Critical quantum chaos in 2D disordered systems with spin-orbit coupling

We examine the validity of the recently proposed semi-Poisson level spacing distribution function P(S), which characterizes “critical quantum chaos”, in 2D disordered systems with spin-orbit coupling. At the Anderson transition we show that the semi-Poisson P(S) can describe closely the critical distribution obtained with averaged boundary conditions, over Dirichlet in one direction with periodic in the other and Dirichlet in both directions. We also obtain a sub-Poisson linear number variance , with asymptotic value . The obtained critical statistics, intermediate between Wigner and Poisson, is discussed for disordered systems and chaotic models. Received 1 September 1999     

Two interacting particles in a disordered chain I: Multifractality of the interaction matrix elements

For N interacting particles in a one dimensional random potential, we study the structure of the corresponding network in Hilbert space. The states without interaction play the role of the “sites”. The hopping terms are induced by the interaction. When the one body states are localized, we numerically find that the set of directly connected “sites” is multifractal. For the case of two interacting particles, the fractal dimension associated to the second moment of the hopping term is shown to characterize the Golden rule decay of the non interacting states and the enhancement factor of the localization length. Received: 17 April 1998 / Accepted: 14 May 1998     

Two interacting particles in a disordered chain II: Critical statistics and maximum mixing of the one body states

For two particles in a disordered chain of length L with on-site interaction U, a duality transformation maps the behavior at weak interaction onto the behavior at strong interaction. Around the fixed point of this transformation, the interaction yields a maximum mixing of the one body states. When (the one particle localization length), this mixing results in weak chaos accompanied by multifractal wave functions and critical spectral statistics, as in the one particle problem at the mobility edge or in certain pseudo-integrable billiards. In one dimension, a local interaction can only yield this weak chaos but can never drive the two particle system to full chaos with Wigner-Dyson statistics. Received: 22 May 1998 / Received in final form: 24 August 1998 / Accepted: 4 September 1998     

Critical properties of the metal-insulator transition in anisotropic systems

We study the three-dimensional Anderson model of localization with anisotropic hopping, i.e., weakly coupled chains and weakly coupled planes. In our extensive numerical study we identify and characterize the metal-insulator transition by means of the transfer-matrix method. The values of the critical disorder obtained are consistent with results of previous studies, including multifractal analysis of the wave functions and energy-level statistics. decreases from its isotropic value with a power law as a function of anisotropy. Using high accuracy data for large system sizes we estimate the critical exponent as . This is in agreement with its value in the isotropic case and in other models of the orthogonal universality class. Received 25 October 1999     

Non-linear conductivity and quantum interference in disordered metals

We report on the non-linear electric field effect in the conductivity of disordered conductors. We find that the electron-electron interaction in the particle-hole triplet channel strongly affects the non-linear conductivity. The non-linear effect introduces a field dependent temperature scale T_E and provides a microscopic mechanism for electric field scaling at the metal-insulator transition. We also study the magnetic field dependence of the non-linear conductivity and suggest possible ways to experimentally verify our predictions. These effects offer a new probe to test the role of quantum interference at the metal-insulator transition in disordered conductors. Received 9 February 2000     

Quasi-localization and quasi-mobility edge for light atoms mixed with heavy ones

A mixture of light and heavy atoms is considered. We study the kinetics of the light atoms, scattered by the heavy ones, the latter undergoing slow diffusive motion. In three-dimensional space we claim the existence of a crossover region (in energy), which separates the states of the light atoms with fast diffusion and the states with slow diffusion; the latter is determined by the dephasing time. For the two dimensional case we have a transition between weak localization, observed when the dephasing length is less than the localization length (calculated for static scatterers), and strong localization observed in the opposite case.     

Finite-size scaling of the level compressibility at the Anderson transition

We compute the number level variance Σ ₂ and the level compressibility χ from high precision data for the Anderson model of localization and show that they can be used in order to estimate the critical properties at the metal-insulator transition by means of finite-size scaling. With N, W, and L denoting, respectively, linear system size, disorder strength, and the average number of levels in units of the mean level spacing, we find that both χ(N, W) and the integrated Σ ₂ obey finite-size scaling. The high precision data was obtained for an anisotropic three-dimensional Anderson model with disorder given by a box distribution of width W/2. We compute the critical exponent as ν≈ 1.45±0.12 and the critical disorder as W _c≈ 8.59±0.05 in agreement with previous transfer-matrix studies in the anisotropic model. Furthermore, we find χ≈ 0.28±0.06 at the metal-insulator transition in very close agreement with previous results. Received 1st November 2001 and Received in final form 8 March 2002 Published online 6 June 2002     

