Kohn-Luttinger instability of the t-t' Hubbard model in two dimensions: variational approach

An effective Hamiltonian for the Kohn-Luttinger superconductor is constructed and solved in the BCS approximation. The method is applied to the t-t' Hubbard model in two dimensions with the following results: (i) The superconducting phase diagram at half filling is shown to provide a weak-coupling analog of the recently proposed spin liquid state in the J_1-J_2 Heisenberg model. (ii) In the parameter region relevant for the cuprates we have found a nontrivial energy dependence of the gap function in the dominant d-wave pairing sector. The hot spot effect in the angular dependence of the superconducting gap is shown to be quite weak

Magnetic and superconducting instabilities of the Hubbard model at the van Hove filling

We use a novel temperature-flow renormalization group technique to analyze magnetic and superconducting instabilities in the two-dimensional t-t' Hubbard model for particle densities close to the van Hove filling as a function of the next-nearest neighbor hopping t'. In the one-loop flow at the van Hove filling, the characteristic temperature for the flow to strong coupling is suppressed drastically around t'_c approx. -0.33t, suggesting a quantum critical point between d-wave pairing at moderate t'>t'_c and ferromagnetism for t'<t'_c. Upon increasing the particle density in the latter regime the leading instability occurs in the triplet pairing channel.Comment: 4 pages, to appear in Physical Review Letter

The Superconducting Instabilities of the non half-filled Hubbard Model in Two Dimensions

The problem of weakly correlated electrons on a square lattice is formulated in terms of one-loop renormalization group. Starting from the action for the entire Brillouin zone (and not with a low-energy effective action) we reduce successively the cutoff $\Lambda$ about the Fermi surface and follow the renormalization of the coupling $U$ as a function of three energy-momenta. We calculate the intrinsic scale $T_{co}$ where the renormalization group flow crosses over from the regime ($\Lambda > T_{co}$) where the electron-electron (e-e) and electron-hole (e-h) terms are equally important to the regime ($\Lambda < T_{co}$) where only the e-e term plays a role. In the low energy regime only the pairing interaction $V$ is marginally relevant, containing contributions from all renormalization group steps of the regime $\Lambda > T_{co}$. After diagonalization of $V_{\Lambda =T_{co}}$, we identify its most attractive eigenvalue $\lambda _{\min}$. At low filling, $\lambda _{\min}$ corresponds to the $B_2$ representation ($d_{xy}$ symmetry), while near half filling the strongest attraction occurs in the $B_1$ representation ($d_{x^2-y^2}$ symmetry). In the direction of the van Hove singularities, the order parameter shows peaks with increasing strength as one approaches half filling. Using the form of pairing and the structure of the renormalization group equations in the low energy regime, we give our interpretation of ARPES experiments trying to determine the symmetry of the order parameter in the Bi2212 high-$T_{c}$ compound.Comment: 24 pages (RevTeX) + 11 figures (the tex file appeared incomplete

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

Crossover of superconducting properties and kinetic-energy gain in two-dimensional Hubbard model

Superconductivity in the Hubbard model on a square lattice near half filling is studied using an optimization (or correlated) variational Monte Carlo method. Second-order processes of the strong-coupling expansion are considered in the wave functions beyond the Gutzwiller factor. Superconductivity of d_x^2-y^2-wave is widely stable, and exhibits a crossover around U=U_co\sim 12t from a BCS type to a new type. For U\gsim U_co (U\lsim U_co), the energy gain in the superconducting state is derived from the kinetic (potential) energy. Condensation energy is large and \propto exp(-t/J) [tiny] on the strong [weak] coupling side of U_co. Cuprates belong to the strong-coupling regime.Comment: 4 pages, 6 figure

Collective modes in a system with two spin-density waves: the `Ribault' phase of quasi-one-dimensional organic conductors

We study the long-wavelength collective modes in the magnetic-field-induced spin-density-wave (FISDW) phases experimentally observed in organic conductors of the Bechgaard salts family, focusing on phases that exhibit a sign reversal of the quantum Hall effect (Ribault anomaly). We have recently proposed that two SDW's coexist in the Ribault phase, as a result of Umklapp processes. When the latter are strong enough, the two SDW's become circularly polarized (helicoidal SDW's). In this paper, we study the collective modes which result from the presence of two SDW's. We find two Goldstone modes, an out-of-phase sliding mode and an in-phase spin-wave mode, and two gapped modes. The sliding Goldstone mode carries only a fraction of the total optical spectral weight, which is determined by the ratio of the amplitude of the two SDW's. In the helicoidal phase, all the spectral weight is pushed up above the SDW gap. We also point out similarities with phase modes in two-band or bilayer superconductors. We expect our conclusions to hold for generic two-SDW systems.Comment: Revised version, 25 pages, RevTex, 7 figure

