[Show abstract][Hide abstract] ABSTRACT: Recently [Europhys. Lett. {\bf 98}, 37006 (2012)], based on heuristic
arguments, it was conjectured that an intimate relation exists between the
eigenfunction multifractal dimensions $D_q$ of the eigenstates of critical
random matrix ensembles $D_{q'} \approx qD_q[q'+(q-q')D_q]^{-1}$, $1\le q \le
2$. Here, we verify this relation by extensive numerical calculations on
critical random matrix ensembles and extend its applicability to $q<1/2$ and
also to deterministic models producing multifractal eigenstates. We also
demonstrate, for the scattering version of the power-law banded random matrix
model at criticality, that the scaling exponents $\sigma_q$ of the inverse
moments of Wigner delay times, $\bra \tau_{\tbox W}^{-q} \ket \propto
N^{-\sigma_q}$ where $N$ is the linear size of the system, are related to the
level compressibility $\chi$ as $\sigma_q\approx q(1-\chi)[1+q\chi]^{-1}$ for a
limited range of $q$; thus providing a way to probe level correlations by means
of scattering experiments.
Journal of Statistical Mechanics Theory and Experiment 03/2013; 2014(11). DOI:10.1088/1742-5468/2014/11/P11012 · 2.40 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The localization of one-electron states in the large (but finite) disorder
limit is investigated. The inverse participation number shows a non--monotonic
behavior as a function of energy owing to anomalous behavior of few-site
localization. The two-site approximation is solved analytically and shown to
capture the essential features found in numerical simulations on one-, two- and
three-dimensional systems. Further improvement has been obtained by solving a
three-site model.
[Show abstract][Hide abstract] ABSTRACT: 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 $T_{K}$ 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 function of temperature. We find a phase diagram with finite
temperature transitions between 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 (KATs).
Physical Review B 03/2012; 85(11). DOI:10.1103/PhysRevB.85.115112 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Based on heuristic arguments we conjecture that an intimate relation exists
between the eigenfunction multifractal dimensions $D_q$ of the eigenstates of
critical random matrix ensembles $D_{q'} \approx qD_q[q'+(q-q')D_q]^{-1}$,
$1\le q \le 2$. We verify this relation by extensive numerical calculations. We
also demonstrate that the level compressibility $\chi$ describing level
correlations can be related to $D_q$ in a unified way as
$D_q=(1-\chi)[1+(q-1)\chi]^{-1}$, thus generalizing existing relations with
relevance to the disorder driven Anderson--transition.
[Show abstract][Hide abstract] ABSTRACT: At the Anderson metal-insulator transition the eigenstates develop
multifractal fluctuations. Therefore their properties are intermediate
between being extended and localized. As a result these wave functions
are power-law correlated, which causes a substantial suppression of the
local density of states at some random positions, resembling random
local pseudogaps at the Fermi energy. Consequently the Kondo screening
of magnetic moments is suppressed when a magnetic impurity happens to be
at such a position. Due to these unscreened magnetic moments the
critical exponents and multifractal dimensions at the metal-insulator
transition take their smaller, unitary ensemble values for exchange
couplings not exceeding a certain critical value J* ≈ .3D, where D is
the band width. Here we present numerical calculations of the
distribution of Kondo temperatures for the critical Power-law Band
Random Matrix (PBRM) ensemble, whose properties are similar to that of
the Anderson transition with the advantage of using a continuous
parameter for tuning the generalized multifractal dimensions of the
eigenstates.
[Show abstract][Hide abstract] ABSTRACT: In this work we investigate the inverse of the celebrated Bohigas-Giannoni-Schmit conjecture. Using two inversion methods we compute a one-dimensional potential whose lowest N eigenvalues obey random matrix statistics. Our numerical results indicate that in the asymptotic limit N→∞ the solution is nowhere differentiable and most probably nowhere continuous. Thus such a counterexample does not exist.