Interaction-dependent enhancement of the localisation length for two interacting particles in a one-dimensional random potential

We present calculations of the localisation length, , for two interacting particles (TIP) in a one-dimensional random potential, presenting its dependence on disorder, interaction strength U and system size. is computed by a decimation method from the decay of the Green function along the diagonal of finite samples. Infinite sample size estimates are obtained by finite-size scaling. For U=0 we reproduce approximately the well-known dependence of the one-particle localisation length on disorder while for finite U, we find that with varying between and . We test the validity of various other proposed fit functions and also study the problem of TIP in two different random potentials corresponding to interacting electron-hole pairs. As a check of our method and data, we also reproduce well-known results for the two-dimensional Anderson model without interaction. Received 19 June 1998 and Received in final form 29 October 1998     

Metal-insulator transition in two-dimensional systems with long-range correlated disorder

We study the localization properties of electrons in a two-dimensional model with on-site energies exhibiting long-range correlated disorder. The localization length and conductance of the system are calculated by using the finite size scaling method combined with transfer matrix technique. In the presence of long-range correlations, we find that there is a continuous line of fixed points indicating that the system undergoes a disorder driven Kosterlitz-Thouless-type metal-insulator transition. Received 6 March 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: wsliu@sjtu.edu.cn     

Numerical analysis of the dissipative two-state system with the density-matrix Hilbert-space-reduction algorithm

To investigate the influence of electronic interaction on the metal-insulator transition (MIT), we consider the Aubry-André (or Harper) model which describes a quasiperiodic one-dimensional quantum system of non-interacting electrons and exhibits an MIT. For a two-particle system, we study the effect of a Hubbard interaction on the transition by means of the transfer-matrix method and finite-size scaling. In agreement with previous studies we find that the interaction localizes some states in the otherwise metallic phase of the system. Nevertheless, the MIT remains unaffected by the interaction. For a long-range interaction, many more states become localized for sufficiently large interaction strength and the MIT appears to shift towards smaller quasiperiodic potential strength. Received 17 August 1998     

Coherent transport in disordered metals out of equilibrium

We derive a formula for the quantum corrections to the electrical current for a metal out of equilibrium. In the limit of linear current-voltage characteristics our formula reproduces the well known Altshuler-Aronov correction to the conductivity of a disordered metal. The current formula is obtained by a direct diagrammatic approach, and is shown to agree with what is obtained within the Keldysh formulation of the non-linear sigma model. As an application we calculate the current of a mesoscopic wire. We find a current-voltage characteristics that scales with eV/kT, and calculate the different scaling curves for a wire in the hot-electron regime and in the regime of full non-equilibrium. Received 13 June 2001     

Enhancement of magnetoresistance in cobaltites by manganese substitution: the oxide La 0.8 Sr 0.2 Co 1-x Mn x O 3

The substitution of manganese for cobalt in the perovskite La _0.8 Sr _0.2 CoO ₃ has been studied. A significant increase of the magnetoresistance (MR) is obtained, reaching 60% at 5 K under 7 T for . This behavior originates from a spectacular increase of the resistivity correlated to a significant decrease of ferromagnetism by Mn doping. This enhancement of magnetoresistance can be interpreted by the growth of ferromagnetic clusters in the insulating matrix, by applying a magnetic field. Received 7 May 1999     

Distribution of resonance widths in localized tight-binding models

We numerically analyze the distribution of scattering resonance widths in one- and quasi-one dimensional tight binding models, in the localized regime. We detect and discuss an algebraic decay of the distribution, similar, though not identical, to recent theoretical predictions. Received 14 April 2000 and Received in final form 27 July 2000     

Series expansion study of quantum percolation on the square lattice

We study the site and bond quantum percolation model on the two-dimensional square lattice using series expansion in the low concentration limit. We calculate series for the averages of , where T _ij (E) is the transmission coefficient between sites i and j, for k=0, 1, , 5 and for several values of the energy E near the center of the band. In the bond case the series are of order p¹⁴ in the concentration p(some of those have been formerly available to order p¹⁰) and in the site case of order p¹⁶. The analysis, using the Dlog-Padé approximation and the techniques known as M1 and M2, shows clear evidence for a delocalization transition (from exponentially localized to extended or power-law-decaying states) at an energy-dependent threshold p _q(E) in the range , confirming previous results (e.g. and for bond and site percolation) but in contrast with the Anderson model. The divergence of the series for different kis characterized by a constant gap exponent, which is identified as the localization length exponent from a general scaling assumption. We obtain estimates of . These values violate the bound of Chayes et al. Received 28 February 2000     

