Scaling in the One-Dimensional Anderson Localization Problem in the Region of Fluctuation States

Deych, Lev; Erementchouk, Mikhail; Lisyansky, A. A.

doi:10.1103/physrevlett.90.126601

Cited by 31 publications

(38 citation statements)

References 14 publications

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“…The determination of this scattering length allows a precise study of average conductance, and in particular the study of the classical part as described in the next subsection. Figure 23 shows the scaling form of these fluctuations (as a function of L x /L m (J )) in excellent agreement with the theory (17). Moreover, for long wires (and large values of J ) conductance fluctuations are no longer L x dependent and are equal to 1/15, in units of G 2 0 .…”

Section: Conductance Fluctuations and Universal Crossoversupporting

confidence: 76%

“…In figure 22, these conductance fluctuations are plotted as a function of longitudinal length L x for different values of J . A single-parameter fit by (17) provides the determination of the magnetic dephasing length L m as a function of the magnetic disorder J . The Universal behavior is also highlighted for strong enough magnetic disorder.…”

Section: Conductance Fluctuations and Universal Crossovermentioning

confidence: 99%

“…To optimize the efficiency of the numerical study, we fix t // = 2t ⊥ and stay near the band center, avoiding in particular the presence of fluctuating states studied in [17].…”

mentioning

confidence: 99%

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Crossover between universality classes in a magnetically disordered metallic wire

Paulin

Carpentier²

2012

New J. Phys.

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In this paper, we present the numerical results of conduction in a disordered quasi-one-dimensional wire in the possible presence of magnetic impurities. Our analysis leads us to the study of universal properties in different conduction regimes, such as the localized and metallic ones. In particular, we analyze the crossover between universality classes occurring when the strength of magnetic disorder is increased. For this purpose, we use a numerical Landauer approach, and derive the scattering matrix of the wire from the electron's Green's function. t i j is the hopping term from site i to j. In the following, t i j will take two different values: t i j = t // in the longitudinal x-direction and t i j = t ⊥ in the transverse y-direction. The scalar disorder potential V = {v i } i is diagonal in electron-spin space. We choose the v i to be random scalars uniformly distributed in the interval [−W/2, W/2]. In this work, we have chosen without loss of generality to fix t // = 1 so that all energy scales are relative to the bandwidth t // = 1, and the amplitude of disorder W = 0.6. In equation (1), s, s label the SU(2) spin of electrons and the S i account for spins of the frozen magnetic impurities. A realistic choice for these frozen New Journal of Physics 14 (2012) 023026 (http://www.njp.org/) 〈 g 2 〉 c J = 0.025 J = 0.05 J = 0.075 J = 0.1 J = 0.15 J = 0.2 J = 0.3 J = 0.4 Analytical fits Quasi 1d UCF L y = 40

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Section: Conductance Fluctuations and Universal Crossoversupporting

confidence: 76%

Section: Conductance Fluctuations and Universal Crossovermentioning

confidence: 99%

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Crossover between universality classes in a magnetically disordered metallic wire

Paulin

Carpentier²

2012

New J. Phys.

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“…Our approach allows one to describe statistical properties of conductance in the vicinity of E 0 within the framework of the scaling approach of Ref. [17]. …”

Section: P H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 99%

Scaling and the Center-of-Band Anomaly in a One-Dimensional Anderson Model with Diagonal Disorder

et al. 2003

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We resolve the problem of the violation of single parameter scaling at the zero energy of the Anderson tight-binding model with diagonal disorder. It follows from the symmetry properties of the tight-binding Hamiltonian that this spectral point is, in fact, a boundary between two adjacent bands. The states in the vicinity of this energy behave similarly to states at other band boundaries, which are known to violate single parameter scaling.

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“…[27][28][29] On the other hand, universality of the distributions of macroscopic transportrelated quantities characterizing disordered systems has been studied by scaling theory ͑see Ref. 30͒, which is still evolving nowadays: the conditions for the validity of single parameter scaling ͑SPS͒ have been recently reformulated 31,32 and it has been found that different scaling regimes appear when disorder is correlated. 33 The interest for disorder is also currently registering a noticeable increase in the field of ultracold atomic lattice gases.…”

Section: Introductionmentioning

confidence: 99%

One-dimensional disordered wires with Pöschl-Teller potentials

Rodríguez

Cerveró

2006

Phys. Rev. B

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We study the electronic properties of a one-dimensional disordered chain made up of Pöschl-Teller potentials. The features of the whole spectrum of the random chain in the thermodynamic limit are analyzed in detail by making use of the functional equation formalism. The disordered system exhibits a fractal distribution of states within certain energy intervals and two types of resonances exist for the uncorrelated case. These extended states are characterized by different values of their critical exponents and different behaviors near the critical energies when the system is finite, but their existence can be defined by a single common condition. The chain is also considered including a natural model of short-range correlated disorder. The results show that the effects of the correlations considered are independent of the potential model.

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Scaling in the One-Dimensional Anderson Localization Problem in the Region of Fluctuation States

Cited by 31 publications

References 14 publications

Crossover between universality classes in a magnetically disordered metallic wire

Crossover between universality classes in a magnetically disordered metallic wire

Scaling and the Center-of-Band Anomaly in a One-Dimensional Anderson Model with Diagonal Disorder

One-dimensional disordered wires with Pöschl-Teller potentials

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