[Show abstract][Hide abstract] ABSTRACT: We study numerically the conductance statistics of the one-dimensional (1D) Anderson model with random long-range hoppings described by the Power-law Banded Random Matrix (PBRM) model. Within a scattering approach to electronic transport, we consider two scattering setups in absence and presence of direct processes: 2M single-mode leads attached to one side and to opposite sides of 1D circular samples. For both setups we show that (i) the probability distribution of the logarithm of the conductance T behaves as w(lnT)~TM2/2, for T
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: Excitonic spectra of weakly disordered semiconductor heterostructures are simulated on the basis of a one-dimensional tight-binding model. The influence of the length scale of weak disorder in quantum wells on the redshift of the excitonic peak and its linewidth is studied. By calculating two-dimensional Fourier-transform spectra we are able to determine the contribution of disorder to inhomogeneous and also to homo-geneous broadenings separately. This disorder-induced dephasing is related to a Fano-type coupling and leads to contributions to the homogeneous linewidth that depends on energy within the inhomogeneously broadened line. The model includes heavy-and light-hole excitons and yields smaller inhomogeneous broadening for the light-hole exciton if compared to the heavy-hole exciton, which agrees qualitatively with the experiment.
[Show abstract][Hide abstract] ABSTRACT: Localization of the center-of-mass (com) motion of an exciton in a disordered semiconductor structure is studied theoretically by focusing on nonlinear optical spectroscopy. A one-dimensional tight-binding model with diagonal disorder is applied and the Coulomb interaction is treated consistently. In the ordered situation the center-of-mass momentum (K) selection rule leads to only the lowest transition for K = 0. The break down of the com-K-selection rule produces the well known asymmetric excitonic lines of disordered semiconductors. The coupling between the lowest dominant transition to this modified com-continuum yields Fano-like features in the nonlinear spectra.
[Show abstract][Hide abstract] ABSTRACT: We study numerically the conductance distribution function w(T) for the one-dimensional Anderson model with random long-range hopping described by the Power-law Banded Random Matrix model at criticality. We concentrate on the case of two single-channel leads attached to the system. We observe a smooth transition from localized to delocalized behavior in the conductance distribution by increasing b, the effective bandwidth of the model. Also, for b < 1 we show that w(ln T/Ttyp) is scale invariant, where Ttyp = exp 〈 ln T 〉 is the typical value of T. Moreover, we find that for T < Ttyp, w(ln T/Ttyp) shows a universal behavior proportional to (T/Ttyp)-1/2.
[Show abstract][Hide abstract] ABSTRACT: We study numerically the statistical properties of some scattering quantities for the Power-law Banded Random Matrix model at criticality in the absence of time-reversal symmetry, with a small number of single-channel leads attached to it. We focus on the average scattering matrix elements, the conductance probability distribution, and the shot noise power as a function of the effective bandwidth b of the model. We find a smooth transition from insulating- to metallic-like behavior in the scattering properties of the model by increasing b. We contrast our results with existing random matrix theory predictions.
[Show abstract][Hide abstract] ABSTRACT: It is well known that magnetic impurities can change the symmetry class of disordered metallic systems by breaking spin and time-reversal symmetry. At low temperature, these symmetries can be restored by Kondo screening. It is also known that at the Anderson metal-insulator transition, wave functions develop multifractal fluctuations with power-law correlations. Here, we consider the interplay of these two effects. We show that multifractal correlations open local pseudogaps at the Fermi energy at some random positions in space. When dilute magnetic impurities are at these locations, Kondo screening is strongly suppressed. When the exchange coupling J is smaller than a certain value J;{*}, the metal-insulator transition point extends to a critical region in the disorder strength parameter and to a band of critical states.
[Show abstract][Hide abstract] ABSTRACT: In a recent publication [Phys. Rev. Lett. 97, 227402 (2006)], it has been demonstrated numerically that a long-range disorder potential in a semiconductor quantum well
can be reconstructed reliably via single-photon interferometry of spontaneously emitted light. In the present paper, a simplified
analytical model of independent two-level systems is presented in order to study the reconstruction procedure in more detail.
