Effect of a lattice upon an interacting system of electrons: Breakdown of scaling and decay of persistent currents

For an interacting system of N electrons, we study the conditions under which a lattice model of size L with nearest neighbor hopping t and U/r Coulomb repulsion has the same ground state as a continuum model. For a fixed value of N, one gets identical results when the inter-electron spacing to the Bohr radius ratio r_s < r_s^*. Above r_s^*, the persistent current created by an enclosed flux begins to decay and r_s ceases to be the scaling parameter. Three criteria giving similar r_s^* are proposed and checked using square lattices.Comment: 7 pages, 5 postscript figure

The optical conductivity of the quasi one-dimensional conductors: the role of forward scattering by impurities

We calculate the average conductivity sigma (omega) of interacting electrons in one dimension in the presence of a long-range random potential (forward scattering disorder). Taking the curvature of the energy dispersion into account, we show that weak disorder leads to a transport scattering rate that vanishes as omega^2 for small frequency omega. This implies that the real part of the conductivity remains finite for omega -> 0, while the imaginary part diverges. These effects are lost within the usual bosonization approach, which relies on the linearization of the energy dispersion. We discuss our result in the light of a recent experiment.Comment: 5 RevTex pages; more careful comparison with experiments and discussion of interchain hopping added; some references added; to appear in Phys. Rev.

Zn-doping effect on the magnetotransport properties of Bi_{2}Sr_{2-x}La_{x}CuO_{6+\delta} single crystals

We report the magnetotransport properties of Bi_{2}Sr_{2-x}La_{x}Cu_{1-z}Zn_{z}O_{6+\delta} (Zn-doped BSLCO) single crystals with z of up to 2.2%. Besides the typical Zn-doping effects on the in-plane resistivity and the Hall angle, we demonstrate that the nature of the low-temperature normal state in the Zn-doped samples is significantly altered from that in the pristine samples under high magnetic fields. In particular, we observe nearly-isotropic negative magnetoresistance as well as an increase in the Hall coefficient at very low temperatures in non-superconducting Zn-doped samples, which we propose to be caused by the Kondo scattering from the local moments induced by Zn impurities.Comment: 4 pages, 4 figures, final version (one reference added), published in Phys. Rev.

Short Range Interaction Effects on the Density of States of Disordered Two Dimensional Crystals with a half--filled band

The Density of electronic States (DoS) of a two--dimensional square lattice with substitutional impurities is calculated in the presence of short--range electron--electron interactions. In the middle of the energy band, the Bragg reflections off the Brillouin zone boundary are shown to lead to additional quantum corrections to the DoS, the sign of which is opposite to the sign of the Altshuler--Aronov's logarithmic correction. The resulting quantum correction to the DoS at half--filling is positive, i.e. the DoS increases logarithmically as the Fermi energy is approached. However, far from the commensurate points where the Bragg reflections are suppressed, the negative logarithmic corrections to the DoS survive.Comment: 5 pages 2 figure

Quantum Breathers in a Nonlinear Lattice

We study nonlinear phonon excitations in a one-dimensional quantum nonlinear lattice model using numerical exact diagonalization. We find that multi-phonon bound states exist as eigenstates which are natural counterparts of breather solutions of classical nonlinear systems. In a translationally invariant system, these quantum breather states form particle-like bands and are characterized by a finite correlation length. The dynamic structure factor has significant intensity for the breather states, with a corresponding quenching of the neighboring bands of multi-phonon extended states.Comment: 4 pages, RevTex, 4 postscript figures, Physical Relview Letters (in press

Evidence for strong electron-phonon coupling and polarons in the optical response of La_{2-x}Sr_xCuO_4

The normal state optical response of La_{2-x}Sr_xCuO_4 is found to be consistent with a simple multi-component model, based on free carriers with strong electron-phonon interaction, localized polaronic states near 0.15 eV and a mid-infrared band at 0.5 eV. Normal state reflectance and absorbance of La_{1.83}Sr_{0.17}CuO_4 are investigated and their temperature dependence is explained. Both, the ac and dc response are recovered and the quasi-linear behavior of the optical scattering rate up to 3000- 4000 cm^{-1} is found to be consistent with strong electron-phonon interaction, which also accounts for the value of T_c. Although not strictly applicable in the superconducting state, our simple model accounts for the observed penetration depth and the optical response below T_c can be recovered by introducing a small amount of additional carriers. Our findings suggest that the optical response of La_{2-x}Sr_xCuO_4 could be explained both, in the normal and superconducting state, by a simple multi-fluid model with strong electron-phonon interaction if the gap symmetry and the temperature dependence of the 0.5 eV mid-infrared band are adequately taken into account.Comment: 22 pages, REVTeX, 12 figures in ps-fil

Critical temperature of the superfluid transition in bose liquids

A phenomenological criterion for the superfluid transition is proposed, which is similar to the Lindemann criterion for the crystal melting. Then we derive a new formula for the critical temperature, relating $T_{\lambda}$ to the mean kinetic energy per particle above the transition. The suppression of the critical temperature in a sufficiently dense liquid is described as a result of the quantum decoherence phenomenon. The theory can account for the observed dependence of $T_{\lambda}$ on density in liquid helium and results in an estimate $T_{\lambda} \sim 1.1$ K for molecular hydrogen.Comment: 4 pages, 1 fi

Superconductivity in the Pseudogap State due to Fluctuations of Short-Range Order

We analyze the anomalies of superconducting state (s and d-wave pairing) in a simple model of pseudogap state, induced by fluctuations of short - range order (e.g. antiferromagnetic), based on the model Fermi surface with "hot patches". We derive a system of recursion relations for Gorkov's equations which take into account all diagrams of perturbation theory for electron interaction with fluctuations of short-range order. Then we find superconducting transition temperature and gap behavior for different values of the pseudogap width and correlation lengths of short-range order fluctuations. In a similar approximation we derive the Ginzburg-Landau expansion and study the main physical characteristics of a superconductor close to the transition temperature, both as functions of the pseudogap width and correlation length of fluctuations. Results obtained are in qualitative agreement with a number of experiments on underdoped HTSC-cuprates.Comment: 18 pages, 12 figures, RevTeX 3.0, minor misprints corrected, to appear in JET