Compressibility crossover and quantum opening of a gap for two-dimensional disordered clusters with Coulomb repulsion

Using Hartree-Fock orbitals with residual Coulomb repulsion, we study spinless fermions in a two-dimensional random potential. When we increase the system size L at fixed particle density, the size dependence of the average inverse compressibility exhibits a smooth crossover from a 1/L ² towards a 1/L decay when the Coulomb energy to Fermi energy ratio increases from 0 to 3. In contrast, the distribution of the first energy excitation displays a sharp Poisson-Wigner-like transition at . Received 13 March 2000     

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     

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     

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     

Localization-delocalization transition in one-dimensional system with long-range correlated diagonal disorder

We show that the electronic states in a one-dimensional (1D) Anderson model of diagonal disorder with long-range correlation proposed by de Moura and Lyra exhibit localization-delocalization phase transition in varying the energy of electrons. Using transfer matrix method, we calculate the average resistivity and investigate how it changes with the size of the system N. For given value of α (> 2) we find critical energies E_c1 and E_c2 such that the resistivity decreases with N as a power law ∝ N ^{- γ} for electron energies within the range of [E _c1, E _c2], and exponentially grows with N outside this range. Such behaviors persist in approaching the transition points and the exponent γ is in the range from 0.92 to 0.96. The origin of the delocalization in this 1D model is discussed. Received 18 December 2001 / Received in final form 2 May 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: sjxiong@nju.edu.cn     

Anderson transition in 1D systems with spatial disorder

A simple Kronig-Penney model for 1D mesoscopic systems with δ peak potentials is used to study numerically the influence of spatial disorder on conductance fluctuations and distribution at different regimes. The Lévy laws are used to investigate the statistical properties of the eigenstates. It is found that an Anderson transition occurs even in 1D meaning that the disorder can also provide constructive quantum interferences. The critical disorder W_c for this transition is estimated. In these 1D systems, the metallic phase is well characterized by a Gaussian conductance distribution. Indeed, the results relative to conductance distribution are in good agreement with the previous works in 2D and 3D systems for other models. At this transition, the conductance probability distribution has a system size independent shape with large fluctuations in good agreement with previous works.     

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 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     

Magnetic scattering effects on magnetoresistance in a quasi-two-dimensional disordered electron system

Magnetic-impurity-scattering effects in a quasi-2D disordered electron system have been investigated theoretically with the diagrammatic techniques in perturbation theory. The analytical expressions for magnetoconductivities due to weak-localization effects have been obtained as functions of elastic, inelastic and magnetic scattering times. The relevant dimensional crossover behavior from 3D to 2D with decreasing the interlayer coupling has been discussed, and the condition for the crossover has been obtained. Received 20 March 2001 and Received in final form 28 June 2001     

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     

Localization properties of two interacting particles in a quasi-periodic potential with a metal-insulator transition

We study the influence of many-particle interactions on a metal-insulator transition. We consider the two-interacting-particle problem for onsite interacting particles on a one-dimensional quasiperiodic chain, the so-called Aubry-André model. We show numerically by the decimation method and finite-size scaling that the interaction does not modify the critical parameters such as the transition point and the localization-length exponent. We compare our results to the case of finite density systems studied by means of the density-matrix renormalization scheme. Received 28 June 2001     

Thermoelectric transport properties in disordered systems near the Anderson transition

We study the thermoelectric transport properties in the three-dimensional Anderson model of localization near the metal-insulator transition (MIT). In particular, we investigate the dependence of the thermoelectric power S, the thermal conductivity K, and the Lorenz number L₀ on temperature T. We first calculate the T dependence of the chemical potential μ from the number density n of electrons at the MIT using an averaged density of states obtained by diagonalization. Without any additional approximation, we determine from the behavior of S, K and L₀ at low T as the MIT is approached. We find that and K decrease to zero at the MIT as and show that S does not diverge. Both S and L₀ become temperature independent at the MIT and depend only on the critical behavior of the conductivity. Received 5 February 1999     

Localization properties of driven disordered one-dimensional systems

We generalize the definition of localization length to disordered systems driven by a time-periodic potential using a Floquet-Green function formalism. We study its dependence on the amplitude and frequency of the driving field in a one-dimensional tight-binding model with different amounts of disorder in the lattice. As compared to the autonomous system, the localization length for the driven system can increase or decrease depending on the frequency of the driving. We investigate the dependence of the localization length with the particle's energy and prove that it is always periodic. Its maximum is not necessarily at the band center as in the non-driven case. We study the adiabatic limit by introducing a phenomenological inelastic scattering rate which limits the delocalizing effect of low-frequency fields.     

Femtosecond ionization of magnesium clusters grown in ultracold helium droplets

Magnesium clusters grown in helium droplets and ionized with femtosecond laser pulses have been studied by high resolution mass spectrometry. For moderate laser intensities the abundance spectra show characteristic features indicating electronic shell effects. Compared to clusters of s¹-electron metals additional shell closures appear resulting from an electron rearrangement. Irradiation with higher laser intensities leads to a decomposition of the magnesium clusters into atomic ions. Due to charge exchange with the surrounding helium matrix mainly singly and doubly charged magnesium ions remain. In addition, the occurrence of MgHe_N ⁺-complexes is observed. Their abundance depends on the shape of the laser field, i.e. the laser width and the optical delay when applying the pump-probe technique. Received 2 January 2001     

Overhauser shift of the electron spin-resonance line of Si:P at the metal-insulator transition: II. 29 Si contribution

The electron-spin resonance (ESR) line of delocalised electrons shifts upon saturation due to the hyperfine interaction with the dynamically polarized nuclear spins. The ²⁹ Si part of the Overhauser shift of the ESR line of phosphorus doped silicon (Si:P) is separated in the concentration range 2.7 ... 7.3×10 ¹⁸ / cm ³ covering the metal-insulator transition. The Overhauser shift profiles, recorded versus ²⁹ Si nuclear magnetic resonance (NMR) frequency, are asymmetric. Their dependence on temperature and ESR saturation compares reasonably with simulations. Time and NMR frequency dependence of the dynamic nuclear polarization is studied in detail. No pronounced variation of the ²⁹ Si Overhauser shift profiles with P concentration is observed, but the maximum value of the shift profile decreases with increasing P concentration. In contrast to standard ²⁹ Si NMR results, these measurements reveal the behaviour of the ²⁹ Si nuclei close to the P doping sites. Received 8 November 2001     

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     

Magnetism and phase separation in the ground state of the Hubbard model

We discuss the ground state magnetic phase diagram of the Hubbard model off half filling within the dynamical mean-field theory. The effective single-impurity Anderson model is solved by Wilson's numerical renormalization group calculations, adapted to symmetry broken phases. We find a phase separated, antiferromagnetic state up to a critical doping for small and intermediate values of U, but could not stabilize a Néel state for large U and finite doping. At very large U, the phase diagram exhibits an island with a ferromagnetic ground state. Spectral properties in the ordered phases are discussed. Received 9 January 2002 Published online 25 June 2002     

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