Dimensional crossover in Sr2_2RuO4_4 within slave-boson mean-field theory

Motivated by the anomalous temperature dependence of the c-axis resistivity of Sr$_2$RuO$_4$, the dimensional crossover from a network of perpendicular one-dimensional chains to a two-dimensional system due to a weak hybridization between the perpendicular chains is studied. The corresponding two-orbital Hubbard model is treated within a slave-boson mean-field theory (SBMFT) to take correlation effects into account such as the spin-charge separation on the one-dimensional chains. Using an RPA-like formulation for the Green's function of collective spinon-holon excitations the emergence of quasiparticles at low-temperatures is examined. The results are used to discuss the evolution of the spectral density and the c-axis transport within a tunneling approach. For the latter a regime change between low- and high-temperature regime is found in qualitative accordance with experimental data

Effective charging energy for a regular granular metal array

We study the Ambegaokar-Eckern-Sch\"{o}n (AES) model for a regular array of metallic grains coupled by tunnel junctions of conductance $g$ and calculate both paramagnetic and diamagnetic terms in the Kubo formula for the conductivity. We find analytically, and confirm by numerical path integral Monte Carlo methods, that for $0<g<4$ the conductivity obeys an Arrhenius law $\sigma(T)\sim\exp[-E^{*}(g)/T]$ with an effective charging energy $E^{*} (g)$ when the temperature is sufficiently low, due to a subtle cancellation between $T^2$ inelastic-cotunneling contributions in the paramagnetic and diamagnetic terms. We present numerical results for the effective charging energy and compare the results with recent theoretical analyses. We discuss the different ways in which the experimentally observed $\sigma(T)\sim\exp[-\sqrt{T_{0}/T}]$ law could be attributed to disorder.Comment: 5 pages, 3 figures, ReVTeX; added estimates of effective charging energies and discussion of effects of disorde

Coulomb blockade and quantum tunnelling in the low-conductivity phase of granular metals

We study the effects of Coulomb interaction and inter-grain quantum tunnelling in an array of metallic grains using the phase-functional approach for temperatures $T$ well below the charging energy $E_{c}$ of individual grains yet large compared to the level spacing in the grains. When the inter-grain tunnelling conductance $g\gg1$, the conductivity $\sigma$ in $d$ dimensions decreases logarithmically with temperature ($\sigma/\sigma_{0}\sim1-\frac{1}{2\pi gd}\ln(gE_{c}/T)$), while for $g\to0$, the conductivity shows simple activated behaviour ($\sigma \sim \exp(-E_c/T)$). We show, for bare tunnelling conductance $g \gtrsim 1$, that the parameter $\gamma \equiv g(1-2/(g\pi)\ln(gE_{c}/T))$ determines the competition between charging and tunnelling effects. At low enough temperatures in the regime $1\gtrsim \gamma \gg 1/\sqrt{\beta E_{c}}$, a charge is shared among a finite number $N=\sqrt{(E_{c}/T)/\ln(\pi/2\gamma z)}$ of grains, and we find a soft activation behaviour of the conductivity, $\sigma\sim z^{-1}\exp(-2\sqrt{(E_{c}/T)\ln(\pi/2\gamma z)})$, where $z$ is the effective coordination number of a grain.Comment: 11 pages REVTeX, 3 Figures. Appendix added, replaced with published versio

Coherent-incoherent transition in the sub-Ohmic spin-boson model

We study the spin-boson model with a sub-Ohmic bath using a variational method. The transition from coherent dynamics to incoherent tunneling is found to be abrupt as a function of the coupling strength $\alpha$ and to exist for any power $0 < s< 1$, where the bath coupling is described by $J(\omega) \sim \alpha \omega^{s}$. We find non-monotonic temperature dependence of the two-level gap $\tilde{K}$ and a re-entrance regime close to the transition due to non-adiabatic low-frequency bath modes. Differences between thermodynamic and dynamic conditions for the transition as well as the limitations of the simplified bath description are discussed.Comment: 12 pages, 4 figure

Interlayer c-axis transport in the normal state of cuprates

A theoretical model of c-axis transport properties in cuprates is proposed. Inter-plane and in-plane charge fluctuations make hopping between planes incoherent and diffusive (the in-plane momentum is not conserved after tunneling). The non-Drude optical conductivity $\sigma_c(\omega)$ and the power-law temperature dependence of the {\it dc} conductivity are generically explained by the strong fluctuations excited in the process of tunneling. Several microscopic models of the charge fluctuation spectrum are considered.Comment: 8 page

Sum rule analysis of Umklapp processes and Coulomb energy: application to cuprate superconductivity

The third moment frequency sum rule for the density-density correlation function is rederived in the presence of Umklapp processes. Upper and lower bounds on the electron-electron Coulomb energy are derived in two-dimensional and three-dimensional media, and the Umklapp processes are shown to be crucial in determining the spectrum of the density fluctuations (especially for the two-dimensional systems). This and other standard sum rules can be used in conjunction with experimental spectroscopies (electron-energy loss spectroscopy, optical ellipsometry, etc.) to analyse changes of the electron-electron Coulomb energy at the superconducting transition in cuprates

Indications of coherence-incoherence crossover in layered transport

For many layered metals the temperature dependence of the interlayer resistance has a different behavior than the intralayer resistance. In order to better understand interlayer transport we consider a concrete model which exhibits this behavior. A small polaron model is used to illustrate how the interlayer transport is related to the coherence of quasi-particles within the layers. Explicit results are given for the electron spectral function, interlayer optical conductivity and the interlayer magnetoresistance. All these quantities have two contributions: one coherent (dominant at low temperatures) and one incoherent (dominant at high temperatures).Comment: 6 pages, 4 figures, REVTEX

Interlayer hopping properties of electrons in layered metals

A formalism is proposed to study the electron tunneling between extended states, based on the spin-boson Hamiltonian previously used in two-level systems. It is applied to analyze the out--of--plane tunneling in layered metals considering different models. By studying the effects of in--plane interactions on the interlayer tunneling of electrons near the Fermi level, we establish the relation between departure from Fermi liquid behavior driven by electron correlations inside the layer and the out of plane coherence. Response functions, directly comparable with experimental data are obtained