The DOI matches its Crossref record; 23 of the 23 references it cites were found in a registry or an index.
Hopping Conductivity in Disordered Systems
Abstract
By considering a model in which charge is transported via phonon-induced tunneling of electrons between localized states which are randomly distributed in energy and position, Mott has obtained an electrical conductivity of the form $\ensuremath{\sigma}\ensuremath{\propto}\mathrm{exp}[\ensuremath{-}{(\frac{\ensuremath{\lambda}{\ensuremath{\alpha}}^{3}}{{\ensuremath{\rho}}_{0}\mathrm{kT}})}^{\frac{1}{4}}]$. Here $T$ is the temperature of the system, ${\ensuremath{\rho}}_{0}$ is the density of states at the Fermi level, $\ensuremath{\lambda}$ is a dimensionless constant, and ${\ensuremath{\alpha}}^{\ensuremath{-}1}$ is the distance for exponential decay of the wave functions. We rederive these results, relating $\ensuremath{\lambda}$ to the critical density of a certain dimensionless percolation problem, and we estimate $\ensuremath{\lambda}$ to be approximately 16. The applicability of the model to experimental observations on amorphous Ge, Si, and C is discussed.
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Cites
Absence of Diffusion in Certain Random Lattices
Anderson, P. W. (1958) · Physical Review · doi:10.1103/physrev.109.1492 · Cited by 12,468
Bruggeman, D. A. G. (1935) · Annalen der Physik · doi:10.1002/andp.19354160705 · Cited by 8,645
Amorphous and Liquid Semiconductors
(1974) · Springer eBooks · doi:10.1007/978-1-4615-8705-7 · Cited by 6,370
Mott, N. F. (1969) · Philosophical Magazine · doi:10.1080/14786436908216338 · Cited by 3,520
Holstein, T. (1959) · Annals of Physics · doi:10.1016/0003-4916(59)90003-x · Cited by 2,801
Impurity Conduction at Low Concentrations
Miller, A., & Abrahams, E. (1960) · Physical Review · doi:10.1103/physrev.120.745 · Cited by 2,589
The Electrical Resistance of Binary Metallic Mixtures
Landauer, R. (1952) · Journal of Applied Physics · doi:10.1063/1.1702301 · Cited by 1,928
Electrons in disordered structures
Mott, N. F. (1967) · Advances in Physics · doi:10.1080/00018736700101265 · Cited by 1,765
Simple Band Model for Amorphous Semiconducting Alloys
Cohen, M. H., Fritzsche, H., & Ovshinsky, S. R. (1969) · Physical Review Letters · doi:10.1103/physrevlett.22.1065 · Cited by 1,041
Critical Density in Percolation Processes
Scher, H., & Zallen, R. (1970) · The Journal of Chemical Physics · doi:10.1063/1.1674565 · Cited by 907
Cited by
Electronic properties of two-dimensional systems
Ando, T., Fowler, A. B., & Stern, F. (1982) · Reviews of Modern Physics · doi:10.1103/revmodphys.54.437 · Cited by 7,455
Electrical Conductivity in Doped Polyacetylene
Chiang, C. K., Fincher, C. R., Park, Y. W., Heeger, A. J., Shirakawa, H., Louis, E. J., Gau, S. C., & MacDiarmid, A. G. (1977) · Physical Review Letters · doi:10.1103/physrevlett.39.1098 · Cited by 3,369
Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy
Ulbricht, R., Hendry, E., Shan, J., Heinz, T. F., & Bonn, M. (2011) · Reviews of Modern Physics · doi:10.1103/revmodphys.83.543 · Cited by 1,293
Sahimi, M. (1993) · Reviews of Modern Physics · doi:10.1103/revmodphys.65.1393 · Cited by 1,082
Percolation and conductivity: A computer study. I
Pike, G. E., & Seager, C. H. (1974) · Physical Review B · doi:10.1103/physrevb.10.1421 · Cited by 1,031
Metadata
- Authors
- Ambegaokar, V., Halperin, B. I., & Langer, J. S.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 1971-10-15
- Volume
- 4
- Issue
- 8
- Pages
- 2612-2620
- ISSN
- 0556-2805 (ISSN-L)
- OpenAlex
- W2087375600
- Cited by
- 1,917
- References
- 23
- FWCI
- 26.42
- Type
- journal article
- Language
- en
- Open access
- closed
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Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
