Scaling of the conductance distribution near the Anderson transition

Abstract

The single parameter scaling hypothesis is the foundation of our understanding of the Anderson transition. However, the conductance of a disordered system is a fluctuating quantity which does not obey a one parameter scaling law. It is essential to investigate the scaling of the full conductance distribution to establish the scaling hypothesis. We present a clear cut numerical demonstration that the conductance distribution indeed obeys one parameter scaling near the Anderson transition.

References in corpus (3)

• Reconciling Conductance Fluctuations and the Scaling Theory of Localization
• Numerical verification of universality for the Anderson transition
• Reentrant behaviour and universality in the Anderson transition

Cited by in corpus (30)

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• Numerical estimation of the $\beta$-function in 2D systems with spin-orbit coupling
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• Transfer matrix study of the Anderson transition in non-Hermitian systems
• Ioffe-Regel criterion of Anderson localization in the model of resonant point scatterers
• Fluctuations of the Lyapunov exponent in 2D disordered systems
• Finite-size scaling analysis of localization transition for scalar waves in a 3D ensemble of resonant point scatterers
• Isosbestic points in the spectral function of correlated electrons
• Finite Size Scaling Analysis of the Anderson Transition
• Evolutions of helical edge states in disordered HgTe/CdTe quantum wells
• Universality of the metal-insulator transition in three-dimensional disordered systems
• Search for Anderson localization of light by cold atoms in a static electric field
• Unusual Metal to Marginal-Metal Transition in Two-Dimensional Ferromagnetic Electron Gases
• Localization of light in a three-dimensional disordered crystal of atoms
• Anomalously Localized States in the Anderson Model
• Scaling and localization lengths of a topologically disordered system
• Possible Anderson transition below two dimensions in disordered systems of noninteracting electrons
• Diffusion in the Anderson model in higher dimensions
• Intensity distribution of scalar waves propagating in random media
• Optimisation of multifractal analysis using box-size scaling
• Character of eigenstates of the 3D disordered Anderson Hamiltonian
• Conductance distribution near the Anderson transition
• Borel-Padé re-summation of the $\beta$-functions describing Anderson localisation in the Wigner-Dyson symmetry classes
• Metal - Insulator Transition in 3D Quantum Percolation
• Conductance fluctuations in disordered superconductors with broken time-reversal symmetry near two dimensions
• Quantum transport phenomena in disordered electron systems with spin-orbit coupling in two dimensions and below
• Boundary hopping and the mobility edge in the Anderson model in three dimensions
• Reply to comment by P.Markos [arXiv:1205.0689]
• Localization of non-interacting electrons in thin layered disordered systems
• Critical behavior of Anderson transitions in higher dimensional Bogoliubov-de Gennes symmetry classes