Conductivity and mobility edges for two-dimensional disordered systems

Licciardello, D.C.; Thouless, D. J.

doi:10.1088/0022-3719/8/24/009

Cited by 213 publications

(57 citation statements)

References 20 publications

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“…In order to study localization effects in antidot lattices, conventional Thoulessnumber method [33,34] was used recently [35,36]. This method is known to be useful also in magnetic fields [37].…”

Section: Thouless Number Methodsmentioning

confidence: 99%

Advanced Luminescent Materials and Quantum Confinement: Proceedings of the International Symposium Held in Honolulu, Hawaii on 18-20 October 1999

Cahay¹,

Bandyopadhyay²,

Lockwood³

et al. 1999

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Section: Thouless Number Methodsmentioning

confidence: 99%

Advanced Luminescent Materials and Quantum Confinement: Proceedings of the International Symposium Held in Honolulu, Hawaii on 18-20 October 1999

Cahay¹,

Bandyopadhyay²,

Lockwood³

et al. 1999

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“…Using prior work of Thouless and co-workers (Edwards and Thouless, 1972;Thouless, 1974;Licciardello and Thouless, 1975) and Wegner (1976), Abrahams et al (1979) argued that the average dimensionless conductance g = Gh/e 2 should obey a single parameter scaling relation. They calculated the β function of the conductance,…”

Section: A Anderson Localizationmentioning

confidence: 99%

“…Extended states should feel the change in the boundary conditions and the shift in energy should be of the order ofh/τ , where τ is the time it takes the electron to diffuse to the boundary (Thouless, 1974). In second-order perturbation theory the change in energy δE when periodic boundary conditions are replaced by anti-periodic boundary conditions is approximately related to the conductivity σ by (Licciardello and Thouless, 1975) …”

Section: A Thouless Numbermentioning

confidence: 99%

Scaling theory of the integer quantum Hall effect

1995

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The scaling theory of the transitions between plateaus of the Hall conductivity in the integer Quantum Hall effect is reviewed. In the model of twodimensional noninteracting electrons in strong magnetic fields the transitions are disorder-induced localization-delocalization transitions. While experimental and analytical approaches are surveyed, the main emphasis is on numerical studies, which successfully describe the experiments. The theoretical models for disordered systems are described in detail. An overview of the finitesize scaling theory and its relation to Anderson localization is given. The field-theoretical approach to the localization problem is outlined. Numerical methods for the calculation of scaling quantities, in particular the localization length, are detailed. The properties of local observables at the localizationdelocalization transition are discussed in terms of multifractal measures. Finally, the results of extensive numerical investigations are compared with experimental findings.

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“…The sensitivity of the electron eigenstates to the boundary conditions provides us with another criterion for localization [62,63]. Consider a disordered d dimensional system of size L. We can calculate all the eigenenergies of the system with periodic boundary conditions,…”

Section: Boundary Conditionsmentioning

confidence: 99%

Numerical analysis of the Anderson localization

Markoš¹

2006

Acta Physica Slovaca. Reviews and Tutorials

136

242

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The aim of this paper is to demonstrate, by simple numerical simulations, the main transport properties of disordered electron systems. These systems undergo the metal insulator transition when either Fermi energy crosses the mobility edge or the strength of the disorder increases over critical value. We study how disorder affects the energy spectrum and spatial distribution of electronic eigenstates in the diffusive and insulating regime, as well as in the critical region of the metal-insulator transition. Then, we introduce the transfer matrix and conductance, and we discuss how the quantum character of the electron propagation influences the transport properties of disordered samples. In the weakly disordered systems, the weak localization and anti-localization as well as the universal conductance fluctuation are numerically simulated and discussed. The localization in the one dimensional system is described and interpreted as a purely quantum effect. Statistical properties of the conductance in the critical and localized regimes are demonstrated. Special attention is given to the numerical study of the transport properties of the critical regime and to the numerical verification of the single parameter scaling theory of localization. Numerical data for the critical exponent in the orthogonal models in dimension 2 < d ≤ 5 are compared with theoretical predictions. We argue that the discrepancy between the theory and numerical data is due to the absence of the self-averaging of transmission quantities. This complicates the analytical analysis of the disordered systems. Finally, theoretical methods of description of weakly disordered systems are explained and their possible generalization to the localized regime is discussed. Since we concentrate on the one-electron propagation at zero temperature, no effects of electronelectron interaction and incoherent scattering are discussed in the paper.

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Conductivity and mobility edges for two-dimensional disordered systems

Cited by 213 publications

References 20 publications

Advanced Luminescent Materials and Quantum Confinement: Proceedings of the International Symposium Held in Honolulu, Hawaii on 18-20 October 1999

Advanced Luminescent Materials and Quantum Confinement: Proceedings of the International Symposium Held in Honolulu, Hawaii on 18-20 October 1999

Scaling theory of the integer quantum Hall effect

Numerical analysis of the Anderson localization

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