Conductance distribution in strongly disordered mesoscopic systems in three dimensions

Abstract

Recent numerical simulations have shown that the distribution of conductance P(g) in 3D strongly localized regiem differs significally from the expected log normal distribution. To understand the origin of this difference analytically, we used a generalized DMPK equation for the joint probablity distribution of the transmission eigenvalues which includes a phenomenological (disorder and dimensionality dependent) matrix K containing certain correlations of the transfer matrices. We first of all examine the assumptions made in the derivation if the generalized DMPK and find that to a good approximation they remain valid in 3D. We then evaluate the matrix K numerically for various strength of the disorder and various system sizes. In the strong disorder limit we find that K can be described by a simple model which, for a cubic system, depends on a single parameter. We use this phenomenological model to analytically evaluate the full distribution P(g) for Anderson insulators in 3D. The analytic results allow us to develop an intuitive understanding of the entire distribution, which differs qualitatively from the log-normal distribution of a Q1D wire. We also show that out method could be applicable in the critical regime of the Anderson transition.

References in corpus (10)

• Reconciling Conductance Fluctuations and the Scaling Theory of Localization
• Universal Conductance Distributions in the Crossover between Diffusive and Localization Regimes
• Generalization of the DMPK equation beyond quasi one dimension
• Conductance distribution in disordered quantum wires: Crossover between the metallic and insulating regimes
• Conductance distribution in quasi-one-dimensional disordered quantum wires
• Symmetry, dimension and the distribution of the conductance at the mobility edge
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• Conductance distribution in 3D Anderson insulators: deviation from log-normal form
• Conductance fluctuations and boundary conditions
• Magnetic Field Effects on the Transport Properties of One-sided Rough Wires

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• Distribution of conductance for Anderson Insulators: A theory with a single parameter
• Largest Schmidt eigenvalue of entangled random pure states and conductance distribution in chaotic cavities
• The Generalized DMPK equation revisited: A systematic derivation
• DMPK Equation for the Edge Transport of Quantum Spin Hall Insulator
• Generalized DMPK equation for strongly localized regime - numerical solution
• General form of DMPK equation
• Character of eigenstates of the 3D disordered Anderson Hamiltonian
• Generalized random matrix model with additional interactions
• Electron transport in strongly disordered structures
• Conductance distribution in the magnetic field
• Nonmonotonic confining potential and eigenvalue density transition for generalized random matrix model
• On the role of the symmetry parameter $\beta$ in the strongly localized regime