Metal-insulator transition in two-dimensional disordered systems with power-law transfer terms

Potempa, H.; Schweitzer, L.

doi:10.1103/physrevb.65.201105

Cited by 22 publications

(21 citation statements)

References 46 publications

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“…8 According to general scaling arguments, all states shall be exponentially localized by any degree of disorder in one-dimensional ͑1D͒ systems, a scaling prediction widely supported numerically. 2 However, it has been reported along the last two decades that the presence of short-range [9][10][11][12][13][14] or long-range correlations [15][16][17][18] in the disorder distribution, as well as long-range couplings [19][20][21][22] can induce the appearance of truly delocalized states in low-dimensional Anderson models. In particular, such correlation-induced de-localization has been explored in several studies of the electronic transport along DNA-based chains motivated by recent claims of long-range correlations in the base-pairs sequence.…”

Section: Introductionmentioning

confidence: 99%

Stationary, dynamical, and spectral electronic properties of a correlated random ladder model with coexisting extended and localized states

2010

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We study some stationary, dynamical, and spectral properties of a tight-binding Hamiltonian model for noninteracting electrons in a random two-channels ladder with correlated disorder that presents superposed bands of localized and extended states. We compute the participation number, Kubo-Greenwood conductance, Lyapunov exponent, the spread of an initially localized wave packet, as well as the level-spacing statistics in the band of coexisting localized and extended states. All stationary quantities show a metallic character at the coexistence energy band, such as a finite conductance and vanishing Lyapunov exponent. The wave packet exhibits a ballistic spread due to the Bloch-type nature of the extended states. On the other hand, the levelspacing statistics is characterized by a new distribution function which accounts for the superposition of uniformly distributed Bloch-type states and Poissonian-distributed localized states.

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Section: Introductionmentioning

confidence: 99%

Stationary, dynamical, and spectral electronic properties of a correlated random ladder model with coexisting extended and localized states

2010

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“…6 24 reported the f (␣) spectrum for a critical wave function of a finite sample in 2D of linear size Lϭ150 for ϭ6. For this value of , we found ⌬ ␣2 ϭ0.084, indicating that we are very close to the regime where deviations are practically unobservable.…”

Section: B 2d Systemmentioning

confidence: 99%

f(α)multifractal spectrum at strong and weak disorder

Cuevas

2003

Phys. Rev. B

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The system size dependence of the multifractal spectrum f (␣) and its singularity strength ␣ is investigated numerically. We focus on one-dimensional ͑1D͒ and 2D disordered systems with long-range random hopping amplitudes in both the strong and the weak disorder regime. At the macroscopic limit, it is shown that f (␣) is parabolic in the weak disorder regime. In the case of strong disorder, on the other hand, f (␣) strongly deviates from parabolicity. Within our numerical uncertainties it has been found that all corrections to the parabolic form vanish at some finite value of the coupling strength.

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“…The existence of the Anderson transition in such one-dimensional systems is related to the long-range nature of the hopping amplitudes. In our recent work [14], we studied the scaling of the moments of the eigenstates in a two-dimensional generalization of the powerlaw banded random matrix model [15,16]. In this ensemble, the matrix elements of the Hamiltonian H mn are complex independent Gaussian random variables, whose mean values are equal to zero and whose variances are determined by the distance between sites of a two-dimensional lattice:…”

Section: Introductionmentioning

confidence: 99%

Level-number variance and spectral compressibility in a critical two-dimensional random-matrix model

Ossipov

Rushkin²,

Cuevas³

2012

Phys. Rev. E

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We study level-number variance in a two-dimensional random matrix model characterized by a power-law decay of the matrix elements. The amplitude of the decay is controlled by the parameter b. We find analytically that at small values of b the level number variance behaves linearly, with the compressibility χ between 0 and 1, which is typical for critical systems. For large values of b, we derive that χ=0, as one would normally expect in the metallic phase. Using numerical simulations we determine the critical value of b at which the transition between these two phases occurs.

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Metal-insulator transition in two-dimensional disordered systems with power-law transfer terms

Cited by 22 publications

References 46 publications

Stationary, dynamical, and spectral electronic properties of a correlated random ladder model with coexisting extended and localized states

Stationary, dynamical, and spectral electronic properties of a correlated random ladder model with coexisting extended and localized states

f(α)multifractal spectrum at strong and weak disorder

Level-number variance and spectral compressibility in a critical two-dimensional random-matrix model

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