Unusually flat hole dispersion relation in the two-dimensional Hubbard model and restoration of coherence by addition of pair-hopping processes

The dispersion relation of a doped hole in the half-filled 2D Hubbard model is shown to follow a law around the and points in the Brillouin zone. Upon addition of pair-hopping processes this dispersion relation is unstable towards a law. The above follows from T=0 Quantum Monte-Carlo calculations of the single particle spectral function on lattices. We discuss finite dopings and argue that the added term restores coherence to charge dynamics and drives the system towards a d _{x2 - y2} superconductor. Received 22 March 1999     

Zero bias anomaly in the density of states of low-dimensional metals

We consider the effect of Coulomb interactions on the average density of states (DOS) of disordered low-dimensional metals for temperatures T and frequencies ω smaller than the inverse elastic life-time 1/τ. Using the fact that long-range Coulomb interactions in two dimensions (2d) generate ln²-singularities in the DOS ν(ω) but only ln-singularities in the conductivity σ(ω), we can re-sum the most singular contributions to the average DOS via a simple gauge-transformation. If σ(ω) > 0, then a metallic Coulomb gapν(ω) ∝ |ω|/e ⁴ appears in the DOS at T = 0 for frequencies below a certain crossover frequency Ω ₂ which depends on the value of the DC conductivity σ(0). Here, - e is the charge of the electron. Naively adopting the same procedure to calculate the DOS in quasi 1d metals, we find ν(ω) ∝ (|ω|/Ω ₁)^1/2exp(- Ω ₁/|ω|) at T = 0, where Ω ₁ is some interaction-dependent frequency scale. However, we argue that in quasi 1d the above gauge-transformation method is on less firm grounds than in 2d. We also discuss the behavior of the DOS at finite temperatures and give numerical results for the expected tunneling conductance that can be compared with experiments. Received 28 August 2001 / Received in final form 28 January 2002 Published online 9 July 2002     

Two interacting particles in a disordered chain IV: Scaling of level curvatures

The curvatures of two-particle energy levels with respect to the enclosed magnetic flux in mesoscopic disordered rings are investigated numerically. We find that the typical value of the curvatures is increased by interactions in the localised regime and decreased in the metallic regime. This confirms a prediction by Akkermans and Pichard (Eur. Phys. J. B 1, 223 (1998)). The interaction-induced changes of the typical curvatures at different energies and disorder strengths exhibit one-parameter scaling with a conductance-like single parameter. This suggests that interactions could influence the conductance of mesoscopic systems similarly. Received 24 August 1998     

Two interacting particles in a disordered chain III: Dynamical aspects of the interplay disorder-interaction

The interplay between the quantum interferences responsible for one particle localization over a length L₁, and the partial dephasing induced by a local interaction of strength U with another particle leading to partial delocalization over a length L ₂ > L ₁ , is illustrated by a study of the motion of two particles put close to each other at the initial time. Localization is reached in two steps. First, before the time t₁ necessary to propagate over L₁, the interaction slows down the ballistic motion. On the contrary, after t₁ the interaction favors a very slow delocalization, characterized by a spreading of the center of mass, until L₂ is reached. This slow motion is related to the absence of quantum chaos in this one dimensional model, the interaction being only able to induce weaker chaos with critical spectral statistics. Under appropriate initial conditions, the motion remains invariant under the duality transformation mapping the behavior at small U onto the behavior at large U. Received 24 August 1998     

Optimisation of multifractal analysis at the 3D Anderson transition using box-size scaling

We study various box-size scaling techniques to obtain the multifractal properties, in terms of the singularity spectrum f(α), of the critical eigenstates at the metal-insulator transition within the 3-D Anderson model of localisation. The typical and ensemble averaged scaling laws of the generalised inverse participation ratios are considered. In pursuit of a numerical optimisation of the box-scaling technique we discuss different box-partitioning schemes including cubic and non-cubic boxes, use of periodic boundary conditions to enlarge the system and single and multiple origins for the partitioning grid are also implemented. We show that the numerically most reliable method is to divide a system of linear size L equally into cubic boxes of size l for which L/l is an integer. This method is the least numerically expensive while having a good reliability.     

Magnetic susceptibility and electrical conductivity of Perylene radical cation salts

Conduction electron properties of the quasi-one-dimensional conductors and (PE = perylene, THF = tetrahydrofurane) were investigated by measuring magnetic susceptibility and microwave conductivity in the temperature range from 10 K to 300 K. For quantitative analysis of the measurements a microscopic model was developed. Received 23 November 1999