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Kettemann S.,Jacobs University Bremen | Kettemann S.,Pohang University of Science and Technology | Mucciolo E.R.,University of Central Florida | Varga I.,Elmeleti Fizika Tanszek | Slevin K.,Osaka University
Physical Review B - Condensed Matter and Materials Physics | Year: 2012

Dilute magnetic impurities in a disordered Fermi liquid are considered close to the Anderson metal-insulator transition (AMIT). Critical power-law correlations between electron wave functions at different energies in the vicinity of the AMIT result in the formation of pseudogaps of the local density of states. Magnetic impurities can remain unscreened at such sites. We determine the density of the resulting free magnetic moments in the zero-temperature limit. While it is finite on the insulating side of the AMIT, it vanishes at the AMIT, and decays with a power law as function of the distance to the AMIT. Since the fluctuating spins of these free magnetic moments break the time-reversal symmetry of the conduction electrons, we find a shift of the AMIT, and the appearance of a semimetal phase. The distribution function of the Kondo temperature TK is derived at the AMIT, in the metallic phase, and in the insulator phase. This allows us to find the quantum phase diagram in an external magnetic field B and at finite temperature T. We calculate the resulting magnetic susceptibility, the specific heat, and the spin relaxation rate as a function of temperature. We find a phase diagram with finite-temperature transitions among insulator, critical semimetal, and metal phases. These new types of phase transitions are caused by the interplay between Kondo screening and Anderson localization, with the latter being shifted by the appearance of the temperature-dependent spin-flip scattering rate. Accordingly, we name them Kondo-Anderson transitions. © 2012 American Physical Society. Source


Mendez-Bermudez J.A.,Autonomous University of Puebla | Martinez-Mendoza A.J.,Autonomous University of Puebla | Gopar V.A.,University of Zaragoza | Varga I.,Elmeleti Fizika Tanszek
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2016

We perform a detailed numerical study of the conductance G through one-dimensional (1D) tight-binding wires with on-site disorder. The random configurations of the on-site energies ε of the tight-binding Hamiltonian are characterized by long-tailed distributions: For large ε, P(ε)∼1/ε1+α with α(0,2). Our model serves as a generalization of the 1D Lloyd model, which corresponds to α=1. First, we verify that the ensemble average -lnG is proportional to the length of the wire L for all values of α, providing the localization length ξ from -lnG=2L/ξ. Then, we show that the probability distribution function P(G) is fully determined by the exponent α and -lnG. In contrast to 1D wires with standard white-noise disorder, our wire model exhibits bimodal distributions of the conductance with peaks at G=0 and 1. In addition, we show that P(lnG) is proportional to Gβ, for G→0, with β≤α/2, in agreement with previous studies. © 2016 American Physical Society. Source


Mendez-Bermudez J.A.,Autonomous University of Puebla | Gopar V.A.,University of Zaragoza | Varga I.,Elmeleti Fizika Tanszek | Varga I.,University of Marburg
Physical Review B - Condensed Matter and Materials Physics | Year: 2010

We study numerically scattering and transport statistical properties of the one-dimensional Anderson model at the metal-insulator transition described by the power-law banded random matrix (PBRM) model at criticality. Within a scattering approach to electronic transport, we concentrate on the case of a small number of single-channel attached leads. We observe a smooth crossover from localized to delocalized behavior in the average-scattering matrix elements, the conductance probability distribution, the variance of the conductance, and the shot noise power by varying b (the effective bandwidth of the PBRM model) from small (b≪1) to large (b>1) values. We contrast our results with analytic random matrix theory predictions which are expected to be recovered in the limit b→∞. We also compare our results for the PBRM model with those for the three-dimensional (3D) Anderson model at criticality, finding that the PBRM model with b∈ [0.2,0.4] reproduces well the scattering and transport properties of the 3D Anderson model. © 2010 The American Physical Society. Source


Mendez-Bermudez J.A.,Autonomous University of Puebla | Alcazar-Lopez A.,Autonomous University of Puebla | Varga I.,Elmeleti Fizika Tanszek
Journal of Statistical Mechanics: Theory and Experiment | Year: 2014

Recently, based on heuristic arguments, it was conjectured that an intimate relation exists between any multifractal dimensions, Dq and Dq′, of the eigenstates of critical random matrix ensembles: Dq′ ≈ qDq [q′ + (q - q′)Dq]-1, 1 ≤ q, q′ ≤ 2. Here, we verify this relation by extensive numerical calculations on critical random matrix ensembles and extend its applicability to q < 1/2, but also to deterministic models producing multifractal eigenstates and to generic multifractal structures. We also demonstrate, for the scattering version of the power-law banded random matrix model at criticality, that the scaling exponents σq of the inverse moments of Wigner delay times, 〈τW -q〉 ∝ N-σqwhere N is the linear size of the system, are related to the level compressibility χ as σq ≈ q(1 - χ)[1 + qχ]-1 for a limited range of q, thus providing a way to probe level correlations by means of scattering experiments. © 2014 IOP Publishing Ltd and SISSA Medialab srl. Source


Mendez-Bermudez J.A.,Autonomous University of Puebla | Alcazar-Lopez A.,Autonomous University of Puebla | Martinez-Mendoza A.J.,Elmeleti Fizika Tanszek | Rodrigues F.A.,University of Sao Paulo | Peron T.K.D.,University of Sao Paulo
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2015

By the use of extensive numerical simulations, we show that the nearest-neighbor energy-level spacing distribution P(s) and the entropic eigenfunction localization length of the adjacency matrices of Erdos-Rényi (ER) fully random networks are universal for fixed average degree ξ≡αN (α and N being the average network connectivity and the network size, respectively). We also demonstrate that the Brody distribution characterizes well P(s) in the transition from α=0, when the vertices in the network are isolated, to α=1, when the network is fully connected. Moreover, we explore the validity of our findings when relaxing the randomness of our network model and show that, in contrast to standard ER networks, ER networks with diagonal disorder also show universality. Finally, we also discuss the spectral and eigenfunction properties of small-world networks. © 2015 American Physical Society. Source

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