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Relation between conductivity and transmission matrix
Abstract
The dc conductance $\ensuremath{\Gamma}$ of a finite system with static disorder is related to its transmission matrix $t$ by the simple relation $\ensuremath{\Gamma}=(\frac{{e}^{2}}{2\ensuremath{\pi}\ensuremath{\hbar}}) \mathrm{Tr}({t}^{\ifmmode\dagger\else\textdagger\fi{}}t)$. This relation is derived from the Kubo formula and is valid for any number of scattering channels with or without time-reversal symmetry. Differences between various definitions of the conductance of a finite system are discussed.
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Citations
Cited by
Maximally localized Wannier functions: Theory and applications
Marzari, N., Mostofi, A. A., Yates, J. R., Souza, I., & Vanderbilt, D. (2012) · Reviews of Modern Physics · doi:10.1103/revmodphys.84.1419 · Cited by 3,283
Random-matrix theory of quantum transport
Beenakker, C. W. J. (1997) · Reviews of Modern Physics · doi:10.1103/revmodphys.69.731 · Cited by 2,551
Localization: theory and experiment
Kramer, B., & MacKinnon, A. (1993) · Reports on Progress in Physics · doi:10.1088/0034-4885/56/12/001 · Cited by 1,926
Absence of backscattering in the quantum Hall effect in multiprobe conductors
Büttiker, M. (1988) · Physical Review B · doi:10.1103/physrevb.38.9375 · Cited by 1,555
Universal Conductance Fluctuations in Metals
Lee, P. A., & Stone, A. D. (1985) · Physical Review Letters · doi:10.1103/physrevlett.55.1622 · Cited by 1,369
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Metadata
- Authors
- Fisher, D. S., & Lee, P. A.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 1981-06-15
- Volume
- 23
- Issue
- 12
- Pages
- 6851-6854
- ISSN
- 0163-1829 (ISSN-L)
- OpenAlex
- W2121023772
- Cited by
- 1,774
- References
- 0
- FWCI
- 2.29
- Type
- journal article
- Language
- en
- Open access
- closed
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