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     

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     

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     

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.     

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     

Delocalization in disordered chains with random symmetrical impurities

We study in this paper, with the context of a tight-binding on-side model, the electronic properties of one-dimensional random lattices with correlated impurities. We show that, when symmetrical impurities are inserted in a host chain of site energy and a constant hopping interaction V, diffusion will occur even when is random. We provide analytic expressions for the transmittance and confirm the theoretical results by a great deal of numerical calculations. When = V, we find that the mean-square displacement (MSD) follows the law m ² ∝t ^β with β = 2.0 for = constant and β = 1.0 for = = random, respectively. Received 15 January 2001 and Received in final form 30 April 2001     

Coherent transport in disordered metals: zero dimensional limit

We consider non-equilibrium transport in disordered conductors. We calculate the interaction correction to the current for a short wire connected to electron reservoirs by resistive interfaces. In the absence of charging effects we find a universal current-voltage-characteristics. The relevance of our calculation for existing experiments is discussed as well as the connection with alternative theoretical approaches. Received 2 September 2002 Published online 29 October 2002     

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     

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     

Electronic structure and anomalous physical properties of metastable Al-Si solid solutions

Al-Si solid solutions synthesized under high pressure demonstrate striking physical properties, such as enhanced superconductivity and peculiarities of low-temperature transport coefficients. In order to understand the connection of these effects to the electronic structure changes we have performed a first-principles study of the electronic spectra and Fermi surfaces of Al-Si solid solutions. We show that two electronic topological transitions (ETT's) lead to unusual concentration dependencies of the resistivity, thermoelectric power and Hall constant of the system while a variety of other interesting phenomena such as lattice instability and superconductivity enhancement may be a result of the nesting features appearing upon Si doping. We present also the results of our theoretical calculations of the thermodynamic and transport properties of Al-Si solid solutions which are in good agreement with experiment and reproduce nicely the experimentally observed peculiarities. Received 31 January 2002     

Time evolution of wave-packets in quasi-1D disordered media

We have investigated numerically the quantum evolution of a -like wave-packet in a quenched disordered medium described by a tight-binding Hamiltonian with long-range hopping (band random matrix approach). We have obtained clean data for the scaling properties in time and in the bandwidth b of the packet width and its fluctuations with respect to disorder realizations. We confirm that the fluctuations of the packet width in the steady-state show an anomalous scaling [0pt] with [0pt] . This can be related to the presence of non-Gaussian tails in the distribution of [0pt]. Finally, we have analysed the steady state probability profile and we have found 1/b corrections with respect to the theoretical formula derived by Zhirov in the limit, except at the origin, where the corrections are . Received 6 August 1999 and Received in final form 22 October 1999     

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     

The influence of the dynamics of ionic multiplets onto electronic transport properties of heavy-fermion systems: a semi-phenomenological approach

We present calculations of the electronic transport properties of heavy-fermion systems within a semi-phenomenological approach to the dynamical mean field theory. In this approach the dynamics of the Hund's rules 4f (5f )-ionic multiplet split in a crystalline environment is taken into account. Within the scope of this calculation we use the linear response theory to reproduce qualitative features of the temperature-dependent resistivity and hall conductivity, the magneto-resistivity and the thermoelectric power typical for heavy-fermion systems. The model calculations are directly compared with experimental results on CeCu ₂ Si ₂. Received 30 June 2000 and Received in final form 15 December 2000     

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.     

Lifshitz-like argument for low-lying states in a strong magnetic field

Localization of an electron moving in two dimensions, submitted to a strong magnetic field and scattered by randomly distributed zero-range impurities is investigated. Considering the explicit expression for the density of states obtained by Brézin, Gross and Itzykson, the Lifshitz argument is adapted in order to analyze the unusual power-law behavior of the low energy spectrum. When the impurity density is smaller than the Landau degeneracy, typical configurations of disorder responsible for low energy states are identified as cluster of impurities of well defined form. This allows for an interpretation of low-lying states, localized around these clusters, whose size diverges logarithmically as the energy goes to zero. Received 5 January 2000     

Selective advantage of topological disorder in biological evolution

We examine a model of biological evolution of Eigen's quasispecies in a so-called holey fitness landscape, where the fitness of a site is either 0 (lethal site) or a uniform positive constant (viable site). The evolution dynamics is therefore determined by the topology of the genome space which is modelled by the random Bethe lattice. We use the effective medium and single-defect approximations to find the criteria under which the localized quasispecies cloud is created. We find that shorter genomes, which are more robust to random mutations than average, represent a selective advantage which we call “topological”. A way of assessing empirically the relative importance of reproductive success and topological advantage is suggested. Received 9 August 2002 / Received in final form 7 November 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: slanina@fzu.cz     

Quantum switch based on coupled waveguides

The problem of construction of quantum multiplexer is discussed. A possible construction based on resonance transport properties of quantum waveguides coupled through small windows is considered. Small apertures play double role of “connecting channels" and “resonant elements". Transmission coefficients for the system are determined. The workability of the device as a quantum switch to one of three (or to two of three) channels is discussed. Control parameters for the switch are electron energy and bias voltage. Received 13 August 2000 and Received in final form 19 February 2001     

Spin-Hall transport in a two-dimensional electron system with magnetic impurities

The spin Hall transport properties in a two-dimensional electron system with both Rashba spin-orbit coupling (SOC) and magnetic impurities are investigated. Electrons are scattered by impurities through an exchange interaction that leads to spin flip-flop processes and so changes the spin Hall effect induced by the SOC. The spin Hall conductance is calculated in a 4-terminal system using the Landauer-Buttiker formula and Green function approach. In comparison with the simulation results on nonmagnetic impurities doping systems, our results reveal that the spin Hall conductance is still nonzero in a system with a large density of magnetic impurities and a finite intensity of the exchange interaction between the electrons and impurities, and its sign may be altered when the doping density and interaction strength are large enough.     

CPA density of states and conductivity in a double-exchange system containing impurities

We study density of states and conductivity of the doped double-exchange system, treating interaction of charge carriers both with the localized spins and with the impurities in the coherent potential approximation. It is shown that under appropriate conditions there is a gap between the conduction band and the impurity band in paramagnetic phase, while the density of states is gapless in ferromagnetic phase. This can explain metal-insulator transition frequently observed in manganites and magnetic semiconductors. Activated conductivity in the insulator phase is numerically calculated. Received 13 June 2000 and Received in final form 5 January 2001     

Magnetoconductance of a two-dimensional metal in the presence of spin-orbit coupling

We show that in the metallic phase of a two dimensional electron gas the spin-orbit coupling due to structure inversion asymmetry leads to a characteristic anisotropy in the magnetoconductance. Within the assumption that the metallic phase can be described by a Fermi liquid, we compute the conductivity in the presence of an in-plane magnetic field. Both the spin-orbit coupling and the Zeeman coupling with the magnetic field give rise to two spin subbands, in terms of which most of the transport properties can be discussed. The strongest conductivity anisotropy occurs for Zeeman energies of the order of the Fermi energy corresponding to the depopulation of the upper spin subband. The energy scale associated with the spin-orbit coupling controls the strength of the effect. More in particular, we find that the detailed behavior and the sign of the anisotropy depends on the underlying scattering mechanism. Assuming small angle scattering to be the dominant scattering mechanism our results agree with recent measurement on Si-MOSFET's in the vicinity of the metal-insulator transition. Received 11 July 2001