Comment on mott’s localization criterion for disordered systems

P. D. Antoniou; Morrel H. Cohen; Joshua Jortner

doi:10.1080/14786437708232967

Comment on mott’s localization criterion for disordered systems

P. D. Antoniou, Morrel H. Cohen, Joshua Jortner

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Abstract

We investigate the validity of Mott’s localization criterion originally applied by him when a pseudogap opens. Values of the ratio η(E_c) of the perturbed to the unperturbed density of states at the mobility edges are obtained via approximate numerical calculations. They suggest that η, while slowly varying with disorder, is a function of the kind of disorder, the probability distribution of the disorder and the kind of mobility edge, exterior or interior to the band. The value of η for the interior mobility edges is found to be approximately²/₃ rather than¹/₃. The value of η approaches¹/₃ as the exterior mobility edge approaches the band edge, when the density of states become free-electron like and η becomes equivalent to Mott’s g. The product of the transfer integral for nearest neighbours with the density of states at the mobility edge is found to be practically constant for the interior mobility edges.

Original language	English (US)
Pages (from-to)	1435-1440
Number of pages	6
Journal	Philosophical Magazine
Volume	35
Issue number	5
DOIs	https://doi.org/10.1080/14786437708232967
State	Published - May 1977
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Engineering
General Physics and Astronomy

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title = "Comment on mott{\textquoteright}s localization criterion for disordered systems",

abstract = "We investigate the validity of Mott{\textquoteright}s localization criterion originally applied by him when a pseudogap opens. Values of the ratio η(Ec) of the perturbed to the unperturbed density of states at the mobility edges are obtained via approximate numerical calculations. They suggest that η, while slowly varying with disorder, is a function of the kind of disorder, the probability distribution of the disorder and the kind of mobility edge, exterior or interior to the band. The value of η for the interior mobility edges is found to be approximately2/3 rather than1/3. The value of η approaches1/3 as the exterior mobility edge approaches the band edge, when the density of states become free-electron like and η becomes equivalent to Mott{\textquoteright}s g. The product of the transfer integral for nearest neighbours with the density of states at the mobility edge is found to be practically constant for the interior mobility edges.",

author = "Antoniou, {P. D.} and Cohen, {Morrel H.} and Joshua Jortner",

note = "Funding Information: t Research supported by NSF Grant DMR75-13343, the L. Block Fund, and the Materials Research Laboratory of the National Science Foundation at The University of Chicago, U.S.A.",

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T1 - Comment on mott’s localization criterion for disordered systems

AU - Antoniou, P. D.

AU - Cohen, Morrel H.

AU - Jortner, Joshua

N1 - Funding Information: t Research supported by NSF Grant DMR75-13343, the L. Block Fund, and the Materials Research Laboratory of the National Science Foundation at The University of Chicago, U.S.A.

PY - 1977/5

Y1 - 1977/5

N2 - We investigate the validity of Mott’s localization criterion originally applied by him when a pseudogap opens. Values of the ratio η(Ec) of the perturbed to the unperturbed density of states at the mobility edges are obtained via approximate numerical calculations. They suggest that η, while slowly varying with disorder, is a function of the kind of disorder, the probability distribution of the disorder and the kind of mobility edge, exterior or interior to the band. The value of η for the interior mobility edges is found to be approximately2/3 rather than1/3. The value of η approaches1/3 as the exterior mobility edge approaches the band edge, when the density of states become free-electron like and η becomes equivalent to Mott’s g. The product of the transfer integral for nearest neighbours with the density of states at the mobility edge is found to be practically constant for the interior mobility edges.

AB - We investigate the validity of Mott’s localization criterion originally applied by him when a pseudogap opens. Values of the ratio η(Ec) of the perturbed to the unperturbed density of states at the mobility edges are obtained via approximate numerical calculations. They suggest that η, while slowly varying with disorder, is a function of the kind of disorder, the probability distribution of the disorder and the kind of mobility edge, exterior or interior to the band. The value of η for the interior mobility edges is found to be approximately2/3 rather than1/3. The value of η approaches1/3 as the exterior mobility edge approaches the band edge, when the density of states become free-electron like and η becomes equivalent to Mott’s g. The product of the transfer integral for nearest neighbours with the density of states at the mobility edge is found to be practically constant for the interior mobility edges.

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Comment on mott’s localization criterion for disordered systems

Abstract

All Science Journal Classification (ASJC) codes

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