Finite size scaling approach to Anderson localisation

Pichard, Jean‐Louis; Sarma, G.

doi:10.1088/0022-3719/14/6/003

Cited by 384 publications

(331 citation statements)

References 12 publications

Supporting

Mentioning

311

Contrasting

Unclassified

Order By: Relevance

“…This was supported by numerical 8,9,17,18 and analytical investigations 3,5 , with d = 2 being the lower critical dimension of the transition. The question then can be posed what happens in thin films of finite thickness.…”

Section: Introductionmentioning

confidence: 59%

Localization of non-interacting electrons in thin layered disordered systems

Cerovski¹,

Singh²,

Schreiber³

2006

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

Localization of electronic states in disordered thin layered systems with b layers is studied within the Anderson model of localization using the transfer-matrix method and finite-size scaling of the inverse of the smallest Lyapunov exponent. The results support the one-parameter scaling hypothesis for disorder strengths W studied and b = 1, . . . , 6. The obtained results for the localization length are in good agreement with both the analytical results of the self-consistent theory of localization and the numerical scaling studies of the two-dimensional Anderson model. The localization length near the band center grows exponentially with b for fixed W but no localization-delocalization transition takes place.

show abstract

Section: Introductionmentioning

confidence: 59%

Localization of non-interacting electrons in thin layered disordered systems

Cerovski¹,

Singh²,

Schreiber³

2006

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

show abstract

“…We compute it using the TMM [8,20,21] for quasi-1D bars of cross section M × M and length L ≫ M . The stationary Schrödinger equation HΨ = EΨ is rewritten in a recursive form:…”

Section: Transfer-matrix Methods In Anisotropic Systemsmentioning

confidence: 99%

“…It is characterized by a divergent correlation length ξ ∞ (W ) = C|W − W c | −ν , where ν is the critical exponent and C is a constant [8]. To construct the correlation length of the infinite system ξ ∞ from finite size data Λ M [3,8,20,21], the one-parameter scaling hypothesis [24] is employed,…”

Section: Finite-size Scalingmentioning

confidence: 99%

Critical properties of the metal-insulator transition in anisotropic systems

et al. 2000

View full text Add to dashboard Cite

Abstract. We study the three-dimensional Anderson model of localization with anisotropic hopping, i.e., weakly coupled chains and weakly coupled planes. In our extensive numerical study we identify and characterize the metal-insulator transition by means of the transfer-matrix method. The values of the critical disorder Wc obtained are consistent with results of previous studies, including multifractal analysis of the wave functions and energy level statistics. Wc decreases from its isotropic value with a power law as a function of anisotropy. Using high accuracy data for large system sizes we estimate the critical exponent as ν = 1.62 ± 0.07. This is in agreement with its value in the isotropic case and in other models of the orthogonal universality class.

show abstract

“…Pichard and Sarma [43] suggest the following in order to calculate the exponent x for the powerlaw decay of the wave function ψ Ec :…”

Section: Where and How Does The Localization Length Diverge?mentioning

confidence: 99%