The Conductor Insulator Transition in Strongly Disordered Systems

Götze, W.

doi:10.1007/978-3-642-82516-3_7

Cited by 5 publications

(3 citation statements)

References 45 publications

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“…Consequences of band tailing are treated in Sects. 2 and 4 of chapter ▶ "Carrier Transport Induced and Controlled by Defects", when carrier transport is discussedsee also Götze (1981), and Lee and Ramakrishna (1985).…”

Section: Band Tails Localization and Mobility Edgementioning

confidence: 99%

Defects in Amorphous and Organic Semiconductors

Böer¹,

Pohl²

2017

Semiconductor Physics

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Amorphous and organic semiconductors have strong topological irregularities with respect to specific ideal structures, which depend on the particular class of such semiconductors. Most of these defects are rather gradual displacements from an ideal surrounding. The disorder leads to defects levels with a broad energy distribution which extends as band tails into the bandgap. Instead of a sharp band edge known from crystalline solids a mobility edge

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Section: Band Tails Localization and Mobility Edgementioning

confidence: 99%

Defects in Amorphous and Organic Semiconductors

Böer¹,

Pohl²

2017

Semiconductor Physics

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“…. , (19) where the inhomogeneities I , ' " ( . ) are given in terms of derivatives of functional f q at the critical point, in terms of $)(z), and in terms of F',"(z) for j = 1, .…”

Section: The Two Critical Exponents and The Critical Spectrummentioning

confidence: 99%

“…Again eq. (7) can be formulated as a set of equations (19), where now the inhomogeneities depend on E as well as on z. The leading order equation remains unchanged and implies again the factorization of the known wave vector dependence from the rest q')(z) = I;F(z, E).…”

Section: First Scaling Lawsmentioning

confidence: 99%

Structural Arrest and the Dynamics of the Liquid Glass Transition

Götze

1986

Phys. Scr.

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Concepts, mathematical argumentation, physical picture and scope of the mode coupling theory for the liquid glass transition as developed in a paper by Bengtzelius et al. and in succeeding work are summarized. An extensive discussion of the results for the glass form factors, discontinuities of thermodynamical functions, variation of transport coefficients, non exponential structural relaxation and scaling laws for the low frequency excitation spectra is presented.

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Dynamics of a quantum particle in a random potential

1993

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The motion of a quantum particle in a random potential with short-range fluctuations is analyzed using a generalized mode-coupling approximation. The original theory of GUtze was extended by introducing a wave-vector dependent current relaxation kernel. Here we apply the theory to the special case of exciton dynamics in a binary molecular crystal. We find a localization-delocalization transition in three dimensions with a critical exponent of 1 for the inverse localization length. In the intermediate time regime, our theory predicts a region of anomalous diffusion. This can be interpreted as a precursor to localization. At the transition point it leads to the known asymptotic low-frequency behaviour D"(o) 0: o "~. Ever since Anderson [l]introduced the concept of localization of electrons by disorder, physicists have tried to describe the implications of this phenomenon on the behaviour of measurable quantities of metallic conductors such as conductivity, chargecarrier diffusion coefficient, etc. In this case two problems are intimately entangled: the dynamics of suppressed diffusion (localization) in a random potential, on the one hand, and the statistics of a degenerate fermion gas in this potential (particle statistics), on the other. Allowing to disentangle these two problems in a simple way is one of the appealing aspects of mode-coupling theory, which was introduced in the present context by Gotze [2] in his pioneering work on electron localization.Since earlier attempts failed to render a correct description of the localization transition within mode-coupling theory, we will in this note report on an improved version (details will be published in a forthcoming paper). We calculate the probability density P(r, t ) for a single particle to move by r in time t. In P(r, t ) the random potential has already been averaged over. It exhibits translational symmetry, thus depending on r = r2 -rl , only. This probability density ("incoherent" density relaxation function) will in the following play a fundamental role in understanding the dynamical properties of a system of non-interacting quantum particles (including the ac-conductivity of a dilute gas of such particles). In contrast to earlier self-consistent theories of the Anderson transition [2, 3, 61, which calculate the "coherent" density-relaxation function @ (9, t ) and thus require an a-priori knowledge of the isothermal susceptibility @(q, t = 01, we benefit here from the known initial value P(q, t = 0), Eq. (8) below. This simplification stems from the fact that P ( q , t ) is a one-particle quantity.

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The Conductor Insulator Transition in Strongly Disordered Systems

Cited by 5 publications

References 45 publications

Defects in Amorphous and Organic Semiconductors

Defects in Amorphous and Organic Semiconductors

Structural Arrest and the Dynamics of the Liquid Glass Transition

Dynamics of a quantum particle in a random potential

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