h/2eh/2e--Oscillations for Correlated Electron Pairs in Disordered Mesoscopic Rings

The full spectrum of two interacting electrons in a disordered mesoscopic one--dimensional ring threaded by a magnetic flux is calculated numerically. For ring sizes far exceeding the one--particle localization length $L_1$ we find several $h/2e$--periodic states whose eigenfunctions exhibit a pairing effect. This represents the first direct observation of interaction--assisted coherent pair propagation, the pair being delocalized on the scale of the whole ring.Comment: 4 pages, uuencoded PostScript, containing 5 figures

Spectral correlations in the crossover between GUE and Poisson regularity: on the identification of scales

Motivated by questions of present interest in nuclear and condensed matter physics we consider the superposition of a diagonal matrix with independent random entries and a GUE. The relative strength of the two contributions is determined by a parameter $\lambda$ suitably defined on the unfolded scale. Using results for the spectral two-point correlator of this model obtained in the framework of the supersymmetry method we focus attention on two different regimes. For $\lambda$ << 1 the correlations are given by Dawson's integral while for $\lambda$ >> 1 we derive a novel analytical formula for the two-point function. In both cases the energy scales, in units of the mean level spacing, at which deviations from pure GUE behavior become noticable can be identified. We also derive an exact expansion of the local level density for finite level number.Comment: 15 pages, Revtex, no figures, to be published in special issue of J. Math. Phys. (1997

Influence of spin on the persistent current of strongly interacting electrons

The lowest eigenenergies of few, strongly interacting electrons in a one--dimensional ring are studied in the presence of an impurity barrier. The persistent current $\:I\:$, periodic in an Aharonov--Bohm flux penetrating the ring, is strongly influenced by the electron spin. The impurity does not remove discontinuities in $\:I\:$ at zero temperature. The total electron spin of the ground state oscillates with the flux. Strong electron--electron interaction enhances $\:I\:$, albeit not up to the value of the clean ring which itself is smaller than $\:I\:$ for free electrons. $\:I\:$ disappears on a temperature scale that depends exponentially on the electron density. In the limit of very strong interaction the response to small fluxes is diamagnetic.Comment: Latex file, 15 pages, 13 figures available in uuencoded PostScript from the autho

Mesoscopic Luttinger Liquid Theory in an Aharonov-Bohm Ring

A careful study on the mesoscopic PC in a Luttinger liquid ring is carried out. It is shown that discreteness plays an important role in calculating the PC caused by the magnetic flux. At zero temperature, the current is shown to be independent of the interaction even when $g=g_2-g_4$ is not zero. The current becomes enhanced at finite temperatures comparing to the non-interacting case, when the parameter g is positive.Comment: 4 pages, 2 figures. Version to appear in PR

Half-filled Hubbard ring with alternating site potentials in a magnetic field

We have studied a Hubbard ring with alternating site potentials for half filling in presence of a magnetic flux. Using a mean field approach we have calculated the conductivity of such a ring at low and high temperatures. The interplay of correlation, the polarizing field and the chemical modulation in the site potentials tune the conductivity in an interesting fashion. In presence of the modulation in the site energy an appreciable variation in the conductance is observed with the change in flux. Finite size effects are also identified and they are found to be quickly disappearing with increasing system size. Sharp changes in the magnetoconductance is found to disappear at higher temperatures.Comment: 15 page

Between Poisson and GUE statistics: Role of the Breit-Wigner width

We consider the spectral statistics of the superposition of a random diagonal matrix and a GUE matrix. By means of two alternative superanalytic approaches, the coset method and the graded eigenvalue method, we derive the two-level correlation function $X_2(r)$ and the number variance $\Sigma^2(r)$. The graded eigenvalue approach leads to an expression for $X_2(r)$ which is valid for all values of the parameter $\lambda$ governing the strength of the GUE admixture on the unfolded scale. A new twofold integration representation is found which can be easily evaluated numerically. For $\lambda \gg 1$ the Breit-Wigner width $\Gamma_1$ measured in units of the mean level spacing $D$ is much larger than unity. In this limit, closed analytical expression for $X_2(r)$ and $\Sigma^2(r)$ can be derived by (i) evaluating the double integral perturbatively or (ii) an ab initio perturbative calculation employing the coset method. The instructive comparison between both approaches reveals that random fluctuations of $\Gamma_1$ manifest themselves in modifications of the spectral statistics. The energy scale which determines the deviation of the statistical properties from GUE behavior is given by $\sqrt{\Gamma_1}$. This is rigorously shown and discussed in great detail. The Breit-Wigner $\Gamma_1$ width itself governs the approach to the Poisson limit for $r\to\infty$. Our analytical findings are confirmed by numerical simulations of an ensemble of $500\times 500$ matrices, which demonstrate the universal validity of our results after proper unfolding.Comment: 25 pages, revtex, 5 figures, Postscript file also available at http://germania.ups-tlse.fr/frah

Spin and interaction effects on charge distribution and currents in one-dimensional conductors and rings within the Hartree-Fock approximation

Using the self--consistent Hartree-Fock approximation for electrons with spin at zero temperature, we study the effect of the electronic interactions on the charge distribution in a one-dimensional continuous ring containing a single $\delta$ scatterer. We reestablish that the interaction suppresses the decay of the Friedel oscillations. Based on this result, we show that in an infinite one dimensional conductor containing a weak scatterer, the current is totally suppressed because of a gap opened at the Fermi energy. In a canonical ensemble of continuous rings containing many scatterers, the interactions enhance the average and the typical persistent current.Comment: 5 pages, 4 figure

Recovery of the persistent current induced by the electron-electron interaction in mesoscopic metallic rings

Persistent currents in mesoscopic metallic rings induced by static magnetic fields are investigated by means of a Hamiltonian which incorporates diagonal disorder and the electron-electron interaction through a Hubbard term ($U$). Correlations are included up to second order perturbation theory which is shown to work accurately for $U$ of the order of the hopping integral. If disorder is not very strong, interactions increase the current up to near its value for a clean metal. Averaging over ring lengths eliminates the first Fourier component of the current and reduces its value, which remains low after interactions are included.Comment: uuencoded gzipped tar file containing the manuscript (tex file) and four figures (postscript files). Accepted for publication in Solid State Communications. Send e-mail to: [email protected]

Analytical Results for Random Band Matrices with Preferential Basis

Using the supersymmetry method we analytically calculate the local density of states, the localiztion length, the generalized inverse participation ratios, and the distribution function of eigenvector components for the superposition of a random band matrix with a strongly fluctuating diagonal matrix. In this way we extend previously known results for ordinary band matrices to the class of random band matrices with preferential basis. Our analytical results are in good agreement with (but more general than) recent numerical findings by Jacquod and Shepelyansky.Comment: 8 pages RevTex and 1 Figure, both uuencode