With the help of this model, the measured photon correlations can be calculated analytically and the influence of parameters,
such as the disorder length scale, the wavelength of the used light, or the spotsize can be investigated systematically. Furthermore,
the relation between the proposed angle-resolved single-photon correlations and the disorder potential can be understood and
the measured signal is expected to be closely related to the characteristic strength and length scale of the disorder.
Journal of Materials Science Materials in Electronics 12/2008; 20:23-29. DOI:10.1007/s10854-007-9424-0 · 1.57 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Entanglement is a physical resource of a quantum system just like mass, charge or energy. Moreover it is an essential tool for many purposes of nowadays quantum information processing, e.g. quantum teleportation, quantum cryptography or quantum computation. In this work we investigate an extended system of N qubits. In our system a qubit is the absence or presence of an electron at a site of a tight-binding system. Several measures of entanglement between a given qubit and the rest of the system and also the entanglement between two qubits and the rest of the system is calculated in a one-electron picture in the presence of disorder. We invoke the power law band random matrix model which even in one dimension is able to produce multifractal states that fluctuate at all length scales. The concurrence, the tangle and the entanglement entropy all show interesting scaling properties.
physica status solidi (c) 03/2008; 5(3). DOI:10.1002/pssc.200777589
[Show abstract][Hide abstract] ABSTRACT: We study the relaxation of a non-equilibrium carrier distribution under the influence of the electron-electron interaction in the presence of disorder. Based on the Anderson model, our Hamiltonian is composed from a single particle part including the disorder and a two-particle part accounting for the Coulomb interaction. We apply the equation-of-motion approach for the density matrix, which provides a fully microscopic description of the relaxation. Our results show that the nonequlibrium distribution in this closed and internally interacting system relaxes exponentially fast during the initial dynamics. This fast relaxation can be described by a phenomenological damping rate. The total single particle energy decreases in the redistribution process, keeping the total energy of the system fixed. It turns out that the relaxation rate decreases with increasing disorder.
physica status solidi (c) 03/2008; 5(3). DOI:10.1002/pssc.200777553
[Show abstract][Hide abstract] ABSTRACT: The system size dependence of the conductance in a class of tight-binding quasi-periodic potentials V0cos(παnν), where 0 < ν < 1, has been investigated numerically. It has been shown that at the metal-insulator transition (MIT), V0c = 2−|E|, the conductance follows a clear power law decay vs. system size, g ~ N−δ, which corroborates the existence of a pronounced power law localization at the MIT.
[Show abstract][Hide abstract] ABSTRACT: Based on differences of generalized Rényi entropies nontrivial constraints on the shape of the distribution function of broadly distributed observables are derived introducing a new parameter in order to quantify the deviation from lognormality. As a test example the properties of the two-measure random Cantor set are calculated exactly and finally, using the results of numerical simulations, the distribution of the eigenvector components calculated in the critical region of the lowest Landau band is analyzed.
[Show abstract][Hide abstract] ABSTRACT: The method of angular photonic correlations of spontaneous emission is introduced as an experimental, purely optical scheme to characterize disorder in semiconductor nanostructures. The theoretical expression for the angular correlations is derived and numerically evaluated for a model system. The results demonstrate how the proposed experimental method yields direct information about the spatial distribution of the relevant states and thus on the disorder present in the system.
[Show abstract][Hide abstract] ABSTRACT: A microscopic theory for the luminescence of ordered semiconductors is modified to describe photoluminescence of strongly disordered semiconductors. The approach includes both diagonal disorder and the many-body Coulomb interaction. As a case study, the light emission of a correlated plasma is investigated numerically for a one-dimensional two-band tight-binding model. The band structure of the underlying ordered system is assumed to correspond to either a direct or an indirect semiconductor. In particular, luminescence and absorption spectra are computed for various levels of disorder and sample temperature to determine thermodynamic relations, the Stokes shift, and the radiative lifetime distribution.
Journal of Luminescence 06/2005; 124(1-124):99-112. DOI:10.1016/j.jlumin.2006.02.005 · 2.72 Impact Factor