Anomalous resistivity and superconductivity in the two-band Hubbard model with one narrow band (Review Article)

We search for marginal Fermi-liquid behavior in the two-band Hubbard model with one narrow band. We consider the limit of low electron densities in the bands and strong intraband and interband Hubbard interactions. We analyze the influence of electron–polaron effect and other mechanisms of mass-enhancement (related to momentum dependence of the self-energies) on effective mass and scattering times of light and heavy components in the clean case (electron–electron scattering and no impurities). We find the tendency towards phaseseparation (towards negative partial compressibility of heavy particles) in a 3D case for large mismatch between the densities of heavy and light bands in a strong coupling limit. We also observe that for low temperatures and equal densities the resistivity in a homogeneous state R(T)~T² behaves in a Fermi-liquid fashion both in 3D and 2D cases. For temperatures higher then effective bandwidth for heavy electrons T>Wh* the coherent behavior of heavy component is totally destroyed. The heavy particles move diffusively in the surrounding of light particles. In the same time the light particles scatter on the heavy ones as if on immobile (static) impurities. In this regime the heavy component is marginal, while the light one is not. The resistivity goes on saturation for T>Wh* in the 3D case. In 2D the resistivity has a maximum and localization tail due to weak-localization corrections of Altshuler–Aronov type. Such behavior of resistivity in 3D could be relevant for some uranium-based heavy-fermion compounds like UNi₂Al₃ and in 2D for some other mixed-valence compounds possibly including the layered manganites. We also consider briefly the superconductive (SC) instability in the model. The leading instability is towards p-wave pairing and is governed by enhanced Kohn–Luttinger mechanism of SC at low electron density. The critical temperature corresponds to the pairing of heavy electrons via polarization of the light ones in 2D

BCS-BEC crossover and nodal points contribution in p-wave resonance superfluids

We solve the Leggett equations for BCS–BEC crossover of the resonance p-wave superfluid. We calculate sound velocity, specific heat and the normal density for the BCS-domain (μ > 0), BEC-domain (μ < 0) as well as for the interesting interpolation point (μ = 0) in the triplet A₁-phase in 3D. We are especially interested in the quasiparticle contribution coming from the zeroes of the superfluid gap in the A1-phase. We discuss the spectrum of orbital waves and the superfluid hydrodynamics at temperature T → 0. In this context we elucidate the difficult problem of chiral anomaly and mass-current nonconcervation appearing in the BCS-domain. We present the different approaches to solve this problem. To clarify this problem experimentally we propose an experiment for the measurement of anomalous current in superfluid A1-phase in the presence of aerogel for ³He and in the presence of Josephson tunneling structures for the ultracold gases in magnetic traps

Two-particle pairing and phase separation in a two-dimensional Bose-gas with one or two sorts of bosons

We present a phase diagram for a dilute two-dimensional Bose-gas on a lattice. For one sort of boson we consider a realistic case of the van der Waals interaction between particles with a strong hard-core repulsion $U$ and a van der Waals attractive tail $V$. For $V< 2 t$, $t$ being a hopping amplitude, the phase diagram of the system contains regions of the usual one-particle Bose-Einstein condensation (BEC). However for $V>2t$ we have total phase separation on a Mott-Hubbard Bose solid and a dilute Bose gas. For two sorts of structureless bosons described by the two band Hubbard model an s-wave pairing of the two bosons of different sort $\neq 0$ is possible. The results we obtained should be important for different Bose systems, including submonolayers of $^4$He, excitons in semiconductors, Schwinger bosons in magnetic systems and holons in HTSC. In the HTSC case a possibility of two-holon pairing in the slave-bosons theories of superconductivity can restore a required charge $2e$ of a Cooper pair.Comment: 10 pages, 2 figure

Manifestation of the Upper Hubbard band in the 2D Hubbard model at low electron density

We consider the 2D Hubbard model in the strong-coupling case (U >> W) and at low electron density (nd² > W and low electron density. Both poles produce nontrivial corrections to Landau Fermi-liquid picture already at low electron density but do not destroy it in 2D

Kohn–Luttinger effect and anomalous pairing in repulsive Fermi-systems at low density

In the large variety of models such as 3D and 2D Fermi-gas model with hard-core repulsion, 3D and 2D Hubbard model, and Shubin–Vonsovsky model we demonstrate the possibility of triplet p-wave pairing at low electron density. We show that the critical temperature of the p-wave pairing can be strongly increased in a spinpolarized case or in a two-band situation already at low density and reach experimentally observable values of (1–5) K. We also discuss briefly d-wave pairing and high-Tc superconductivity with Tc ~ 100 K which arises in the extended Hubbard model and in the generalized t-J model close to half-filling

Detecting Super-Counter-Fluidity by Ramsey Spectroscopy

Spatially selective Ramsey spectroscopy is suggested as a method for detecting the super-counter-fluidity of two-component atomic mixture in optical lattice.Comment: 3pages, no figures, replaced with revised version accepted by PRA. Discussion of the Ramsey pattern specific for topological excitations is adde

Partially gapped fermions in 2D

We compute mean field phase diagrams of two closely related interacting fermion models in two spatial dimensions (2D). The first is the so-called 2D t-t'-V model describing spinless fermions on a square lattice with local hopping and density-density interactions. The second is the so-called 2D Luttinger model that provides an effective description of the 2D t-t'-V model and in which parts of the fermion degrees of freedom are treated exactly by bosonization. In mean field theory, both models have a charge-density-wave (CDW) instability making them gapped at half-filling. The 2D t-t'-V model has a significant parameter regime away from half-filling where neither the CDW nor the normal state are thermodynamically stable. We show that the 2D Luttinger model allows to obtain more detailed information about this mixed region. In particular, we find in the 2D Luttinger model a partially gapped phase that, as we argue, can be described by an exactly solvable model.Comment: v1: 36 pages, 10 figures, v2: minor corrections; equation references to arXiv:0903.0055 updated

Effects of Electron-Electron and Electron-Phonon Interactions in Weakly Disordered Conductors and Heterostuctures

We investigate quantum corrections to the conductivity due to the interference of electron-electron (electron-phonon) scattering and elastic electron scattering in weakly disordered conductors. The electron-electron interaction results in a negative $T^2 \ln T$-correction in a 3D conductor. In a quasi-two-dimensional conductor, $d < v_F/T$ ($d$ is the thickness, $v_F$ is the Fermi velocity), with 3D electron spectrum this correction is linear in temperature and differs from that for 2D electrons (G. Zala et. al., Phys. Rev.B {\bf 64}, 214204 (2001)) by a numerical factor. In a quasi-one-dimensional conductor, temperature-dependent correction is proportional to $T^2$. The electron interaction via exchange of virtual phonons also gives $T^2$-correction. The contribution of thermal phonons interacting with electrons via the screened deformation potential results in $T^4$-term and via unscreened deformation potential results in $T^2$-term. The interference contributions dominate over pure electron-phonon scattering in a wide temperature range, which extends with increasing disorder.Comment: 6 pages, 2figure

Cantor Spectra for Double Exchange Model

We numerically study energy spectra and localization properties of the double exchange model at irrational filling factor. To obtain variational ground state, we use a mumerical technique in momentum space by ``embedded'' boundary condition which has no finite size effect a priori. Although the Hamiltonian has translation invariance, the ground state spontaneously exhibits a self-similarity. Scaling and multi-fractal analysis for the wave functions are performed and the scaling indices $\alpha$'s are obtained. The energy spectrum is found to be a singular continuous, so-called the Cantor set with zero Lebesque measure.Comment: 4 pages, 4 figures, revtex, corrected some typos, accepted for publication in PR