Geometrical frustration induced (semi-)metal to insulator transition

We study the low-energy properties of the geometrically frustrated Hubbard model on a three-dimensional pyrochlore lattice and a two-dimensional checkerboard lattice on the basis of the renormalization group method and mean field analysis. It is found that in the half-filling case, a (semi-)metal to insulator transition (MIT) occurs. Also, in the insulating phase, which has a spin gap, the spin rotational symmetry is not broken, while charge ordering exists. The results are applied to the description of the MIT observed in the pyrochlore system ${\rm Tl_2Ru_2O_7}$.Comment: 4 pages, 5 figure

Landau's quasi-particle mapping: Fermi liquid approach and Luttinger liquid behavior

A continuous unitary transformation is introduced which realizes Landau's mapping of the elementary excitations (quasi-particles) of an interacting Fermi liquid system to those of the system without interaction. The conservation of the number of quasi-particles is important. The transformation is performed numerically for a one-dimensional system, i.e. the worst case for a Fermi liquid approach. Yet evidence for Luttinger liquid behavior is found. Such an approach may open a route to a unified description of Fermi and Luttinger liquids on all energy scales.Comment: 4 pages, 3 figures included, final version to appear in Phys. Rev. Lett., references updated, slight re-focus on the treatment of all energy scale

W=0 pairing in Hubbard and related models of low-dimensional superconductors

Lattice Hamiltonians with on-site interaction $W$ have W=0 solutions, that is, many-body {\em singlet} eigenstates without double occupation. In particular, W=0 pairs give a clue to understand the pairing force in repulsive Hubbard models. These eigenstates are found in systems with high enough symmetry, like the square, hexagonal or triangular lattices. By a general theorem, we propose a systematic way to construct all the W=0 pairs of a given Hamiltonian. We also introduce a canonical transformation to calculate the effective interaction between the particles of such pairs. In geometries appropriate for the CuO$_{2}$ planes of cuprate superconductors, armchair Carbon nanotubes or Cobalt Oxides planes, the dressed pair becomes a bound state in a physically relevant range of parameters. We also show that W=0 pairs quantize the magnetic flux like superconducting pairs do. The pairing mechanism breaks down in the presence of strong distortions. The W=0 pairs are also the building blocks for the antiferromagnetic ground state of the half-filled Hubbard model at weak coupling. Our analytical results for the $4\times 4$ Hubbard square lattice, compared to available numerical data, demonstrate that the method, besides providing intuitive grasp on pairing, also has quantitative predictive power. We also consider including phonon effects in this scenario. Preliminary calculations with small clusters indicate that vector phonons hinder pairing while half-breathing modes are synergic with the W=0 pairing mechanism both at weak coupling and in the polaronic regime.Comment: 42 pages, Topical Review to appear in Journal of Physics C: Condensed Matte

Critical State Behaviour in a Low Dimensional Metal Induced by Strong Magnetic Fields

We present the results of magnetotransport and magnetic torque measurements on the alpha-(BEDT-TTF)2KHg(SCN)4 charge-transfer salt within the high magnetic field phase, in magnetic fields extending to 33 T and temperatures as low as 27 mK. While the high magnetic field phase (at fields greater than ~ 23 T) is expected, on theoretical grounds, to be either a modulated charge-density wave phase or a charge/spin-density wave hybrid, the resistivity undergoes a dramatic drop below ~ 3 K within the high magnetic field phase, falling in an approximately exponential fashion at low temperatures, while the magnetic torque exhibits pronounced hysteresis effects. This hysteresis, which occurs over a broad range of fields, is both strongly temperature-dependent and has several of the behavioural characteristics predicted by critical-state models used to describe the pinning of vortices in type II superconductors in strong magnetic fields. Thus, rather than exhibiting the usual behaviour expected for a density wave ground state, both the transport and the magnetic properties of alpha-(BEDT-TTF)2KHg(SCN)4, at high magnetic fields, closely resembles those of a type II superconductor