Multifractal analysis of disorder induced metal-insulator transitions

Fastenrath, Ulrich; Janβen, Martin; Pook, W.

doi:10.1016/0378-4371(92)90557-7

Cited by 18 publications

(18 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[5] we derived scaling relations which relate the critical exponents of the spatial correlation of amplitudes (for a fixed energy in the critical regime) to the multifractal spectrum (Eqs. (11,12,13)) and demonstrated that they are consistent with numerical data obtained for QHS (Sec. III).…”

Section: Discussionsupporting

confidence: 87%

“…We worked out the representing Hamiltonian matrix in the Landau representation which is convenient for periodic boundary conditions in one direction (say y−direction). To account for a finite system size in x−direction we adopted the Landau counting procedure which results in a matrix The determination of the range ∆E of critical states was based on a previous analysis of Thouless numbers within the same model [13].…”

Section: Distribution Of Local Amplitudesmentioning

confidence: 99%

See 1 more Smart Citation

Correlation of eigenstates in the critical regime of quantum Hall systems

Pracz¹,

Janssen²,

Freche³

1996

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

show abstract

Section: Discussionsupporting

confidence: 87%

Section: Distribution Of Local Amplitudesmentioning

confidence: 99%

Correlation of eigenstates in the critical regime of quantum Hall systems

Pracz¹,

Janssen²,

Freche³

1996

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

show abstract

“…where ν is the localization critical exponent [9]. After the initial calculations of Aoki and Ando [10][11][12], several groups attempted to determine this critical exponent [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Experimental results [28][29][30][31][32] are generally in good agreement with the calculated values.…”

mentioning

confidence: 89%

Disorder and localization in the lowest Landau level in the presence of dilute point scatterers

Gedik

Bayındır

1999

Solid State Communications

View full text Add to dashboard Cite

Cataloged from PDF version of article.We study the localization properties of a two-dimensional noninteracting electron gas in the presence of randomly distributed short-range scatterers in very high magnetic fields. We evaluate the participation number of the eigenstates obtained by exact diagonalization technique. At low impurity concentrations we obtain self-averaged values showing that all states, except those exactly at the Landau level, are localized with finite localization length. We conclude that in this dilute regime the localization length does not diverge. We also find that the maximum localization length increases exponentially with impurity concentration. Our calculations suggest that scaling behavior may be absent even for higher concentrations of scatterers. (C) 1999 Elsevier Science Ltd. All rights reserved

show abstract

“…In Ref. 8 it was pointed out that multifractality can show up in the size dependence of the conductance distribution close to the LD transition. Further suggestions for an experimental determination were made in Ref.…”

Section: Introductionmentioning

confidence: 99%

Point-contact conductances at the quantum Hall transition

1999

View full text Add to dashboard Cite

On the basis of the Chalker-Coddington network model, a numerical and analytical study is made of the statistics of point-contact conductances for systems in the integer quantum Hall regime. In the Hall plateau region the point-contact conductances reflect strong localization of the electrons, while near the plateau transition they exhibit strong mesoscopic fluctuations. By mapping the network model on a supersymmetric vertex model with GL(2͉2) symmetry, and postulating a two-point correlator in keeping with the rules of conformal field theory, we derive an explicit expression for the distribution of conductances at criticality. There is only one free parameter, the power law exponent of the typical conductance. Its value is computed numerically to be X t ϭ0.640Ϯ0.009. The predicted conductance distribution agrees well with the numerical data. For large distances between the two contacts, the distribution can be described by a multifractal spectrum solely determined by X t . Our results demonstrate that multifractality can show up in appropriate transport experiments.

show abstract

Multifractal analysis of disorder induced metal-insulator transitions

Cited by 18 publications

References 10 publications

Correlation of eigenstates in the critical regime of quantum Hall systems

Correlation of eigenstates in the critical regime of quantum Hall systems

Disorder and localization in the lowest Landau level in the presence of dilute point scatterers

Point-contact conductances at the quantum Hall transition

Contact Info

Product

Resources

About