well defined quasiparticle excitations, and single particle properties are only weakly affected by the presence of the van-Hove singularities. The relevance to high temperature superconductivity is also discussed.Comment: 10 pages, 4 postscript figure

Superconductivity in the two dimensional Hubbard Model.

Quasiparticle bands of the two-dimensional Hubbard model are calculated using the Roth two-pole approximation to the one particle Green's function. Excellent agreement is obtained with recent Monte Carlo calculations, including an anomalous volume of the Fermi surface near half-filling, which can possibly be explained in terms of a breakdown of Fermi liquid theory. The calculated bands are very flat around the (pi,0) points of the Brillouin zone in agreement with photoemission measurements of cuprate superconductors. With doping there is a shift in spectral weight from the upper band to the lower band. The Roth method is extended to deal with superconductivity within a four-pole approximation allowing electron-hole mixing. It is shown that triplet p-wave pairing never occurs. Singlet d_{x^2-y^2}-wave pairing is strongly favoured and optimal doping occurs when the van Hove singularity, corresponding to the flat band part, lies at the Fermi level. Nearest neighbour antiferromagnetic correlations play an important role in flattening the bands near the Fermi level and in favouring superconductivity. However the mechanism for superconductivity is a local one, in contrast to spin fluctuation exchange models. For reasonable values of the hopping parameter the transition temperature T_c is in the range 10-100K. The optimum doping delta_c lies between 0.14 and 0.25, depending on the ratio U/t. The gap equation has a BCS-like form and (2*Delta_{max})/(kT_c) ~ 4.Comment: REVTeX, 35 pages, including 19 PostScript figures numbered 1a to 11. Uses epsf.sty (included). Everything in uuencoded gz-compressed .tar file, (self-unpacking, see header). Submitted to Phys. Rev. B (24-2-95

Phase transitions in two-dimensional anisotropic quantum magnets

We consider quantum Heisenberg ferro- and antiferromagnets on the square lattice with exchange anisotropy of easy-plane or easy-axis type. The thermodynamics and the critical behaviour of the models are studied by the pure-quantum self-consistent harmonic approximation, in order to evaluate the spin and anisotropy dependence of the critical temperatures. Results for thermodynamic quantities are reported and comparison with experimental and numerical simulation data is made. The obtained results allow us to draw a general picture of the subject and, in particular, to estimate the value of the critical temperature for any model belonging to the considered class.Comment: To be published on Eur. Phys. J.

Specific Heat of the 2D Hubbard Model

Quantum Monte Carlo results for the specific heat c of the two dimensional Hubbard model are presented. At half-filling it was observed that $c \sim T^2$ at very low temperatures. Two distinct features were also identified: a low temperature peak related to the spin degrees of freedom and a higher temperature broad peak related to the charge degrees of freedom. Away from half-filling the spin induced feature slowly disappears as a function of hole doping while the charge feature moves to lower temperature. A comparison with experimental results for the high temperature cuprates is discussed.Comment: 6 pages, RevTex, 11 figures embedded in the text, Submitted to Phys. Rev.

Superconducting and pseudogap phases from scaling near a Van Hove singularity

We study the quantum corrections to the Fermi energy of a two-dimensional electron system, showing that it is attracted towards the Van Hove singularity for a certain range of doping levels. The scaling of the Fermi level allows to cure the infrared singularities left in the BCS channel after renormalization of the leading logarithm near the divergent density of states. A phase of d-wave superconductivity arises beyond the point of optimal doping corresponding to the peak of the superconducting instability. For lower doping levels, the condensation of particle-hole pairs due to the nesting of the saddle points takes over, leading to the opening of a gap for quasiparticles in the neighborhood of the singular points.Comment: 4 pages, 6 Postscript figures, the physical discussion of the results has been clarifie

Electronic susceptibilities in systems with anisotropic Fermi surfaces

The low temperature dependence of the spin and charge susceptibilities of an anisotropic electron system in two dimensions is analyzed. It is shown that the presence of inflection points at the Fermi surface leads, generically, to a $T \log T$ dependence, and a more singular behavior, $\chi \sim T ^{3/4} \log T$, is also possible. Applications to quasi two-dimensional materials are discussed.Comment: 8 pages, 5 figures, revtex 4 styl

Heavy-fermion and spin-liquid behavior in a Kondo lattice with magnetic frustration

We study the competition between the Kondo effect and frustrating exchange interactions in a Kondo-lattice model within a large-${\cal N}$ dynamical mean-field theory. We find a T=0 phase transition between a heavy Fermi-liquid and a spin-liquid for a critical value of the exchange $J_c = T_{K}^0$, the single-impurity Kondo temperature. Close to the critical point, the Fermi liquid coherence scale $T^\star$ is strongly reduced and the effective mass strongly enhanced. The regime $T>T^\star$ is characterized by spin-liquid magnetic correlations and non-Fermi-liquid properties. It is suggested that magnetic frustration is a general mechanism which is essential to explain the large effective mass of some metallic compounds such as LiV$_2$O$_4$.Comment: 7 pages, 1 figure. Late

Thermodynamic properties of the periodic Anderson model:X-boson treatment

We study the specific dependence of the periodic Anderson Model (PAM) in the limit of $U=\infty$ employing the X-boson treatment in two fifferent regimes of the PAM: the heavy fermion Kondo (HF-K) and the heavy fermion local magnetic regime (HF-LMM). We obtain a multiple peak structure for the specific heat in agreement with experimental results as well as the increase of the electronic effective mass at low temperatures associated with the HF-K regime. The entropy per site at low T tends to zero in the HF-K regime, corresponding to a singlet ground state, and it tends to $k_{B}ln(2)$ in the HF-LMM, corresponding to a doublet ground state at each site. The linear coefficient $\gamma(T)=C_{v}/T$ of the specific heat qualitatively agrees with the experimental results obtained for differents materials in the two regimes considered here.Comment: 9 pages, 14 figure

Antiferromagnetic and van Hove Scenarios for the Cuprates: Taking the Best of Both Worlds

A theory for the high temperature superconductors is proposed. Holes are spin-1/2, charge e, quasiparticles strongly dressed by spin fluctuations. Based on their dispersion, it is claimed that the experimentally observed van Hove singularities of the cuprates are likely originated by antiferromagnetic (AF) correlations. From the two carriers problem in the 2D t-J model, an effective Hamiltonian for holes is defined with %no free parameters. This effective model has superconductivity in the ${\rm d_{x^2-y^2}}$ channel, a critical temperature ${\rm T_c \sim 100K}$ at the optimal hole density, ${\rm x=0.15}$, and a quasiparticle lifetime linearly dependent with energy. Other experimental results are also $quantitatively$ reproduced by the theory.Comment: 12 pages, 4 figures (on request), RevTeX (version 3.0), preprint NHMF

Microscopic description of d-wave superconductivity by Van Hove nesting in the Hubbard model

We devise a computational approach to the Hubbard model that captures the strong coupling dynamics arising when the Fermi level is at a Van Hove singularity in the density of states. We rely on an approximate degeneracy among the many-body states accounting for the main instabilities of the system (antiferromagnetism, d-wave superconductivity). The Fermi line turns out to be deformed in a manner consistent with the pinning of the Fermi level to the Van Hove singularity. For a doping rate $\delta \sim 0.2$, the ground state is characterized by d-wave symmetry, quasiparticles gapped only at the saddle-points of the band, and a large peak at zero momentum in the d-wave pairing correlations.Comment: 4 pages, 2 Postscript figure