Superconductivity without attraction in a quasi-one-dimensional metal

An array of one-dimensional conductors coupled by transverse hopping and interaction is studied with the help of a variational wave function. This wave function is devised as to account for one-dimensional correlation effects. We show that under broad conditions our system possesses the superconducting ground state even if no attraction is present. The superconducting mechanism is of many-body nature and deviates substantially from BCS. The phase diagram of the model is mapped. It consists of two ordered phases competing against each other: density wave, spin or charge, and unconventional superconductivity. These phases are separated by the first order transition. The symmetry of the superconducting order parameter is a non-universal property. It depends on particulars of the Hamiltonian. Within the framework of our model possible choices are the triplet $f$-wave and the singlet $d_{xy}$-wave. Organic quasi-one-dimensional superconductors have similar phase diagram.Comment: 12 pages, 2 Encapsulated PostScript figures, revtex4; the model's Hamiltonian is revised as compared to previous version, this revision affects prediction of the order parameter symmetr

Correlations in Chaotic Eigenfunctions at Large Separation

An energy eigenfunction in a classically chaotic system is known to have spatial correlations which (in the limit of small $\hbar$) are governed by a microcanonical distribution in the classical phase space. This result is valid, however, only over coordinate distances which are small compared to any relevant classical distance scales (such as the cyclotron radius for a charged particle in a magnetic field). We derive a modified formula for the correlation function in the regime of large separation. This then permits a complete description, over all length scales, of the statistical properties of chaotic eigenfunctions in the $\hbar\to 0$ limit. Applications to quantum dots are briefly discussed.Comment: 8 pages, 1 figure, RevTeX, eps

Competition between different order parameters in a quasi-one-dimensional superconductor

We show that, under rather general assumptions, the phase diagram of a quasi-one-dimensional repulsive Fermi system consists of two ordered phases: the density wave, spin or charge, and the superconductivity. It is demonstrated that the symmetry of the superconducting order parameter is a non-universal property sensitive to microscopic details of the model. Three potentially stable superconducting states are identified: they are triplet $f$-wave, singlet $d_{x^2-y^2}$-wave, and $d_{xy}$-wave. Presence of multiple competing superconducting states implies that for a real material this symmetry is difficult to predict theoretically and hard to probe experimentally, since artifacts of theoretical approximations or variations in experimental conditions could tip the balance between the superconducting phases.Comment: 6 pages, 1 eps figur

Eigenfunctions of electrons in weakly disordered quantum dots: Crossover between orthogonal and unitary symmetries

A one-parameter random matrix model is proposed for describing the statistics of the local amplitudes and phases of electron eigenfunctions in a mesoscopic quantum dot in an arbitrary magnetic field. Comparison of the statistics obtained with recent results derived from first principles within the framework of supersymmetry technique allows to identify a transition parameter with real microscopic characteristics of the problem. The random-matrix model is applied to the statistics of the height of the resonance conductance of a quantum dot in the regime of the crossover between orthogonal and unitary symmetry classes.Comment: 6 pages (latex), 3 figures available upon request, to appear in Physical Review

Correlations due to localization in quantum eigenfunctions of disordered microwave cavities

Non-universal correlations due to localization are observed in statistical properties of experimental eigenfunctions of quantum chaotic and disordered microwave cavities. Varying energy {E} and mean free path {l} enable us to experimentally tune from localized to delocalized states. Large level-to-level Inverse Participation Ratio (IPR I_{2}) fluctuations are observed for the disordered billiards, whose distribution is strongly asymmetric about . The density auto-correlations of eigenfunctions are shown to decay exponentially and the decay lengths are experimentally determined. All the results are quantitatively consistent with calculations based upon nonlinear sigma-models.Comment: 4 pages, LaTex, 5 .jpg figures. This paper with 5 embedded postscript figures available (PS,PDF) at http://sagar.physics.neu.edu/preprints

Irradiation-induced confinement in a quasi-one-dimensional metal

The anisotropic resistivity of PrBa$_2$Cu$_4$O$_8$ has been measured as a function of electron irradiation fluence. Localization effects are observed for extremely small amounts of disorder corresponding to electron mean-free-paths of order 100 unit cells. Estimates of the localization corrections suggest that this anomalous localization threshold heralds a crossover to a ground state with pronounced one-dimensional character in which conduction electrons become confined to a small cluster of chains.Comment: 4 pages, 4 figure

Low-temperature conductivity of quasi-one-dimensional conductors: Luttinger liquid stabilized by impurities

A new non-Fermi-liquid state of quasi-one-dimensional conductors is suggested in which electronic system exists in a form of collection of bounded Luttinger liquids stabilized by impurities. This state is shown to be stable towards interchain electron hopping at low temperatures. Electronic spectrum of the system contains zero modes and collective excitations of the bounded Luttinger liquids in the segments between impurities. Zero modes give rise to randomly distributed localized electronic levels, and long-range interaction generates the Coulomb gap in the density of states at the Fermi energy. Mechanism of conductivity at low temperatures is phonon-assisted hopping via zero-mode states. At higher voltages the excitations of Luttinger liquid are involved in electron transport, and conductivity obeys power-law dependence on voltage. The results provide a qualitative explanation for recent experimental data for NbSe3 and TaS3 crystals.Comment: 12 pages, 1 figur

From chaos to disorder: Statistics of the eigenfunctions of microwave cavities

We study the statistics of the experimental eigenfunctions of chaotic and disordered microwave billiards in terms of the moments of their spatial distributions, such as the Inverse Participation Ratio (IPR) and density-density auto-correlation. A path from chaos to disorder is described in terms of increasing IPR. In the chaotic, ballistic limit, the data correspond well with universal results from random matrix theory. Deviations from universal distributions are observed due to disorder induced localization, and for the weakly disordered case the data are well-described by including finite conductance and mean free path contributions in the framework of nonlinear sigma models of supersymetry.Comment: 5 pages + 2 JPG figure

Possible co-existence of local itinerancy and global localization in a quasi-one-dimensional conductor

In the chain compound PrBa$_2$Cu$_4$O$_8$ localization appears simultaneously with a dimensional crossover in the electronic ground state when the scattering rate in the chains exceeds the hopping rate between the chains. Here we report the discovery of a large, transverse magnetoresistance in PrBa$_2$Cu$_4$O$_8$ in the localized regime. This result suggests a novel form of localization whereby electrons retain their metallic (quasi-one-dimensional) character over a microscopic length scale despite the fact that macroscopically, they exhibit localized (one-dimensional) behavior.Comment: 4 pages, 4 Figure