Localized states in disordered systems

Herbert, D C; Jones, R. M.

doi:10.1088/0022-3719/4/10/023

Cited by 143 publications

(68 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Later it was, however, proved by Theodorou and Cohen [8] in 1976 that this special state was extended independent of the probability distribution of the off-diagonal disorder, except for distributions equivalent to a chain that is broken. Similar conclusions had been reached earlier for more restricted classes of distributions by Herbert and Jones [9] 1971 and by Bush [10] in 1975.…”

Section: Introductionsupporting

confidence: 87%

Correlated Random Tight-Binding System with One Periodic State: Its Time Evolution and the Effects of an Added Nonlinearity

Lindquist¹,

Riklund²

1998

phys. stat. sol. (b)

View full text Add to dashboard Cite

We study a one-dimensional tight-binding system with constant on-site potential and off-diagonal hopping integrals t binary valued, and distributed as correlated random dimers. An explicit transformation from the system with constant t reveals that not only all states are extended, but in addition one of the states is periodic. The transformation is valid also for the corresponding timedependent system, even including a nonlinear term. An example of the time evolution of a solitonlike state is shown.

show abstract

Section: Introductionsupporting

confidence: 87%

Correlated Random Tight-Binding System with One Periodic State: Its Time Evolution and the Effects of an Added Nonlinearity

Lindquist¹,

Riklund²

1998

phys. stat. sol. (b)

View full text Add to dashboard Cite

show abstract

“…This definition of ξ l bears some similarity to that applied in finite size scaling studies of Anderson localized states [12,13]. When the imaginary part of the Green function vanishes in the insulating phase, ξ l may be used to study the metal-insulator transition.…”

mentioning

confidence: 91%

Insulator-Metal Transition in the One- and Two-Dimensional Hubbard Models

Assaad

Imada

1996

Phys. Rev. Lett.

View full text Add to dashboard Cite

We use Quantum Monte Carlo methods to determine T = 0 Green functions, G( r, ω), on lattices up to 16 × 16 for the 2D Hubbard model at U/t = 4. is approached from the insulating phase. ξ l may be interpreted as the localization length involved in transferring a particle over a distance r from the electronic system to the heat bath lying at energy µ within the charge gap. Under the assumption of hyperscaling, the above quantities are expected to satisfy the scaling relations:where The Hubbard model we consider reads:Here, i, j denotes nearest-neighbors. c † i,σ (c i,σ ) creates (annihilates) an electron with zcomponent of spin σ on site i and n i,σ = c † i,σ c iσ . In this notation half-band filling corresponds to µ = 0. We start by considering the non-interacting case, U/t = 0. In Fourier space, the single particle energies are given by ǫ k = −2t(cos( k a x ) + cos( k a y )), a x , a y being the lattice constants. In this letter, the length scale is set by: | a x | = | a y | = 1. At zero temperature, an insulator-metal transition will occur when µ → µ c = 4t. For those chemical potentials, the zero-temperature Green function [3] at ω = µ is given by:where N denotes the number of sites of the square lattice and the factor 2 corresponds to the summation over the spin degrees of freedom. Numerically, one obtains: G( r, ω = µ) ∼ e Here, b † creates an electron in the impurity state at the origin and energy ǫ b . The hybridization between the localized state and the band electrons alters the energy of the impurity level to the value:. We will assume E b > ǫ k for all k. When all single

show abstract

“…133,[137][138][139][140] However, qualitatively the behavior of a localized wavefunction is the same for all definitions. The original criterion proposed by Anderson is that a wavefunction given by eqn (23) could be considered localized if…”

Section: This Journal Is C the Owner Societies 2010mentioning

confidence: 95%

Single molecule charge transport: from a quantum mechanical to a classical description

Kocherzhenko

Grozema

Siebbeles

2011

Phys. Chem. Chem. Phys.

View full text Add to dashboard Cite

This paper explores charge transport at the single molecule level. The conductive properties of both small organic molecules and conjugated polymers (molecular wires) are considered. In particular, the reasons for the transition from fully coherent to incoherent charge transport and the approaches that can be taken to describe this transition are addressed in some detail. The effects of molecular orbital symmetry, quantum interference, static disorder and molecular vibrations on charge transport are discussed. All of these effects must be taken into account (and may be used in a functional way) in the design of molecular electronic devices. An overview of the theoretical models employed when studying charge transport in small organic molecules and molecular wires is presented.

show abstract

Localized states in disordered systems

Cited by 143 publications

References 10 publications

Correlated Random Tight-Binding System with One Periodic State: Its Time Evolution and the Effects of an Added Nonlinearity

Correlated Random Tight-Binding System with One Periodic State: Its Time Evolution and the Effects of an Added Nonlinearity

Insulator-Metal Transition in the One- and Two-Dimensional Hubbard Models

Single molecule charge transport: from a quantum mechanical to a classical description

Contact Info

Product

Resources

About